From 32937ed1ae8e1d8e026b77405385fa1b3b60ba6c Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Tue, 4 Jun 2024 16:35:41 +0530 Subject: [PATCH 01/24] todo: fix build issues --- CMakeLists.txt | 71 + .../config => config}/bigquad_params.yaml | 0 .../config => config}/crazyflie_params.yaml | 0 .../config => config}/custom_rosconsole.conf | 0 .../config => config}/initial_conditions.yaml | 0 geo_controller/CMakeLists.txt | 30 - geo_controller/LICENSE | 201 -- .../include/geo_controller/controllerImpl.h | 48 - .../include/geo_controller/definitions.h | 44 - geo_controller/package.xml | 69 - geo_controller/src/controllerImpl.cpp | 101 - geo_controller/src/definitions.cpp | 22 - .../mavswarm2/dynamics_provider.h | 25 +- include/mavswarm2/quadrotor.h | 106 + .../mavswarm2/trajectory_t.h | 24 +- .../mavswarm2/utils.h | 50 +- include/mavswarm2/visualizer.h | 0 include/misc/visualizer.hpp | 327 ++ .../launch => launch}/simu.launch | 0 multi_uav_simulator/CMakeLists.txt | 48 - .../bigquad_description/bigquad.dae | 235 -- .../bigquad_description/bigquad.urdf.xacro | 14 - .../cf_description/crazyflie.skp | Bin 286654 -> 0 bytes .../cf_description/crazyflie.urdf.xacro | 14 - .../cf_description/crazyflie2.dae | 2882 ----------------- multi_uav_simulator/config/simulation.rviz | 312 -- .../include/multi_uav_simulator/Quadrotor.h | 95 - .../include/multi_uav_simulator/cfSimUtils.h | 42 - multi_uav_simulator/package.xml | 70 - multi_uav_simulator/src/Quadrotor.cpp | 353 -- package.xml | 27 + rosinstall/dependencies.rosinstall | 8 - simulator_utils/CMakeLists.txt | 210 -- .../include/simulator_utils/Drone.h | 28 - .../include/simulator_utils/simulator_utils.h | 64 - simulator_utils/msg/Waypoint.msg | 4 - simulator_utils/package.xml | 66 - simulator_utils/src/Drone.cpp | 31 - simulator_utils/src/simulator_utils.cpp | 45 - .../dynamics_provider.cpp | 24 +- src/quadrotor.cpp | 257 ++ 41 files changed, 893 insertions(+), 5054 deletions(-) create mode 100644 CMakeLists.txt rename {multi_uav_simulator/config => config}/bigquad_params.yaml (100%) rename {multi_uav_simulator/config => config}/crazyflie_params.yaml (100%) rename {multi_uav_simulator/config => config}/custom_rosconsole.conf (100%) rename {multi_uav_simulator/config => config}/initial_conditions.yaml (100%) delete mode 100755 geo_controller/CMakeLists.txt delete mode 100755 geo_controller/LICENSE delete mode 100755 geo_controller/include/geo_controller/controllerImpl.h delete mode 100644 geo_controller/include/geo_controller/definitions.h delete mode 100755 geo_controller/package.xml delete mode 100644 geo_controller/src/controllerImpl.cpp delete mode 100644 geo_controller/src/definitions.cpp rename multi_uav_simulator/include/multi_uav_simulator/DynamicsProvider.h => include/mavswarm2/dynamics_provider.h (54%) create mode 100644 include/mavswarm2/quadrotor.h rename multi_uav_simulator/include/multi_uav_simulator/Trajectory_t.h => include/mavswarm2/trajectory_t.h (60%) rename multi_uav_simulator/src/cfSimUtils.cpp => include/mavswarm2/utils.h (67%) mode change 100644 => 100755 create mode 100644 include/mavswarm2/visualizer.h create mode 100644 include/misc/visualizer.hpp rename {multi_uav_simulator/launch => launch}/simu.launch (100%) delete mode 100755 multi_uav_simulator/CMakeLists.txt delete mode 100644 multi_uav_simulator/bigquad_description/bigquad.dae delete mode 100644 multi_uav_simulator/bigquad_description/bigquad.urdf.xacro delete mode 100755 multi_uav_simulator/cf_description/crazyflie.skp delete mode 100755 multi_uav_simulator/cf_description/crazyflie.urdf.xacro delete mode 100755 multi_uav_simulator/cf_description/crazyflie2.dae delete mode 100644 multi_uav_simulator/config/simulation.rviz delete mode 100644 multi_uav_simulator/include/multi_uav_simulator/Quadrotor.h delete mode 100755 multi_uav_simulator/include/multi_uav_simulator/cfSimUtils.h delete mode 100755 multi_uav_simulator/package.xml delete mode 100644 multi_uav_simulator/src/Quadrotor.cpp create mode 100644 package.xml delete mode 100644 rosinstall/dependencies.rosinstall delete mode 100644 simulator_utils/CMakeLists.txt delete mode 100644 simulator_utils/include/simulator_utils/Drone.h delete mode 100644 simulator_utils/include/simulator_utils/simulator_utils.h delete mode 100644 simulator_utils/msg/Waypoint.msg delete mode 100644 simulator_utils/package.xml delete mode 100644 simulator_utils/src/Drone.cpp delete mode 100644 simulator_utils/src/simulator_utils.cpp rename multi_uav_simulator/src/DynamicsProvider.cpp => src/dynamics_provider.cpp (86%) create mode 100644 src/quadrotor.cpp diff --git a/CMakeLists.txt b/CMakeLists.txt new file mode 100644 index 0000000..e40f539 --- /dev/null +++ b/CMakeLists.txt @@ -0,0 +1,71 @@ +cmake_minimum_required(VERSION 3.8) +project(mavswarm2) + +if(CMAKE_COMPILER_IS_GNUCXX OR CMAKE_CXX_COMPILER_ID MATCHES "Clang") + add_compile_options(-Wall -Wextra -Wpedantic) +endif() + +# find dependencies +find_package(Armadillo REQUIRED) +find_package(GSL REQUIRED) +find_package(ament_cmake REQUIRED) +find_package(rclcpp REQUIRED) +find_package(simulator_interfaces REQUIRED) +find_package(simulator_utils REQUIRED) +find_package(controller REQUIRED) +find_package(std_msgs REQUIRED) +find_package(geometry_msgs REQUIRED) +find_package(sensor_msgs REQUIRED) +find_package(visualization_msgs REQUIRED) +find_package(tf2_ros REQUIRED) + + +add_library(${PROJECT_NAME} SHARED + src/dynamics_provider.cpp + src/quadrotor.cpp +) + +ament_target_dependencies(mavswarm2 + rclcpp + simulator_utils + simulator_interfaces + controller + tf2 + tf2_ros + visualization_msgs + geometry_msgs + std_msgs + ) + +# if(BUILD_TESTING) +# find_package(ament_lint_auto REQUIRED) + +# set(ament_cmake_copyright_FOUND TRUE) +# set(ament_cmake_cpplint_FOUND TRUE) +# ament_lint_auto_find_test_dependencies() +# endif() + +# find_package(message_runtime REQUIRED) + + +ament_package() + +# install( +# TARGETS ${PROJECT_NAME} +# EXPORT ${PROJECT_NAME} +# LIBRARY DESTINATION lib +# ARCHIVE DESTINATION lib +# RUNTIME DESTINATION bin +# INCLUDES DESTINATION include +# ) + +# install( +# DIRECTORY include/ +# DESTINATION include +# ) + +include_directories( + include/${PROJECT_NAME} + # include/gcopter + # include/misc +) diff --git a/multi_uav_simulator/config/bigquad_params.yaml b/config/bigquad_params.yaml similarity index 100% rename from multi_uav_simulator/config/bigquad_params.yaml rename to config/bigquad_params.yaml diff --git a/multi_uav_simulator/config/crazyflie_params.yaml b/config/crazyflie_params.yaml similarity index 100% rename from multi_uav_simulator/config/crazyflie_params.yaml rename to config/crazyflie_params.yaml diff --git a/multi_uav_simulator/config/custom_rosconsole.conf b/config/custom_rosconsole.conf similarity index 100% rename from multi_uav_simulator/config/custom_rosconsole.conf rename to config/custom_rosconsole.conf diff --git a/multi_uav_simulator/config/initial_conditions.yaml b/config/initial_conditions.yaml similarity index 100% rename from multi_uav_simulator/config/initial_conditions.yaml rename to config/initial_conditions.yaml diff --git a/geo_controller/CMakeLists.txt b/geo_controller/CMakeLists.txt deleted file mode 100755 index ae04b4b..0000000 --- a/geo_controller/CMakeLists.txt +++ /dev/null @@ -1,30 +0,0 @@ -cmake_minimum_required(VERSION 3.10) -project(geo_controller) - -find_package(catkin REQUIRED COMPONENTS - roscpp - std_msgs - simulator_utils - ) - -catkin_package( - INCLUDE_DIRS include - LIBRARIES geo_controller - CATKIN_DEPENDS message_runtime roscpp -) - -include_directories( - include/${PROJECT_NAME} - ${catkin_INCLUDE_DIRS} -) - -#find_package(simulator_utils) - -#add_executable(geo_controller -# include/geo_controller/controllerImpl.h -# src/controllerImpl.cpp include/geo_controller/definitions.h) - -add_library(${PROJECT_NAME} - src/controllerImpl.cpp - src/definitions.cpp - ) \ No newline at end of file diff --git a/geo_controller/LICENSE b/geo_controller/LICENSE deleted file mode 100755 index 261eeb9..0000000 --- a/geo_controller/LICENSE +++ /dev/null @@ -1,201 +0,0 @@ - Apache License - Version 2.0, January 2004 - http://www.apache.org/licenses/ - - TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION - - 1. 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We also recommend that a - file or class name and description of purpose be included on the - same "printed page" as the copyright notice for easier - identification within third-party archives. - - Copyright [yyyy] [name of copyright owner] - - Licensed under the Apache License, Version 2.0 (the "License"); - you may not use this file except in compliance with the License. - You may obtain a copy of the License at - - http://www.apache.org/licenses/LICENSE-2.0 - - Unless required by applicable law or agreed to in writing, software - distributed under the License is distributed on an "AS IS" BASIS, - WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. - See the License for the specific language governing permissions and - limitations under the License. diff --git a/geo_controller/include/geo_controller/controllerImpl.h b/geo_controller/include/geo_controller/controllerImpl.h deleted file mode 100755 index 1e38946..0000000 --- a/geo_controller/include/geo_controller/controllerImpl.h +++ /dev/null @@ -1,48 +0,0 @@ -// -// Created by malintha on 11/27/17. -// - -#ifndef PROJECT_TRACKING_CONTROL_H -#define PROJECT_TRACKING_CONTROL_H - -#pragma once - -#include -#include "simulator_utils/simulator_utils.h" -#include "definitions.h" - -using namespace Eigen; - -class ControllerImpl -{ - -public: - ControllerImpl(params_t params_, init_vals_t init_vals_, gains_t gains_, double dt_); - control_out_t get_control(state_space_t ss_, const desired_state_t& desired_s); - -private: - - params_t params; - init_vals_t init_vals; - - double dt; - gains_t gains; - - // derivative operators - dxdt dxdt_; - dxdt d2xdt; - dxdt d3xdt; - dxdt d4xdt; - dxdt db1dt; - dxdt d2b1dt; - dxdt dvdt; - dxdt d2vdt; - - derivatives_t get_derivatives(const desired_state_t& desired_state, const state_space_t& ss); - - - - -}; - -#endif diff --git a/geo_controller/include/geo_controller/definitions.h b/geo_controller/include/geo_controller/definitions.h deleted file mode 100644 index 713a598..0000000 --- a/geo_controller/include/geo_controller/definitions.h +++ /dev/null @@ -1,44 +0,0 @@ -#include - -using namespace Eigen; - -// compute the derivative of a signal -struct dxdt { - double tau; - double ts; - double a1; - double a2; - int order; - Vector3d dot; - Vector3d x_d1; - int it = 1; - - dxdt(); - dxdt(double tau_, double ts_, int order_); - Vector3d calculate(const Vector3d &x); -}; - -typedef struct -{ - Vector3d ex; - Vector3d ev; - Vector3d ea; - Vector3d ej; - Vector3d er; - Vector3d eomega; -} err_t; - -typedef struct { - // derivatives of desired states - Vector3d d_xd; - Vector3d d2_xd; - Vector3d d3_xd; - Vector3d d4_xd; - Vector3d db1; - Vector3d d2b1; - - // derivatives of current velocity - Vector3d dv; - Vector3d d2v; - -} derivatives_t; \ No newline at end of file diff --git a/geo_controller/package.xml b/geo_controller/package.xml deleted file mode 100755 index b67c086..0000000 --- a/geo_controller/package.xml +++ /dev/null @@ -1,69 +0,0 @@ - - - geo_controller - 0.0.0 - The geo_controller package - - - - - malintha - - - - - - TODO - - - - - - - - - - - - - - - - - - - - - - - - message_generation - - - - - - message_runtime - - - - - catkin - roscpp - - std_msgs - roscpp - - std_msgs - roscpp - - std_msgs - simulator_utils - - - - - - - - diff --git a/geo_controller/src/controllerImpl.cpp b/geo_controller/src/controllerImpl.cpp deleted file mode 100644 index 7837a50..0000000 --- a/geo_controller/src/controllerImpl.cpp +++ /dev/null @@ -1,101 +0,0 @@ -#include "controllerImpl.h" -#include - -namespace su = simulator_utils; - -ControllerImpl::ControllerImpl(params_t params_, init_vals_t init_vals_, gains_t gains_, double dt_) - :params(std::move(params_)), init_vals(std::move(init_vals_)), gains(gains_), dt(dt_) -{ - // initialize derivative operators - dxdt_ = dxdt(0.05, dt, 1); - d2xdt = dxdt(0.05, dt, 2); - d3xdt = dxdt(0.05, dt, 3); - d4xdt = dxdt(0.05, dt, 4); - - db1dt = dxdt(0.05, dt, 1); - d2b1dt = dxdt(0.05, dt, 2); - - dvdt = dxdt(0.05, dt, 1); - d2vdt = dxdt(0.05, dt, 2); -} - -control_out_t ControllerImpl::get_control(state_space_t ss, const desired_state_t& desired_s) -{ - // compute the derivatives of desired state - derivatives_t derivatives = get_derivatives(desired_s, ss); - - Vector3d ex = ss.position - desired_s.x; - Vector3d ev = ss.velocity - derivatives.d_xd; - Vector3d ea = derivatives.dv - derivatives.d2_xd; - Vector3d ej = derivatives.d2v - derivatives.d3_xd; - Vector3d e3(0,0,1); - Vector3d A = -gains.kx * ex - gains.kv * ev - params.mass * params.gravity * e3 + - params.mass * derivatives.d2_xd; - - double f = -A.dot(ss.R*e3); - double nA = A.norm(); - - Vector3d b3c = -A/nA; - Vector3d C = b3c.cross(desired_s.b1); - Vector3d b1c = -(1/C.norm())*b3c.cross(C); - Vector3d b2c = C/C.norm(); - Matrix3d Rc; - Rc << b1c, b2c, b3c; - - double nC = C.norm(); - - Vector3d A_1dot = -gains.kx*ev - gains.kv*ea + params.mass*derivatives.d3_xd; - Vector3d b3c_1dot = -A_1dot / nA + (A.dot(A_1dot)/pow(nA,3))*A; - - Vector3d C_1dot = b3c_1dot.cross(desired_s.b1) + b3c.cross(derivatives.db1); - Vector3d b2c_1dot = C/nC - C.dot(C_1dot)/(pow(nC,3))*C; - Vector3d b1c_1dot = b2c_1dot.cross(b3c) + b2c.cross(b3c_1dot); - - Vector3d A_2dot = -gains.kx*ea -gains.kv*ej + params.mass*derivatives.d4_xd; - Vector3d b3c_2dot = -A_2dot/nA + (2.0/pow(nA,3))*A.dot(A_1dot)*A_1dot + - (pow(A_1dot.norm(),2) + A.dot(A_2dot)/(pow(nA,3)))*A - (3.0/pow(nA,5))*(pow(A.dot(A_1dot),2))*A; - - Vector3d C_2dot = b3c_2dot.cross(desired_s.b1) + (b3c.cross(derivatives.d2b1)) + 2*b3c_1dot.cross(derivatives.db1); - - Vector3d b2c_2dot = C_2dot/nC - 2.0/(pow(nC,3))*C.dot(C_1dot)*C_1dot - (((pow(C_2dot.norm(),2) + C.dot(C_2dot)))/pow(nC,3))*C - + (3.0/pow(nC,5))*(pow(C.dot(C_1dot),2))*C; - - Vector3d b1c_2dot = b2c_2dot.cross(b3c) + b2c.cross(b3c_2dot) + 2.0*b2c_1dot.cross(b3c_1dot); - Matrix3d Rc_1dot, Rc_2dot; - Rc_1dot << b1c_1dot, b2c_1dot, b3c_1dot; - Rc_2dot << b1c_2dot, b2c_2dot, b3c_2dot; - - Vector3d omegac = su::vee(Rc.transpose()*Rc_1dot); - Vector3d omegac_1dot = su::vee(Rc.transpose()*Rc_2dot - - su::hat(omegac)*su::hat(omegac)); - - Vector3d er = 2.0*su::vee(Rc.transpose()*ss.R - ss.R.transpose()*Rc); - Vector3d eomega = ss.omega - ss.R.transpose()*Rc*omegac; - - Vector3d M = -gains.kr*er - gains.komega*eomega + ss.omega.cross(params.J*ss.omega) - - params.J*(su::hat(ss.omega)*ss.R.transpose()*Rc*omegac - ss.R.transpose()*Rc*omegac_1dot); - -// ROS_DEBUG_STREAM("\n eR \n"< - -dxdt::dxdt(double tau_, double ts_, int order_) : tau(tau_), ts(ts_), order(order_) -{ - a1 = (2 * tau - ts) / (2 * tau + ts); - a2 = 2 / (2 * tau + ts); - dot = Vector3d(0, 0, 0); - x_d1 = Vector3d(0, 0, 0); -} - -dxdt::dxdt() {} - -Vector3d dxdt::calculate(const Vector3d &x) -{ - if (it > order) - { - dot = a1 * dot + a2 * (x - x_d1); - } - it++; - x_d1 = x; - return dot; -} diff --git a/multi_uav_simulator/include/multi_uav_simulator/DynamicsProvider.h b/include/mavswarm2/dynamics_provider.h similarity index 54% rename from multi_uav_simulator/include/multi_uav_simulator/DynamicsProvider.h rename to include/mavswarm2/dynamics_provider.h index 45da5ca..918348c 100644 --- a/multi_uav_simulator/include/multi_uav_simulator/DynamicsProvider.h +++ b/include/mavswarm2/dynamics_provider.h @@ -1,12 +1,24 @@ -// -// Created by malintha on 7/31/18. -// +/* +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. +*/ #ifndef CF_SIMULATOR_DYNAMICSPROVIDER_H #define CF_SIMULATOR_DYNAMICSPROVIDER_H #include -#include "tf/tf.h" +// #include "tf2/transform_datatypes.h" #include "simulator_utils/simulator_utils.h" #include @@ -24,7 +36,7 @@ class DynamicsProvider { private: const size_t DIMENSIONS = 18; const gsl_odeiv2_step_type *T = gsl_odeiv2_step_rkf45; - + // Check if GSL is compatible with ROS 2, otherwise use alternatives bool state_set = false; state_space_t state_space; params_t params; @@ -37,5 +49,4 @@ class DynamicsProvider { }; - -#endif \ No newline at end of file +#endif diff --git a/include/mavswarm2/quadrotor.h b/include/mavswarm2/quadrotor.h new file mode 100644 index 0000000..2e9aa11 --- /dev/null +++ b/include/mavswarm2/quadrotor.h @@ -0,0 +1,106 @@ +/* + +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. + +*/ + +#ifndef PROJECT_QUADROTOR_H +#define PROJECT_QUADROTOR_H + +#include +#include +#include +#include +#include "dynamics_provider.h" +#include +#include "rclcpp/rclcpp.hpp" +#include "simulator_interfaces/msg/waypoint.hpp" +#include "trajectory_t.h" + +#include "std_msgs/msg/float32_multi_array.hpp" + +#ifndef STATE_H +#define STATE_H +enum State { + Idle, + TakingOff, + Landing, + Hover, + Autonomous +}; +#endif + +using namespace Eigen; +using namespace std; + +class Quadrotor : public rclcpp::Node { +public: + Quadrotor(int robot_id, double frequency, std::shared_ptr); + void move(const desired_state_t &d_state); + void setState(State m_state); + State getState(); + + bool initialize(double dt); + + void desired_pos_cb(const geometry_msgs::msg::Point &pt); + + void iteration(); + void run(); + + +private: + + State m_state; + double sim_time, tau, dt, frequency; + int robot_id; + std::string worldframe, localframe, robot_link_name; + gains_t gains; + std::vector traj_piece; + int xd_it; + Vector3d u, target_pos; + state_space_t x0, xd0; + desired_state_t dss; + bool set_init_target; + geometry_msgs::msg::Point target_next; + bool set_next_target = false; + + ControllerImpl *controller; + state_space_t state_space; + + DynamicsProvider *dynamics; + params_t params; + init_vals_t init_vals; + + rclcpp::Publisher::SharedPtr marker_pub, goal_pub, state_pub; + visualization_msgs::msg::Marker m, g; + std::vector points; + rclcpp::Subscription::SharedPtr desired_state_sub; + vector positions; + + bool quad_initialized = false; + + // rclcpp::TimerBase::SharedPtr timer; + + void initPaths(); + void set_state_space(); + bool load_params(); + bool load_init_vals(); + void send_transform(); + void publish_path(); + void publish_state(); + +}; + +#endif diff --git a/multi_uav_simulator/include/multi_uav_simulator/Trajectory_t.h b/include/mavswarm2/trajectory_t.h similarity index 60% rename from multi_uav_simulator/include/multi_uav_simulator/Trajectory_t.h rename to include/mavswarm2/trajectory_t.h index f1f27f6..02a8be3 100644 --- a/multi_uav_simulator/include/multi_uav_simulator/Trajectory_t.h +++ b/include/mavswarm2/trajectory_t.h @@ -1,10 +1,26 @@ -// -// Created by malintha on 10/16/20. -// +/* + +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. + +*/ + #include #include #include -#include "std_msgs/Float32MultiArray.h" +#include "std_msgs/msg/float32_multi_array.hpp" + using namespace std; using namespace Eigen; diff --git a/multi_uav_simulator/src/cfSimUtils.cpp b/include/mavswarm2/utils.h old mode 100644 new mode 100755 similarity index 67% rename from multi_uav_simulator/src/cfSimUtils.cpp rename to include/mavswarm2/utils.h index 8f9c517..665bbf7 --- a/multi_uav_simulator/src/cfSimUtils.cpp +++ b/include/mavswarm2/utils.h @@ -1,6 +1,50 @@ -#include "cfSimUtils.h" +/* + +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. + +*/ + +#ifndef PROJECT_CFSIMUTILS_H +#define PROJECT_CFSIMUTILS_H + +#include +#include +#include "ros/ros.h" +#include +#include +#include +#include +#include "tf/tf.h" + +using namespace Eigen; namespace cfSimUtils { + /** + * @param gamma roll + * @param beta pitch + * @param alpha yaw + */ + + struct node { + int id, cluster; + float x, y, z; + std::string type; + node(int id, int cluster, float x, float y, float z, std::string type):id(id), cluster(cluster), x(x), y(y), + z(z), type(type) {}; + }; + Matrix3d getR(double gamma, double beta, double alpha) { Matrix3d R; @@ -71,4 +115,6 @@ namespace cfSimUtils { } return coords_list; } -} \ No newline at end of file +} + +#endif diff --git a/include/mavswarm2/visualizer.h b/include/mavswarm2/visualizer.h new file mode 100644 index 0000000..e69de29 diff --git a/include/misc/visualizer.hpp b/include/misc/visualizer.hpp new file mode 100644 index 0000000..c74c153 --- /dev/null +++ b/include/misc/visualizer.hpp @@ -0,0 +1,327 @@ +#ifndef VISUALIZER_HPP +#define VISUALIZER_HPP + +#include "gcopter/trajectory.hpp" +#include "gcopter/quickhull.hpp" +#include "gcopter/geo_utils.hpp" + +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include + +// Visualizer for the planner +class Visualizer +{ +private: + // config contains the scale for some markers + ros::NodeHandle nh; + + // These are publishers for path, waypoints on the trajectory, + // the entire trajectory, the mesh of free-space polytopes, + // the edge of free-space polytopes, and spheres for safety radius + ros::Publisher routePub; + ros::Publisher wayPointsPub; + ros::Publisher trajectoryPub; + ros::Publisher meshPub; + ros::Publisher edgePub; + ros::Publisher spherePub; + +public: + ros::Publisher speedPub; + ros::Publisher thrPub; + ros::Publisher tiltPub; + ros::Publisher bdrPub; + +public: + Visualizer(ros::NodeHandle &nh_) + : nh(nh_) + { + routePub = nh.advertise("/visualizer/route", 10); + wayPointsPub = nh.advertise("/visualizer/waypoints", 10); + trajectoryPub = nh.advertise("/visualizer/trajectory", 10); + meshPub = nh.advertise("/visualizer/mesh", 1000); + edgePub = nh.advertise("/visualizer/edge", 1000); + spherePub = nh.advertise("/visualizer/spheres", 1000); + speedPub = nh.advertise("/visualizer/speed", 1000); + thrPub = nh.advertise("/visualizer/total_thrust", 1000); + tiltPub = nh.advertise("/visualizer/tilt_angle", 1000); + bdrPub = nh.advertise("/visualizer/body_rate", 1000); + } + + // Visualize the trajectory and its front-end path + template + inline void visualize(const Trajectory &traj, + const std::vector &route) + { + visualization_msgs::Marker routeMarker, wayPointsMarker, trajMarker; + + routeMarker.id = 0; + routeMarker.type = visualization_msgs::Marker::LINE_LIST; + routeMarker.header.stamp = ros::Time::now(); + routeMarker.header.frame_id = "odom"; + routeMarker.pose.orientation.w = 1.00; + routeMarker.action = visualization_msgs::Marker::ADD; + routeMarker.ns = "route"; + routeMarker.color.r = 1.00; + routeMarker.color.g = 0.00; + routeMarker.color.b = 0.00; + routeMarker.color.a = 1.00; + routeMarker.scale.x = 0.1; + + wayPointsMarker = routeMarker; + wayPointsMarker.id = -wayPointsMarker.id - 1; + wayPointsMarker.type = visualization_msgs::Marker::SPHERE_LIST; + wayPointsMarker.ns = "waypoints"; + wayPointsMarker.color.r = 1.00; + wayPointsMarker.color.g = 0.00; + wayPointsMarker.color.b = 0.00; + wayPointsMarker.scale.x = 0.35; + wayPointsMarker.scale.y = 0.35; + wayPointsMarker.scale.z = 0.35; + + trajMarker = routeMarker; + trajMarker.header.frame_id = "odom"; + trajMarker.id = 0; + trajMarker.ns = "trajectory"; + trajMarker.color.r = 0.00; + trajMarker.color.g = 0.50; + trajMarker.color.b = 1.00; + trajMarker.scale.x = 0.30; + + if (route.size() > 0) + { + bool first = true; + Eigen::Vector3d last; + for (auto it : route) + { + if (first) + { + first = false; + last = it; + continue; + } + geometry_msgs::Point point; + + point.x = last(0); + point.y = last(1); + point.z = last(2); + routeMarker.points.push_back(point); + point.x = it(0); + point.y = it(1); + point.z = it(2); + routeMarker.points.push_back(point); + last = it; + } + + routePub.publish(routeMarker); + } + + if (traj.getPieceNum() > 0) + { + Eigen::MatrixXd wps = traj.getPositions(); + for (int i = 0; i < wps.cols(); i++) + { + geometry_msgs::Point point; + point.x = wps.col(i)(0); + point.y = wps.col(i)(1); + point.z = wps.col(i)(2); + wayPointsMarker.points.push_back(point); + } + + wayPointsPub.publish(wayPointsMarker); + } + + if (traj.getPieceNum() > 0) + { + double T = 0.01; + Eigen::Vector3d lastX = traj.getPos(0.0); + for (double t = T; t < traj.getTotalDuration(); t += T) + { + geometry_msgs::Point point; + Eigen::Vector3d X = traj.getPos(t); + point.x = lastX(0); + point.y = lastX(1); + point.z = lastX(2); + trajMarker.points.push_back(point); + point.x = X(0); + point.y = X(1); + point.z = X(2); + trajMarker.points.push_back(point); + lastX = X; + } + trajectoryPub.publish(trajMarker); + } + } + + // Visualize some polytopes in H-representation + inline void visualizePolytope(const std::vector &hPolys) + { + + // Due to the fact that H-representation cannot be directly visualized + // We first conduct vertex enumeration of them, then apply quickhull + // to obtain triangle meshs of polyhedra + Eigen::Matrix3Xd mesh(3, 0), curTris(3, 0), oldTris(3, 0); + for (size_t id = 0; id < hPolys.size(); id++) + { + oldTris = mesh; + Eigen::Matrix vPoly; + geo_utils::enumerateVs(hPolys[id], vPoly); + + quickhull::QuickHull tinyQH; + const auto polyHull = tinyQH.getConvexHull(vPoly.data(), vPoly.cols(), false, true); + const auto &idxBuffer = polyHull.getIndexBuffer(); + int hNum = idxBuffer.size() / 3; + + curTris.resize(3, hNum * 3); + for (int i = 0; i < hNum * 3; i++) + { + curTris.col(i) = vPoly.col(idxBuffer[i]); + } + mesh.resize(3, oldTris.cols() + curTris.cols()); + mesh.leftCols(oldTris.cols()) = oldTris; + mesh.rightCols(curTris.cols()) = curTris; + } + + // RVIZ support tris for visualization + visualization_msgs::Marker meshMarker, edgeMarker; + + meshMarker.id = 0; + meshMarker.header.stamp = ros::Time::now(); + meshMarker.header.frame_id = "odom"; + meshMarker.pose.orientation.w = 1.00; + meshMarker.action = visualization_msgs::Marker::ADD; + meshMarker.type = visualization_msgs::Marker::TRIANGLE_LIST; + meshMarker.ns = "mesh"; + meshMarker.color.r = 0.00; + meshMarker.color.g = 0.00; + meshMarker.color.b = 1.00; + meshMarker.color.a = 0.15; + meshMarker.scale.x = 1.0; + meshMarker.scale.y = 1.0; + meshMarker.scale.z = 1.0; + + edgeMarker = meshMarker; + edgeMarker.type = visualization_msgs::Marker::LINE_LIST; + edgeMarker.ns = "edge"; + edgeMarker.color.r = 0.00; + edgeMarker.color.g = 1.00; + edgeMarker.color.b = 1.00; + edgeMarker.color.a = 1.00; + edgeMarker.scale.x = 0.02; + + geometry_msgs::Point point; + + int ptnum = mesh.cols(); + + for (int i = 0; i < ptnum; i++) + { + point.x = mesh(0, i); + point.y = mesh(1, i); + point.z = mesh(2, i); + meshMarker.points.push_back(point); + } + + for (int i = 0; i < ptnum / 3; i++) + { + for (int j = 0; j < 3; j++) + { + point.x = mesh(0, 3 * i + j); + point.y = mesh(1, 3 * i + j); + point.z = mesh(2, 3 * i + j); + edgeMarker.points.push_back(point); + point.x = mesh(0, 3 * i + (j + 1) % 3); + point.y = mesh(1, 3 * i + (j + 1) % 3); + point.z = mesh(2, 3 * i + (j + 1) % 3); + edgeMarker.points.push_back(point); + } + } + + meshPub.publish(meshMarker); + edgePub.publish(edgeMarker); + + return; + } + + // Visualize all spheres with centers sphs and the same radius + inline void visualizeSphere(const Eigen::Vector3d ¢er, + const double &radius) + { + visualization_msgs::Marker sphereMarkers, sphereDeleter; + + sphereMarkers.id = 0; + sphereMarkers.type = visualization_msgs::Marker::SPHERE_LIST; + sphereMarkers.header.stamp = ros::Time::now(); + sphereMarkers.header.frame_id = "odom"; + sphereMarkers.pose.orientation.w = 1.00; + sphereMarkers.action = visualization_msgs::Marker::ADD; + sphereMarkers.ns = "spheres"; + sphereMarkers.color.r = 0.00; + sphereMarkers.color.g = 0.00; + sphereMarkers.color.b = 1.00; + sphereMarkers.color.a = 1.00; + sphereMarkers.scale.x = radius * 2.0; + sphereMarkers.scale.y = radius * 2.0; + sphereMarkers.scale.z = radius * 2.0; + + sphereDeleter = sphereMarkers; + sphereDeleter.action = visualization_msgs::Marker::DELETE; + + geometry_msgs::Point point; + point.x = center(0); + point.y = center(1); + point.z = center(2); + sphereMarkers.points.push_back(point); + + spherePub.publish(sphereDeleter); + spherePub.publish(sphereMarkers); + } + + inline void visualizeStartGoal(const Eigen::Vector3d ¢er, + const double &radius, + const int sg) + { + visualization_msgs::Marker sphereMarkers, sphereDeleter; + + sphereMarkers.id = sg; + sphereMarkers.type = visualization_msgs::Marker::SPHERE_LIST; + sphereMarkers.header.stamp = ros::Time::now(); + sphereMarkers.header.frame_id = "odom"; + sphereMarkers.pose.orientation.w = 1.00; + sphereMarkers.action = visualization_msgs::Marker::ADD; + sphereMarkers.ns = "StartGoal"; + sphereMarkers.color.r = 1.00; + sphereMarkers.color.g = 0.00; + sphereMarkers.color.b = 0.00; + sphereMarkers.color.a = 1.00; + sphereMarkers.scale.x = radius * 2.0; + sphereMarkers.scale.y = radius * 2.0; + sphereMarkers.scale.z = radius * 2.0; + + sphereDeleter = sphereMarkers; + sphereDeleter.action = visualization_msgs::Marker::DELETEALL; + + geometry_msgs::Point point; + point.x = center(0); + point.y = center(1); + point.z = center(2); + sphereMarkers.points.push_back(point); + + if (sg == 0) + { + spherePub.publish(sphereDeleter); + ros::Duration(1.0e-9).sleep(); + sphereMarkers.header.stamp = ros::Time::now(); + } + spherePub.publish(sphereMarkers); + } +}; + +#endif \ No newline at end of file diff --git a/multi_uav_simulator/launch/simu.launch b/launch/simu.launch similarity index 100% rename from multi_uav_simulator/launch/simu.launch rename to launch/simu.launch diff --git a/multi_uav_simulator/CMakeLists.txt b/multi_uav_simulator/CMakeLists.txt deleted file mode 100755 index cb41aba..0000000 --- a/multi_uav_simulator/CMakeLists.txt +++ /dev/null @@ -1,48 +0,0 @@ -cmake_minimum_required(VERSION 2.8.3) - -macro(use_cxx11) - if (CMAKE_VERSION VERSION_LESS "3.1") - if (CMAKE_CXX_COMPILER_ID STREQUAL "GNU") - set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=gnu++11") - endif () - else () - set(CMAKE_CXX_STANDARD 11) - endif () -endmacro(use_cxx11) - -project(multi_uav_simulator) - -find_package(Armadillo REQUIRED) -find_package(GSL REQUIRED) - -find_package(catkin REQUIRED COMPONENTS - roscpp - #rospy - std_msgs - tf - geo_controller - message_generation - simulator_utils - mav_trajectory_generation - ) - -catkin_package( -) - -include_directories( - include/${PROJECT_NAME} - ${catkin_INCLUDE_DIRS} - ${geo_controller_INCLUDE_DIRS} - ${simulator_utils_INCLUDE_DIRS} -) - -add_executable(multi_uav_simulator - src/DynamicsProvider.cpp - src/cfSimUtils.cpp - src/Quadrotor.cpp - ) - -target_link_libraries(multi_uav_simulator - GSL::gsl - GSL::gslcblas - ${catkin_LIBRARIES}) diff --git a/multi_uav_simulator/bigquad_description/bigquad.dae b/multi_uav_simulator/bigquad_description/bigquad.dae deleted file mode 100644 index ab62cd7..0000000 --- a/multi_uav_simulator/bigquad_description/bigquad.dae +++ /dev/null @@ -1,235 +0,0 @@ - - - - - Stefan Kohlbrecher - Blender 2.61.4 r43829 - - 2012-02-03T14:20:49 - 2012-02-03T14:20:49 - - Z_UP - - 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16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 19 19 21 21 24 24 25 25 22 22 26 26 27 27 25 25 28 28 29 29 30 30 31 31 26 26 32 32 29 29 33 33 30 30 34 34 35 35 18 18 36 36 37 37 38 38 36 36 32 32 39 39 40 40 41 41 17 17 42 42 39 39 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 48 48 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 48 48 53 53 46 46 60 60 47 47 46 46 49 49 57 57 61 61 62 62 63 63 51 51 64 64 45 45 65 65 63 63 66 66 43 43 64 64 41 41 67 67 54 54 68 68 34 34 52 52 59 59 58 58 52 52 58 58 53 53 59 59 61 61 57 57 61 61 50 50 49 49 50 50 62 62 51 51 62 62 66 66 63 63 66 66 44 44 43 43 44 44 65 65 45 45 64 64 67 67 45 45 41 41 40 40 67 67 39 39 42 42 40 40 17 17 16 16 42 42 18 18 37 37 16 16 36 36 38 38 37 37 32 32 33 33 38 38 29 29 28 28 33 33 25 25 24 24 28 28 21 21 20 20 24 24 19 19 23 23 20 20 22 22 27 27 23 23 26 26 31 31 27 27 30 30 35 35 31 31 34 34 68 68 35 35 54 54 56 56 68 68 69 69 55 55 70 70 55 55 69 69 56 56 69 69 70 70 71 71

- - - - -

72 72 73 73 74 74 75 75 76 76 77 77 78 78 79 79 80 80 81 81 82 82 83 83 79 79 84 84 85 85 86 86 87 87 88 88 84 84 89 89 90 90 91 91 92 92 93 93 89 89 94 94 95 95 96 96 97 97 98 98 99 99 75 75 100 100 101 101 102 102 94 94 103 103 104 104 105 105 106 106 104 104 107 107 108 108 109 109 110 110 111 111 112 112 113 113 114 114 115 115 116 116 117 117 118 118 113 113 119 119 72 72 120 120 121 121 115 115 122 122 121 121 123 123 73 73 116 116 110 110 124 124 125 125 111 111 126 126 127 127 126 126 128 128 129 129 130 130 108 108 131 131 128 128 103 103 132 132 133 133 134 134 133 133 132 132 117 117 112 112 133 133 117 117 83 83 88 88 87 87 135 135 136 136 137 137 136 136 138 138 129 129 139 139 135 135 140 140 141 141 142 142 139 139 75 75 77 77 100 100 142 142 143 143 144 144 99 99 145 145 75 75 101 101 144 144 146 146 145 145 99 99 147 147 147 147 148 148 145 145 99 99 100 100 149 149 150 150 99 99 151 151 107 107 76 76 106 106 107 107 77 77 76 76 104 104 106 106 105 105 103 103 105 105 131 131 128 128 131 131 127 127 126 126 127 127 125 125 111 111 125 125 112 112 113 113 112 112 117 117 118 118 119 119 120 120 118 118 117 117 119 119 120 120 72 72 74 74 74 74 73 73 123 123 123 123 121 121 122 122 122 122 115 115 114 114 114 114 116 116 124 124 124 124 110 110 109 109 109 109 108 108 130 130 130 130 129 129 138 138 136 136 129 129 137 137 135 135 137 137 140 140 139 139 140 140 141 141 142 142 141 141 143 143 144 144 143 143 146 146 101 101 146 146 102 102 94 94 102 102 95 95 89 89 95 95 90 90 84 84 90 90 85 85 79 79 85 85 80 80 78 78 82 82 81 81 78 78 80 80 82 82 81 81 83 83 87 87 86 86 88 88 91 91 93 93 92 92 97 97 86 86 91 91 93 93 98 98 150 150 96 96 92 92 98 98 97 97 99 99 149 149 151 151 150 150 151 151 96 96

- - - - -

152 152 153 153 154 154 152 152 155 155 153 153

- - - - -

156 156 157 157 158 158 159 159 156 156 160 160 157 157 156 156 161 161 159 159 161 161 156 156

- - - - -

162 162 163 163 164 164 165 165 166 166 162 162 162 162 164 164 165 165 166 166 167 167 168 168 167 167 166 166 165 165 169 169 168 168 170 170 167 167 170 170 168 168 171 171 172 172 169 169 169 169 170 170 171 171 172 172 173 173 174 174 173 173 172 172 171 171 175 175 174 174 176 176 173 173 176 176 174 174 177 177 178 178 175 175 175 175 176 176 177 177 178 178 179 179 180 180 179 179 178 178 177 177 181 181 180 180 182 182 179 179 182 182 180 180 183 183 184 184 181 181 181 181 182 182 183 183 184 184 185 185 186 186 185 185 184 184 183 183 187 187 186 186 188 188 185 185 188 188 186 186 189 189 190 190 187 187 187 187 188 188 189 189 164 164 163 163 191 191 192 192 191 191 193 193 163 163 193 193 191 191 194 194 195 195 192 192 192 192 193 193 194 194 195 195 196 196 197 197 196 196 195 195 194 194 198 198 197 197 199 199 196 196 199 199 197 197 200 200 201 201 198 198 198 198 199 199 200 200 201 201 202 202 203 203 202 202 201 201 200 200 204 204 203 203 205 205 202 202 205 205 203 203 206 206 207 207 204 204 204 204 205 205 206 206 207 207 208 208 209 209 208 208 207 207 206 206 210 210 209 209 211 211 208 208 211 211 209 209 212 212 213 213 210 210 210 210 211 211 212 212 213 213 214 214 215 215 214 214 213 213 212 212 214 214 216 216 215 215 215 215 216 216 217 217

- - - - -

218 218 219 219 220 220 218 218 221 221 219 219 220 220 222 222 218 218 218 218 223 223 221 221

- - - - -

224 224 225 225 226 226 224 224 227 227 225 225

- - - - -

228 228 229 229 230 230 228 228 231 231 229 229

- - - - -

232 232 233 233 234 234 235 235 232 232 236 236 233 233 232 232 237 237 235 235 237 237 232 232

- - - - -

238 238 239 239 240 240 239 239 241 241 242 242 241 241 239 239 238 238 243 243 242 242 244 244 241 241 244 244 242 242 245 245 246 246 243 243 243 243 244 244 245 245 238 238 240 240 247 247 248 248 249 249 247 247 247 247 240 240 248 248 249 249 250 250 251 251 250 250 249 249 248 248 250 250 252 252 251 251 251 251 252 252 253 253

- - - - -

254 254 255 255 256 256 254 254 257 257 255 255 256 256 258 258 254 254 254 254 259 259 257 257

- - - - -

260 260 261 261 262 262 260 260 263 263 261 261

- - - - -

264 264 265 265 266 266 264 264 267 267 268 268 265 265 269 269 266 266 270 270 271 271 272 272 267 267 271 271 270 270 273 273 274 274 275 275 276 276 273 273 277 277 275 275 277 277 273 273 276 276 278 278 279 279 278 278 276 276 277 277 280 280 281 281 279 279 279 279 278 278 280 280 282 282 283 283 284 284 280 280 285 285 281 281 286 286 287 287 274 274 287 287 275 275 274 274 281 281 285 285 288 288 288 288 289 289 290 290 289 289 288 288 285 285 291 291 292 292 290 290 290 290 289 289 291 291 293 293 292 292 294 294 291 291 294 294 292 292 293 293 295 295 296 296 295 295 293 293 294 294 296 296 295 295 297 297 287 287 286 286 282 282 298 298 282 282 284 284 282 282 298 298 287 287 299 299 300 300 298 298 298 298 284 284 299 299 301 301 300 300 302 302 299 299 302 302 300 300 301 301 303 303 304 304 303 303 301 301 302 302 305 305 306 306 304 304 304 304 303 303 305 305 307 307 306 306 308 308 305 305 308 308 306 306 307 307 309 309 310 310 309 309 307 307 308 308 272 272 271 271 310 310 310 310 309 309 272 272 264 264 271 271 267 267 264 264 268 268 265 265 311 311 312 312 313 313 314 314 269 269 312 312 315 315 316 316 317 317 318 318 319 319 320 320 321 321 322 322 323 323 315 315 324 324 325 325 326 326 327 327 328 328 329 329 330 330 331 331 332 332 333 333 334 334 335 335 328 328 336 336 337 337 338 338 339 339 338 338 337 337 334 334 340 340 341 341 339 339 339 339 338 338 340 340 342 342 341 341 343 343 340 340 343 343 341 341 342 342 296 296 297 297 296 296 342 342 343 343 334 334 337 337 332 332 332 332 335 335 333 333 328 328 327 327 336 336 335 335 336 336 333 333 326 326 331 331 327 327 322 322 330 330 329 329 329 329 331 331 326 326 324 324 321 321 323 323 321 321 330 330 322 322 315 315 325 325 316 316 324 324 323 323 325 325 317 317 316 316 319 319 318 318 320 320 313 313 317 317 319 319 318 318 311 311 314 314 312 312 320 320 311 311 313 313 314 314 266 266 269 269

- - - - -

344 344 345 345 346 346 344 344 347 347 348 348 347 347 349 349 348 348 348 348 345 345 344 344

- - - - -

350 350 351 351 352 352 351 351 353 353 354 354 350 350 353 353 351 351 353 353 355 355 354 354

- - - - - - - 34.1418 10.22 36.3772 34.7233 10.22 36.0885 33.8757 10.22 35.5135 35.2946 10.22 34.2964 35.7096 10.22 35.2505 36.0885 10.22 34.7233 35.6656 10.22 33.4264 36.3772 10.22 34.1418 36.5681 10.22 33.5212 34.2964 10.22 35.2946 35.2505 10.22 35.7096 34.6788 10.22 35.0142 35.0142 10.22 34.6788 33.4264 10.22 35.6656 33.5212 10.22 36.5681 35.5135 10.22 33.8757 30.5881 10.22 34.9714 29.5776 10.22 35.2164 30.0669 10.22 35.711 31.491 10.22 35.5347 31.2629 10.22 36.4115 32.0014 10.22 35.6922 28.8897 10.22 34.0132 29.7151 10.22 33.6467 28.712 10.22 33.3406 31.2826 10.22 28.8969 30.6526 10.22 29.1917 31.124 10.22 29.9589 29.1917 10.22 30.6526 29.9907 10.22 31.0693 29.5912 10.22 30.0831 29.7578 10.22 31.5499 28.8969 10.22 31.2826 28.7157 10.22 31.9543 29.6109 10.22 32.0634 29.5891 10.22 33.1277 28.6535 10.22 32.6473 29.5541 10.22 32.5946 30.0831 10.22 29.5912 30.6841 10.22 30.2618 30.3026 10.22 30.6357 29.1812 10.22 34.6448 30.2221 10.22 34.5824 29.9282 10.22 34.1364 31.6093 10.22 29.7359 31.9543 10.22 28.7157 30.6344 10.22 36.1134 31.0153 10.22 35.2921 32.1257 10.22 29.5995 32.6473 10.22 28.6535 32.6579 10.22 29.5535 33.3406 10.22 28.712 34.0132 10.22 28.8897 33.6932 10.22 29.7312 34.1734 10.22 29.9485 34.6099 10.22 30.244 34.6448 10.22 29.1812 31.9337 10.22 36.5962 34.9901 10.22 30.6091 35.3032 10.22 31.0332 35.711 10.22 30.0669 32.6262 10.22 36.6621 32.5313 10.22 35.7597 35.54 10.22 31.5041 36.1134 10.22 30.6344 35.2164 10.22 29.5776 36.4115 10.22 31.2629 35.6936 10.22 32.0083 33.1831 10.22 29.5983 36.5962 10.22 31.9337 35.7597 10.22 32.5313 36.6621 10.22 32.6262 34.0132 0 28.8897 34.1354 1.77636e-015 29.9276 33.6659 1.77636e-015 29.7217 30.6526 0 29.1917 31.2826 1.77636e-015 28.8969 31.1803 1.77636e-015 29.9276 30.374 1.77636e-015 34.7603 30.7512 0 35.1076 30.0669 -1.77636e-015 35.711 31.2629 0 36.4115 31.1803 1.77636e-015 35.3881 31.6498 1.77636e-015 35.5941 29.1917 1.77636e-015 30.6526 29.5912 -1.77636e-015 30.0831 30.059 0 30.96 29.6484 1.77636e-015 33.4201 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0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 10 10 4 4 12 12 1 1 9 9 2 2 13 13 14 14 0 0 0 0 2 2 13 13 10 10 9 9 1 1 10 10 12 12 11 11 4 4 3 3 12 12 5 5 15 15 3 3 6 6 15 15 7 7 5 5 7 7 15 15

- - - - -

16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 28 28 32 32 33 33 34 34 32 32 24 24 35 35 36 36 37 37 33 33 36 36 26 26 38 38 39 39 40 40 38 38 30 30 41 41 17 17 42 42 41 41 43 43 22 22 25 25 44 44 45 45 46 46 47 47 18 18 48 48 49 49 45 45 19 19 46 46 20 20 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 54 54 21 21 20 20 57 57 58 58 59 59 60 60 57 57 61 61 62 62 63 63 64 64 59 59 65 65 55 55 58 58 57 57 62 62 21 21 66 66 63 63 67 67 19 19 47 47 46 46 47 47 16 16 18 18 16 16 42 42 17 17 42 42 43 43 41 41 43 43 23 23 22 22 23 23 35 35 24 24 35 35 37 37 36 36 37 37 34 34 33 33 34 34 31 31 32 32 31 31 29 29 28 28 29 29 40 40 30 30 40 40 39 39 38 38 39 39 27 27 26 26 27 27 44 44 25 25 44 44 48 48 45 45 48 48 50 50 49 49 50 50 68 68 51 51 53 53 52 52 51 51 53 53 51 51 68 68 54 54 56 56 52 52 55 55 65 65 56 56 58 58 60 60 65 65 59 59 64 64 60 60 63 63 66 66 64 64 69 69 67 67 70 70 67 67 69 69 66 66 69 69 70 70 71 71

- - - - -

72 72 73 73 74 74 75 75 76 76 77 77 78 78 79 79 80 80 81 81 82 82 83 83 84 84 85 85 86 86 87 87 88 88 89 89 90 90 91 91 92 92 93 93 94 94 95 95 92 92 84 84 96 96 97 97 85 85 98 98 93 93 87 87 99 99 100 100 88 88 101 101 102 102 98 98 75 75 76 76 103 103 104 104 78 78 105 105 101 101 106 106 103 103 107 107 107 107 108 108 109 109 79 79 82 82 110 110 111 111 83 83 112 112 111 111 81 81 83 83 113 113 111 111 112 112 114 114 73 73 115 115 116 116 113 113 117 117 113 113 112 112 118 118 119 119 120 120 121 121 122 122 123 123 124 124 120 120 113 113 121 121 125 125 126 126 127 127 128 128 129 129 130 130 113 113 116 116 121 121 131 131 132 132 133 133 134 134 135 135 131 131 136 136 137 137 132 132 138 138 139 139 140 140 141 141 142 142 135 135 135 135 143 143 131 131 144 144 124 124 145 145 143 143 135 135 146 146 146 146 147 147 143 143 148 148 149 149 122 122 114 114 150 150 148 148 126 126 125 125 136 136 82 82 81 81 110 110 79 79 110 110 80 80 78 78 80 80 105 105 101 101 105 105 100 100 88 88 100 100 89 89 87 87 89 89 99 99 93 93 99 99 94 94 95 95 91 91 90 90 95 95 94 94 91 91 90 90 92 92 96 96 96 96 84 84 86 86 86 86 85 85 97 97 97 97 98 98 102 102 102 102 75 75 77 77 77 77 76 76 104 104 104 104 103 103 106 106 106 106 107 107 109 109 109 109 108 108 151 151 74 74 108 108 72 72 74 74 151 151 108 108 73 73 72 72 115 115 114 114 115 115 150 150 148 148 150 150 149 149 122 122 149 149 123 123 124 124 123 123 145 145 144 144 142 142 141 141 144 144 145 145 142 142 141 141 135 135 134 134 134 134 131 131 133 133 133 133 132 132 137 137 137 137 136 136 125 125 127 127 126 126 139 139 138 138 140 140 129 129 127 127 139 139 138 138 130 130 116 116 128 128 140 140 130 130 129 129 113 113 118 118 117 117 116 116 117 117 128 128

- - - - -

152 152 153 153 154 154 152 152 155 155 153 153

- - - - -

156 156 157 157 158 158 159 159 156 156 160 160 157 157 156 156 161 161 159 159 161 161 156 156

- - - - -

162 162 163 163 164 164 165 165 166 166 162 162 162 162 164 164 165 165 166 166 167 167 168 168 167 167 166 166 165 165 169 169 168 168 170 170 167 167 170 170 168 168 171 171 172 172 169 169 169 169 170 170 171 171 172 172 173 173 174 174 173 173 172 172 171 171 175 175 174 174 176 176 173 173 176 176 174 174 177 177 178 178 175 175 175 175 176 176 177 177 178 178 179 179 180 180 179 179 178 178 177 177 181 181 180 180 182 182 179 179 182 182 180 180 183 183 184 184 181 181 181 181 182 182 183 183 184 184 185 185 186 186 185 185 184 184 183 183 187 187 186 186 188 188 185 185 188 188 186 186 189 189 190 190 187 187 187 187 188 188 189 189 164 164 163 163 191 191 192 192 191 191 193 193 163 163 193 193 191 191 194 194 195 195 192 192 192 192 193 193 194 194 195 195 196 196 197 197 196 196 195 195 194 194 198 198 197 197 199 199 196 196 199 199 197 197 200 200 201 201 198 198 198 198 199 199 200 200 201 201 202 202 203 203 202 202 201 201 200 200 204 204 203 203 205 205 202 202 205 205 203 203 206 206 207 207 204 204 204 204 205 205 206 206 207 207 208 208 209 209 208 208 207 207 206 206 210 210 209 209 211 211 208 208 211 211 209 209 212 212 213 213 210 210 210 210 211 211 212 212 213 213 214 214 215 215 214 214 213 213 212 212 214 214 216 216 215 215 215 215 216 216 217 217

- - - - -

218 218 219 219 220 220 218 218 221 221 219 219 220 220 222 222 218 218 218 218 223 223 221 221

- - - - -

224 224 225 225 226 226 224 224 227 227 225 225

- - - - -

228 228 229 229 230 230 228 228 231 231 229 229

- - - - -

232 232 233 233 234 234 235 235 232 232 236 236 233 233 232 232 237 237 235 235 237 237 232 232

- - - - -

238 238 239 239 240 240 239 239 241 241 242 242 241 241 239 239 238 238 243 243 242 242 244 244 241 241 244 244 242 242 245 245 246 246 243 243 243 243 244 244 245 245 238 238 240 240 247 247 248 248 249 249 247 247 247 247 240 240 248 248 249 249 250 250 251 251 250 250 249 249 248 248 250 250 252 252 251 251 251 251 252 252 253 253

- - - - -

254 254 255 255 256 256 254 254 257 257 255 255 256 256 258 258 254 254 254 254 259 259 257 257

- - - - -

260 260 261 261 262 262 260 260 263 263 261 261

- - - - -

264 264 265 265 266 266 264 264 267 267 268 268 265 265 269 269 266 266 267 267 270 270 271 271 272 272 270 270 267 267 273 273 274 274 275 275 274 274 276 276 277 277 277 277 275 275 274 274 278 278 279 279 276 276 277 277 276 276 279 279 280 280 278 278 281 281 278 278 280 280 279 279 282 282 283 283 284 284 285 285 280 280 281 281 286 286 287 287 288 288 283 283 287 287 286 286 289 289 285 285 281 281 290 290 291 291 289 289 285 285 289 289 291 291 292 292 290 290 293 293 290 290 292 292 291 291 293 293 294 294 295 295 295 295 292 292 293 293 296 296 297 297 294 294 295 295 294 294 297 297 298 298 296 296 299 299 296 296 298 298 297 297 299 299 300 300 301 301 301 301 298 298 299 299 302 302 303 303 300 300 301 301 300 300 303 303 304 304 302 302 305 305 302 302 304 304 303 303 306 306 304 304 305 305 306 306 305 305 307 307 275 275 308 308 273 273 309 309 310 310 308 308 273 273 308 308 310 310 311 311 309 309 312 312 309 309 311 311 310 310 312 312 313 313 314 314 314 314 311 311 312 312 288 288 315 315 313 313 314 314 313 313 315 315 283 283 282 282 287 287 288 288 287 287 315 315 282 282 316 316 317 317 284 284 316 316 282 282 318 318 319 319 317 317 317 317 316 316 318 318 320 320 319 319 321 321 318 318 321 321 319 319 322 322 320 320 321 321 322 322 323 323 324 324 324 324 320 320 322 322 325 325 326 326 323 323 324 324 323 323 326 326 327 327 325 325 328 328 325 325 327 327 326 326 328 328 270 270 272 272 272 272 327 327 328 328 268 268 265 265 264 264 264 264 272 272 267 267 329 329 330 330 331 331 266 266 269 269 332 332 333 333 334 334 335 335 336 336 337 337 331 331 338 338 339 339 340 340 341 341 340 340 342 342 343 343 338 338 306 306 338 338 343 343 339 339 307 307 343 343 306 306 340 340 339 339 342 342 341 341 342 342 333 333 335 335 334 334 336 336 341 341 333 333 335 335 337 337 329 329 331 331 334 334 337 337 336 336 329 329 332 332 330 330 332 332 269 269 330 330

- - - - -

344 344 345 345 346 346 344 344 346 346 347 347 346 346 348 348 347 347 347 347 348 348 349 349

- - - - -

350 350 351 351 352 352 350 350 353 353 354 354 351 351 350 350 354 354 355 355 352 352 351 351

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33.2517 10.22 -29.6109 32.7364 10.22 -29.5546 31.2826 10.22 -28.8969 31.7135 10.22 -29.7005 36.5962 10.22 -31.9337 35.7597 10.22 -32.5313 35.6954 10.22 -32.0169 34.6436 10.22 -30.2716 34.2188 10.22 -29.9743 35.2164 10.22 -29.5776 36.4115 10.22 -31.2629 35.5465 10.22 -31.5204 36.1134 10.22 -30.6344 35.711 10.22 -30.0669 35.0131 10.22 -30.6354 35.3169 10.22 -31.0556 33.7505 10.22 -29.7521 34.6448 10.22 -29.1812 36.6621 10.22 -32.6262 32.2188 10.22 -29.5847 32.6473 10.22 -28.6535 34.0132 10.22 -28.8897 31.2629 10.22 -36.4115 31.1369 10.22 -35.3642 31.9543 10.22 -28.7157 31.579 10.22 -35.5688 32.0477 10.22 -35.7017 31.9337 10.22 -36.5962 32.5313 10.22 -35.7597 32.6262 10.22 -36.6621 29.6488 0 -33.4213 29.5642 1.77636e-015 -32.9155 28.712 0 -33.3406 36.1134 0 -30.6344 35.5003 -1.83495e-016 -31.4096 36.4115 0 -31.2629 29.8155 0 -33.9063 28.8897 0 -34.0132 29.1812 0 -34.6448 29.5641 0 -32.4026 28.6535 0 -32.6473 29.5776 0 -35.2164 30.0599 0 -34.3572 30.0669 0 -35.711 30.3751 0 -34.7617 30.7525 1.77636e-015 -35.1087 30.6344 0 -36.1134 28.7157 0 -31.9543 29.6483 1.77636e-015 -31.8968 29.8145 1.77636e-015 -31.4117 30.0585 1.77636e-015 -30.9606 29.1917 0 -30.6526 28.8969 0 -31.2826 32.6598 1.77636e-015 -35.7622 32.6262 0 -36.6621 33.1707 1.94289e-015 -35.7196 31.9337 0 -36.5962 31.6516 2.77556e-017 -35.5947 31.2629 0 -36.4115 34.7233 0 -36.0885 34.5661 2.498e-016 -35.1065 34.1371 1.57898e-015 -35.3872 33.6677 1.51114e-016 -35.5935 34.1418 -1.77636e-015 -36.3772 34.0132 0 -28.8897 33.6653 1.77636e-015 -29.7215 34.1347 1.77636e-015 -29.9272 35.7096 0 -35.2505 35.2579 1.99686e-015 -34.3542 34.9432 1.25208e-015 -34.7589 35.6668 0 -31.8943 36.5962 0 -31.9337 35.7516 0 -32.9125 35.6676 0 -33.4182 36.5681 0 -33.5212 36.6621 0 -32.6262 35.7513 0 -32.3998 35.2164 0 -29.5776 34.6448 0 -29.1812 34.5638 4.19418e-016 -30.2074 35.2561 7.77156e-016 -30.9589 35.711 0 -30.0669 34.941 1.11331e-015 -30.5545 33.3406 0 -28.712 32.6473 0 -28.6535 33.1689 1.77636e-015 -29.5959 35.5016 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0 0 1 1 2 2 0 0 3 3 4 4 5 5 6 6 7 7 2 2 6 6 8 8 5 5 8 8 6 6 7 7 9 9 10 10 10 10 5 5 7 7 2 2 8 8 0 0 9 9 11 11 10 10 1 1 0 0 4 4 12 12 3 3 13 13 3 3 12 12 4 4 12 12 13 13 14 14 14 14 13 13 15 15

- - - - -

16 16 17 17 18 18 19 19 20 20 16 16 21 21 17 17 22 22 23 23 20 20 24 24 25 25 26 26 27 27 25 25 28 28 29 29 30 30 29 29 31 31 23 23 32 32 33 33 34 34 35 35 36 36 37 37 35 35 30 30 38 38 39 39 40 40 38 38 34 34 41 41 42 42 43 43 44 44 40 40 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 53 53 47 47 49 49 49 49 54 54 53 53 56 56 57 57 52 52 56 56 55 55 58 58 51 51 59 59 60 60 61 61 48 48 47 47 62 62 63 63 44 44 59 59 43 43 64 64 65 65 33 33 66 66 62 62 46 46 67 67 68 68 69 69 65 65 54 54 58 58 55 55 58 58 57 57 56 56 57 57 50 50 52 52 51 51 60 60 52 52 59 59 64 64 60 60 43 43 42 42 64 64 44 44 63 63 42 42 62 62 67 67 63 63 46 46 45 45 67 67 40 40 39 39 45 45 38 38 41 41 39 39 34 34 36 36 41 41 35 35 37 37 36 36 30 30 31 31 37 37 29 29 28 28 31 31 25 25 27 27 28 28 26 26 21 21 22 22 26 26 22 22 27 27 21 21 18 18 17 17 18 18 19 19 16 16 19 19 24 24 20 20 24 24 32 32 23 23 32 32 66 66 33 33 66 66 68 68 65 65 70 70 69 69 71 71 69 69 70 70 65 65 70 70 71 71 72 72

- - - - -

73 73 74 74 75 75 76 76 77 77 78 78 79 79 80 80 81 81 74 74 82 82 83 83 81 81 84 84 85 85 84 84 86 86 87 87 88 88 86 86 89 89 90 90 82 82 91 91 92 92 93 93 94 94 92 92 95 95 91 91 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 104 104 107 107 108 108 109 109 110 110 111 111 112 112 113 113 114 114 78 78 115 115 116 116 117 117 115 115 118 118 119 119 120 120 121 121 122 122 123 123 124 124 125 125 126 126 127 127 128 128 129 129 130 130 116 116 103 103 131 131 112 112 111 111 132 132 129 129 133 133 134 134 135 135 136 136 137 137 118 118 137 137 136 136 138 138 105 105 98 98 139 139 133 133 140 140 134 134 118 118 117 117 136 136 124 124 123 123 76 76 97 97 141 141 99 99 142 142 143 143 144 144 145 145 146 146 93 93 147 147 145 145 144 144 97 97 148 148 139 139 149 149 89 89 101 101 148 148 97 97 150 150 150 150 151 151 148 148 127 127 133 133 135 135 135 135 152 152 127 127 142 142 140 140 143 143 142 142 134 134 140 140 144 144 143 143 147 147 145 145 147 147 146 146 93 93 146 146 94 94 92 92 94 94 95 95 91 91 95 95 90 90 82 82 90 90 83 83 74 74 83 83 75 75 73 73 80 80 79 79 73 73 75 75 80 80 79 79 81 81 85 85 85 85 84 84 87 87 87 87 86 86 88 88 88 88 89 89 149 149 149 149 101 101 100 100 100 100 99 99 141 141 141 141 97 97 96 96 98 98 97 97 139 139 105 105 139 139 106 106 104 104 106 106 102 102 103 103 102 102 131 131 112 112 131 131 110 110 111 111 110 110 132 132 129 129 132 132 130 130 116 116 130 130 117 117 115 115 117 117 118 118 119 119 114 114 113 113 119 119 118 118 114 114 113 113 78 78 77 77 77 77 76 76 123 123 125 125 124 124 120 120 122 122 121 121 109 109 125 125 120 120 122 122 107 107 126 126 108 108 121 121 107 107 109 109 127 127 152 152 128 128 126 126 128 128 108 108

- - - - -

153 153 154 154 155 155 153 153 156 156 154 154

- - - - -

157 157 158 158 159 159 160 160 157 157 161 161 158 158 157 157 162 162 160 160 162 162 157 157

- - - - -

163 163 164 164 165 165 166 166 167 167 163 163 163 163 165 165 166 166 167 167 168 168 169 169 168 168 167 167 166 166 170 170 169 169 171 171 168 168 171 171 169 169 172 172 173 173 170 170 170 170 171 171 172 172 173 173 174 174 175 175 174 174 173 173 172 172 176 176 175 175 177 177 174 174 177 177 175 175 178 178 179 179 176 176 176 176 177 177 178 178 179 179 180 180 181 181 180 180 179 179 178 178 182 182 181 181 183 183 180 180 183 183 181 181 184 184 185 185 182 182 182 182 183 183 184 184 185 185 186 186 187 187 186 186 185 185 184 184 188 188 187 187 189 189 186 186 189 189 187 187 190 190 191 191 188 188 188 188 189 189 190 190 165 165 164 164 192 192 193 193 192 192 194 194 164 164 194 194 192 192 195 195 196 196 193 193 193 193 194 194 195 195 196 196 197 197 198 198 197 197 196 196 195 195 199 199 198 198 200 200 197 197 200 200 198 198 201 201 202 202 199 199 199 199 200 200 201 201 202 202 203 203 204 204 203 203 202 202 201 201 205 205 204 204 206 206 203 203 206 206 204 204 207 207 208 208 205 205 205 205 206 206 207 207 208 208 209 209 210 210 209 209 208 208 207 207 211 211 210 210 212 212 209 209 212 212 210 210 213 213 214 214 211 211 211 211 212 212 213 213 214 214 215 215 216 216 215 215 214 214 213 213 215 215 217 217 216 216 216 216 217 217 218 218

- - - - -

219 219 220 220 221 221 219 219 222 222 220 220 221 221 223 223 219 219 219 219 224 224 222 222

- - - - -

225 225 226 226 227 227 225 225 228 228 226 226

- - - - -

229 229 230 230 231 231 229 229 232 232 230 230

- - - - -

233 233 234 234 235 235 236 236 233 233 237 237 234 234 233 233 238 238 236 236 238 238 233 233

- - - - -

239 239 240 240 241 241 240 240 242 242 243 243 242 242 240 240 239 239 244 244 243 243 245 245 242 242 245 245 243 243 246 246 247 247 244 244 244 244 245 245 246 246 239 239 241 241 248 248 249 249 250 250 248 248 248 248 241 241 249 249 250 250 251 251 252 252 251 251 250 250 249 249 251 251 253 253 252 252 252 252 253 253 254 254

- - - - -

255 255 256 256 257 257 255 255 258 258 256 256 257 257 259 259 255 255 255 255 260 260 258 258

- - - - -

261 261 262 262 263 263 261 261 264 264 262 262

- - - - -

265 265 266 266 267 267 265 265 268 268 269 269 266 266 270 270 267 267 271 271 272 272 273 273 268 268 272 272 271 271 274 274 275 275 276 276 277 277 278 278 275 275 275 275 274 274 277 277 279 279 278 278 280 280 277 277 280 280 278 278 279 279 281 281 282 282 281 281 279 279 280 280 283 283 284 284 285 285 282 282 281 281 286 286 287 287 288 288 289 289 288 288 290 290 289 289 291 291 282 282 286 286 292 292 291 291 293 293 286 286 293 293 291 291 292 292 294 294 295 295 294 294 292 292 293 293 296 296 297 297 295 295 295 295 294 294 296 296 298 298 297 297 299 299 296 296 299 299 297 297 298 298 300 300 301 301 300 300 298 298 299 299 302 302 303 303 301 301 301 301 300 300 302 302 304 304 303 303 305 305 302 302 305 305 303 303 304 304 306 306 307 307 306 306 304 304 305 305 308 308 309 309 307 307 307 307 306 306 308 308 310 310 309 309 311 311 308 308 311 311 309 309 310 310 312 312 313 313 312 312 310 310 311 311 313 313 312 312 314 314 315 315 274 274 276 276 316 316 315 315 317 317 276 276 317 317 315 315 316 316 318 318 319 319 318 318 316 316 317 317 320 320 321 321 319 319 319 319 318 318 320 320 322 322 321 321 323 323 320 320 323 323 321 321 322 322 324 324 325 325 324 324 322 322 323 323 326 326 290 290 325 325 325 325 324 324 326 326 288 288 287 287 283 283 326 326 289 289 290 290 327 327 283 283 285 285 283 283 327 327 288 288 328 328 329 329 327 327 327 327 285 285 328 328 330 330 329 329 331 331 328 328 331 331 329 329 330 330 332 332 333 333 332 332 330 330 331 331 334 334 335 335 333 333 333 333 332 332 334 334 336 336 335 335 337 337 334 334 337 337 335 335 336 336 338 338 339 339 338 338 336 336 337 337 273 273 272 272 339 339 339 339 338 338 273 273 269 269 266 266 265 265 265 265 272 272 268 268 340 340 341 341 342 342 343 343 270 270 344 344 314 314 345 345 313 313 345 345 314 314 340 340 342 342 345 345 340 340 342 342 341 341 344 344 343 343 267 267 270 270 341 341 343 343 344 344

- - - - -

346 346 347 347 348 348 349 349 350 350 346 346 346 346 348 348 349 349 347 347 351 351 348 348

- - - - -

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0 0 2 2 1 1 3 3 5 5 4 4 6 6 8 8 7 7 9 9 11 11 10 10 12 12 14 14 13 13 15 15 17 17 16 16 18 18 3 3 19 19 20 20 22 22 21 21 23 23 21 21 24 24 25 25 27 27 26 26 28 28 29 29 4 4 30 30 32 32 31 31 33 33 35 35 34 34 19 19 35 35 36 36 37 37 39 39 38 38 40 40 34 34 14 14 41 41 38 38 39 39 7 7 42 42 13 13 6 6 44 44 43 43 20 20 16 16 17 17 43 43 46 46 45 45 47 47 49 49 48 48 50 50 51 51 49 49 51 51 53 53 52 52 54 54 55 55 45 45 52 52 57 57 56 56 55 55 59 59 58 58 43 43 61 61 60 60 62 62 60 60 61 61 61 61 43 43 45 45 63 63 65 65 64 64 66 66 68 68 67 67 58 58 70 70 69 69 65 65 71 71 67 67 72 72 74 74 73 73 75 75 74 74 68 68 76 76 56 56 77 77 78 78 64 64 69 69 74 74 1 1 68 68 1 1 74 74 0 0 39 39 37 37 79 79 79 79 9 9 39 39 48 48 41 41 47 47 48 48 38 38 41 41 49 49 47 47 50 50 51 51 50 50 53 53 52 52 53 53 57 57 56 56 57 57 77 77 76 76 72 72 73 73 76 76 77 77 72 72 73 73 74 74 75 75 75 75 68 68 66 66 66 66 67 67 71 71 71 71 65 65 63 63 63 63 64 64 78 78 78 78 69 69 70 70 70 70 58 58 59 59 59 59 55 55 54 54 54 54 45 45 46 46 46 46 43 43 44 44 6 6 43 43 8 8 7 7 8 8 42 42 13 13 42 42 12 12 14 14 12 12 40 40 34 34 40 40 33 33 35 35 33 33 36 36 19 19 36 36 18 18 3 3 18 18 5 5 4 4 5 5 28 28 29 29 23 23 24 24 29 29 28 28 23 23 24 24 21 21 22 22 22 22 20 20 17 17 15 15 16 16 27 27 25 25 26 26 30 30 15 15 27 27 25 25 32 32 10 10 31 31 26 26 32 32 30 30 9 9 79 79 11 11 10 10 11 11 31 31

- - - - -

80 80 82 82 81 81 80 80 83 83 82 82 82 82 85 85 84 84 82 82 83 83 85 85

- - - - -

86 86 88 88 87 87 87 87 89 89 86 86 90 90 89 89 91 91 89 89 90 90 92 92 89 89 87 87 91 91

- - - - -

93 93 95 95 94 94

- - - - -

96 96 98 98 97 97 98 98 100 100 99 99 100 100 98 98 96 96

- - - - -

101 101 103 103 102 102 104 104 105 105 101 101 101 101 102 102 104 104 105 105 107 107 106 106 107 107 104 104 108 108 107 107 109 109 106 106 110 110 112 112 111 111 113 113 115 115 114 114 114 114 116 116 113 113 113 113 118 118 117 117 118 118 113 113 116 116 119 119 117 117 120 120 118 118 120 120 117 117 121 121 122 122 119 119 119 119 120 120 121 121 122 122 124 124 123 123 124 124 122 122 121 121 125 125 123 123 126 126 124 124 126 126 123 123 127 127 128 128 125 125 125 125 126 126 127 127 128 128 130 130 129 129 130 130 128 128 127 127 131 131 129 129 132 132 130 130 132 132 129 129 133 133 134 134 131 131 131 131 132 132 133 133 102 102 103 103 135 135 136 136 135 135 137 137 103 103 137 137 135 135 138 138 136 136 137 137 137 137 139 139 138 138 140 140 142 142 141 141 141 141 139 139 140 140 143 143 142 142 144 144 140 140 145 145 142 142 146 146 147 147 144 144 144 144 145 145 146 146 147 147 149 149 148 148 149 149 147 147 146 146 150 150 148 148 151 151 149 149 151 151 148 148 152 152 153 153 150 150 150 150 151 151 152 152 153 153 155 155 154 154 155 155 153 153 152 152 156 156 154 154 157 157 155 155 157 157 154 154 158 158 159 159 156 156 156 156 157 157 158 158 159 159 161 161 160 160 161 161 159 159 158 158 161 161 162 162 160 160 160 160 162 162 163 163 104 104 107 107 105 105 115 115 106 106 109 109 109 109 114 114 115 115 111 111 116 116 110 110 116 116 114 114 110 110 164 164 111 111 112 112 104 104 164 164 108 108 112 112 108 108 164 164 144 144 142 142 145 145 165 165 167 167 166 166 141 141 138 138 139 139 165 165 136 136 167 167 136 136 138 138 167 167 168 168 165 165 166 166 144 144 168 168 143 143 166 166 143 143 168 168

- - - - -

169 169 171 171 170 170 172 172 174 174 173 173 169 169 175 175 174 174 172 172 173 173 176 176 177 177 178 178 172 172 172 172 176 176 177 177 179 179 178 178 177 177 179 179 180 180 178 178 174 174 175 175 173 173 181 181 170 170 171 171 175 175 169 169 170 170 171 171 182 182 181 181 181 181 182 182 183 183 183 183 182 182 184 184

- - - - -

185 185 187 187 186 186 188 188 190 190 189 189 188 188 192 192 191 191 193 193 195 195 194 194 196 196 198 198 197 197 199 199 201 201 200 200 189 189 202 202 198 198 201 201 196 196 203 203 199 199 205 205 204 204 192 192 207 207 206 206 208 208 194 194 204 204 209 209 193 193 210 210 186 186 211 211 207 207 212 212 185 185 213 213 214 214 210 210 215 215 213 213 217 217 216 216 218 218 219 219 215 215 216 216 217 217 220 220 221 221 218 218 222 222 223 223 220 220 217 217 224 224 222 222 225 225 226 226 227 227 225 225 228 228 230 230 229 229 231 231 223 223 232 232 233 233 234 234 229 229 235 235 226 226 230 230 223 223 231 231 220 220 236 236 233 233 237 237 216 216 212 212 213 213 212 212 187 187 185 185 187 187 211 211 186 186 211 211 206 206 207 207 206 206 191 191 192 192 191 191 190 190 188 188 190 190 202 202 189 189 202 202 197 197 198 198 197 197 203 203 196 196 203 203 200 200 201 201 200 200 205 205 199 199 205 205 208 208 204 204 194 194 195 195 204 204 193 193 209 209 195 195 210 210 214 214 209 209 215 215 219 219 214 214 218 218 221 221 219 219 222 222 224 224 221 221 225 225 227 227 224 224 226 226 235 235 227 227 230 230 228 228 235 235 229 229 234 234 228 228 233 233 236 236 234 234 238 238 237 237 239 239 237 237 238 238 236 236 238 238 239 239 240 240

- - - - -

241 241 243 243 242 242 241 241 244 244 243 243 242 242 245 245 241 241 241 241 246 246 244 244

- - - - -

247 247 249 249 248 248

- - - - -

250 250 252 252 251 251 252 252 254 254 253 253 250 250 251 251 255 255 256 256 251 251 252 252 252 252 253 253 256 256

- - - - -

257 257 259 259 258 258 259 259 261 261 260 260 261 261 259 259 257 257 262 262 260 260 263 263 261 261 263 263 260 260 264 264 265 265 262 262 262 262 263 263 264 264 257 257 258 258 266 266 267 267 268 268 266 266 266 266 258 258 267 267 268 268 270 270 269 269 270 270 268 268 267 267 270 270 271 271 269 269 269 269 271 271 272 272

- - - - -

273 273 275 275 274 274 273 273 277 277 276 276 275 275 278 278 274 274 277 277 280 280 279 279 281 281 280 280 277 277 282 282 284 284 283 283 284 284 286 286 285 285 285 285 283 283 284 284 285 285 286 286 287 287 282 282 283 283 280 280 281 281 277 277 273 273 282 282 280 280 281 281 273 273 276 276 275 275 288 288 290 290 289 289 274 274 278 278 291 291 292 292 294 294 293 293 295 295 296 296 289 289 297 297 299 299 298 298 300 300 297 297 301 301 302 302 304 304 303 303 305 305 307 307 306 306 308 308 303 303 309 309 310 310 312 312 311 311 313 313 315 315 314 314 316 316 318 318 317 317 319 319 321 321 320 320 313 313 323 323 322 322 324 324 326 326 325 325 326 326 328 328 327 327 329 329 331 331 330 330 332 332 324 324 325 325 333 333 335 335 334 334 336 336 338 338 337 337 339 339 341 341 340 340 341 341 339 339 335 335 340 340 343 343 342 342 342 342 339 339 340 340 344 344 342 342 345 345 343 343 345 345 342 342 344 344 347 347 346 346 347 347 344 344 345 345 348 348 349 349 346 346 346 346 347 347 348 348 286 286 349 349 350 350 348 348 350 350 349 349 287 287 286 286 350 350 328 328 326 326 324 324 333 333 334 334 337 337 351 351 338 338 336 336 330 330 331 331 352 352 336 336 329 329 351 351 331 331 332 332 352 352 319 319 320 320 323 323 328 328 321 321 327 327 334 334 335 335 339 339 337 337 338 338 333 333 325 325 352 352 332 332 351 351 329 329 330 330 321 321 319 319 327 327 313 313 322 322 315 315 323 323 320 320 322 322 314 314 315 315 318 318 316 316 317 317 310 310 314 314 318 318 316 316 312 312 308 308 311 311 317 317 312 312 310 310 303 303 304 304 309 309 308 308 309 309 311 311 302 302 306 306 304 304 299 299 307 307 305 305 305 305 306 306 302 302 297 297 298 298 301 301 297 297 307 307 299 299 300 300 301 301 292 292 293 293 294 294 295 295 300 300 292 292 293 293 296 296 288 288 289 289 294 294 296 296 295 295 288 288 291 291 290 290 291 291 278 278 290 290

- - - - -

353 353 355 355 354 354 353 353 354 354 356 356 353 353 356 356 357 357

- - - - -

358 358 360 360 359 359 360 360 358 358 361 361

- - - - -

362 362 364 364 363 363 364 364 362 362 365 365

- - - - -

366 366 368 368 367 367 368 368 366 366 369 369

- - - - -

370 370 372 372 371 371 372 372 370 370 373 373

- - - - -

374 374 376 376 375 375 376 376 374 374 377 377

- - - - -

378 378 380 380 379 379 380 380 378 378 381 381

- - - - -

382 382 384 384 383 383 382 382 385 385 384 384 382 382 383 383 386 386 386 386 387 387 382 382 388 388 387 387 389 389 386 386 389 389 387 387 390 390 391 391 387 387 388 388 390 390 387 387

- - - - -

392 392 394 394 393 393 395 395 397 397 396 396 392 392 398 398 394 394 396 396 399 399 395 395 399 399 400 400 395 395 397 397 395 395 392 392 398 398 392 392 401 401 397 397 392 392 393 393

- - - - -

402 402 404 404 403 403 404 404 402 402 405 405 402 402 406 406 405 405

- - - - -

407 407 409 409 408 408 407 407 411 411 410 410 407 407 410 410 409 409

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0.372966 -0.927845 -0 0.372965 -0.927845 -0 0.524451 -0.851441 -0 0.660708 -0.750643 -0 0.524451 -0.851441 -0 0.660708 -0.750643 -0 0.777969 -0.628302 -0 0.777969 -0.628302 -0 0.872961 -0.48779 -0 0.942895 -0.333089 -0 0.872961 -0.48779 -0 0.942895 -0.333089 -0 0.985637 -0.168875 -0 0.985637 -0.168875 -0 -0.939265 -0.343194 -0 -0.981928 -0.189254 -0 -0.939265 -0.343193 -0 -0.999534 -0.0305102 -0 -0.981928 -0.189254 -0 -0.999534 -0.0305102 -0 -0.783746 -0.621081 -0 -0.674855 -0.737951 -0 -0.674855 -0.737951 -0 -0.783746 -0.621081 -0 -0.872641 -0.488363 -0 -0.872641 -0.488363 -0 -0.258099 -0.966119 -0 -0.408629 -0.912701 -0 -0.258099 -0.966119 -0 -0.408629 -0.912701 -0 -0.548743 -0.835991 -0 -0.548743 -0.835991 -0 -0.100969 -0.99489 -0 -0.100969 -0.99489 -0 0.0587122 -0.998275 -0 0.0587122 -0.998275 -0 0.258099 -0.966119 -0 0.100969 -0.99489 -0 0.258099 -0.966119 -0 -0.0587122 -0.998275 -0 0.100969 -0.99489 -0 -0.0587122 -0.998275 -0 0.548743 -0.835991 -0 0.674855 -0.737951 -0 0.674855 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0.488363 0 0.872641 0.488363 0 0.258099 0.966119 0 0.408629 0.912701 0 0.258099 0.966119 0 0.408629 0.912701 0 0.548743 0.835991 0 0.548743 0.835991 0 0.100969 0.99489 0 0.100969 0.99489 0 -0.0587122 0.998275 -0 -0.0587122 0.998275 -0 0.332624 -0.943059 -0 0.168719 -0.985664 -0 0.332624 -0.943059 -0 3.43781e-005 -1 -0 0.168719 -0.985664 -0 3.46402e-005 -1 -0 0.627346 -0.778741 -0 0.74976 -0.66171 -0 0.74976 -0.66171 -0 0.627346 -0.778741 -0 0.486963 -0.873423 -0 0.486963 -0.873423 -0 0.977085 -0.21285 -0 0.927166 -0.374652 -0 0.977085 -0.21285 -0 0.927166 -0.374652 -0 0.850648 -0.525736 -0 0.850648 -0.525736 -0 0.998989 -0.0449509 -0 0.998989 -0.0449509 -0 0.992249 0.124267 0 0.992249 0.124267 0 0.957068 0.289864 0 0.957068 0.289864 0 0.998989 0.0449509 0 0.992249 -0.124267 -0 0.998989 0.0449509 0 0.957068 -0.289864 -0 0.992249 -0.124267 -0 0.957068 -0.289863 -0 0.927166 0.374652 0 0.850648 0.525736 0 0.850648 0.525736 0 0.927166 0.374652 0 0.977085 0.21285 0 0.977085 0.21285 0 0.486963 0.873422 0 0.627346 0.778741 0 0.486963 0.873422 0 0.627346 0.778741 0 0.749759 0.66171 0 0.749759 0.66171 0 0.332624 0.94306 0 0.332624 0.94306 0 0.168719 0.985664 0 0.168719 0.985664 0 3.43781e-005 1 0 3.43781e-005 1 0 -0.965549 -0.260221 -0 -0.995024 -0.0996342 -0 -0.965549 -0.260221 -0 -0.997977 0.06358 -0 -0.995024 -0.0996342 -0 -0.997977 0.06358 -0 -0.830867 -0.556471 -0 -0.729246 -0.684252 -0 -0.729245 -0.684252 -0 -0.830867 -0.556471 -0 -0.910342 -0.413856 -0 -0.910342 -0.413856 -0 -0.321101 -0.947045 -0 -0.470914 -0.882179 -0 -0.321101 -0.947045 -0 -0.470914 -0.882179 -0 -0.608186 -0.793795 -0 -0.608186 -0.793795 -0 -0.162714 -0.986673 -0 -0.162714 -0.986673 -0 -1.80222e-005 -1 -0 -1.80222e-005 -1 -0 -0.321101 0.947045 -0 -0.162714 0.986673 -0 -0.321101 0.947045 -0 -1.80498e-005 1 -0 -0.162714 0.986673 -0 -1.80498e-005 1 -0 -0.608186 0.793795 -0 -0.729245 0.684252 -0 -0.729245 0.684252 -0 -0.608186 0.793795 -0 -0.470914 0.882179 -0 -0.470914 0.882179 -0 -0.965549 0.260221 -0 -0.910343 0.413856 -0 -0.965549 0.260221 -0 -0.910343 0.413856 -0 -0.830867 0.556471 -0 -0.830867 0.556471 -0 -0.995024 0.0996341 -0 -0.995024 0.0996341 -0 -0.997977 -0.0635801 -0 -0.997977 -0.0635801 -0 - - - - - - - - - - - - - - -

0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 24 24 25 25 26 26 27 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 36 36 37 37 38 38 32 32 37 37 39 39 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 71 71 72 72 73 73 61 61 72 72 69 69 74 74 75 75 60 60 76 76 77 77 78 78 79 79 54 54 80 80 81 81 75 75 82 82 55 55 83 83 84 84 85 85 86 86 81 81 87 87 88 88 89 89 90 90 91 91 90 90 85 85 40 40 42 42 92 92 93 93 94 94 95 95 96 96 97 97 98 98 98 98 94 94 93 93 93 93 96 96 98 98 99 99 44 44 100 100 100 100 44 44 97 97 43 43 45 45 101 101 44 44 99 99 45 45 101 101 41 41 102 102 102 102 43 43 101 101 41 41 40 40 102 102 103 103 104 104 105 105 105 105 104 104 38 38 106 106 107 107 108 108 105 105 108 108 103 103 109 109 110 110 111 111 112 112 106 106 111 111 113 113 114 114 115 115 116 116 109 109 115 115 113 113 117 117 118 118 118 118 114 114 113 113 119 119 120 120 121 121 117 117 119 119 118 118 119 119 117 117 120 120 120 120 122 122 121 121 123 123 121 121 122 122 122 122 124 124 123 123 122 122 125 125 124 124 115 115 114 114 116 116 126 126 127 127 128 128 112 112 111 111 110 110 109 109 116 116 110 110 103 103 108 108 107 107 106 106 112 112 107 107 37 37 36 36 39 39 38 38 104 104 36 36 24 24 26 26 129 129 39 39 30 30 32 32 27 27 18 18 20 20 29 29 28 28 129 129 22 22 19 19 18 18 19 19 22 22 21 21 21 21 23 23 130 130 28 28 27 27 20 20 25 25 24 24 33 33 26 26 29 29 129 129 130 130 23 23 127 127 126 126 130 130 127 127 25 25 33 33 30 30 131 131 132 132 128 128 126 126 128 128 132 132 131 131 133 133 132 132 6 6 10 10 7 7 134 134 135 135 34 34 136 136 35 35 137 137 138 138 139 139 140 140 134 134 141 141 135 135 8 8 7 7 139 139 138 138 8 8 139 139 11 11 142 142 9 9 6 6 11 11 10 10 143 143 142 142 17 17 9 9 142 142 143 143 16 16 143 143 17 17 144 144 145 145 15 15 16 16 15 15 145 145 144 144 14 14 146 146 144 144 146 146 145 145 14 14 13 13 146 146 138 138 140 140 141 141 135 135 141 141 140 140 13 13 12 12 147 147 33 33 134 134 34 34 12 12 148 148 147 147 147 147 148 148 149 149 150 150 147 147 149 149 137 137 151 151 136 136 152 152 153 153 154 154 155 155 156 156 157 157 151 151 137 137 158 158 159 159 160 160 161 161 156 156 155 155 162 162 163 163 164 164 165 165 160 160 159 159 166 166 167 167 168 168 169 169 170 170 153 153 171 171 172 172 173 173 174 174 169 169 175 175 176 176 177 177 178 178 179 179 172 172 180 180 181 181 182 182 183 183 184 184 185 185 178 178 186 186 187 187 188 188 189 189 182 182 190 190 191 191 192 192 152 152 193 193 194 194 195 195 196 196 170 170 171 171 197 197 198 198 190 190 192 192 199 199 200 200 201 201 202 202 186 186 184 184 177 177 203 203 204 204 175 175 181 181 205 205 204 204 206 206 173 173 207 207 168 168 208 208 164 164 163 163 209 209 210 210 211 211 212 212 164 164 166 166 165 165 158 158 155 155 157 157 213 213 214 214 215 215 216 216 217 217 218 218 219 219 220 220 221 221 220 220 219 219 218 218 222 222 223 223 224 224 224 224 225 225 222 222 226 226 227 227 228 228 213 213 229 229 214 214 222 222 225 225 215 215 217 217 35 35 136 136 151 151 158 158 157 157 162 162 161 161 230 230 161 161 160 160 230 230 162 162 230 230 156 156 30 30 33 33 217 217 213 213 215 215 225 225 231 231 229 229 213 213 227 227 229 229 231 231 232 232 226 226 233 233 228 228 233 233 226 226 234 234 235 235 236 236 234 234 237 237 238 238 232 232 236 236 235 235 239 239 238 238 237 237 238 238 235 235 234 234 237 237 240 240 239 239 241 241 242 242 243 243 244 244 239 239 240 240 3 3 242 242 241 241 245 245 244 244 246 246 4 4 3 3 241 241 247 247 245 245 246 246 248 248 249 249 250 250 221 221 251 251 252 252 246 246 244 244 240 240 253 253 5 5 4 4 221 221 220 220 254 254 232 232 233 233 236 236 227 227 231 231 228 228 223 223 255 255 224 224 255 255 256 256 224 224 254 254 220 220 256 256 254 254 256 256 255 255 242 242 257 257 243 243 258 258 251 251 254 254 252 252 251 251 259 259 5 5 253 253 260 260 259 259 261 261 262 262 263 263 264 264 265 265 266 266 264 264 262 262 267 267 268 268 269 269 270 270 271 271 272 272 272 272 271 271 273 273 267 267 274 274 275 275 276 276 275 275 263 263 277 277 278 278 257 257 243 243 257 257 278 278 251 251 258 258 279 279 277 277 279 279 280 280 280 280 278 278 277 277 279 279 258 258 280 280 251 251 221 221 254 254 259 259 262 262 252 252 266 266 262 262 261 261 265 265 264 264 266 266 276 276 263 263 265 265 274 274 263 263 275 275 269 269 274 274 267 267 269 269 268 268 270 270 273 273 212 212 272 272 270 270 268 268 271 271 212 212 273 273 210 210 211 211 250 250 249 249 250 250 211 211 210 210 249 249 248 248 0 0 248 248 1 1 0 0 163 163 281 281 209 209 281 281 282 282 283 283 284 284 207 207 208 208 166 166 159 159 165 165 285 285 284 284 286 286 287 287 285 285 286 286 288 288 287 287 289 289 218 218 288 288 289 289 288 288 218 218 217 217 217 217 33 33 35 35 216 216 92 92 42 42 216 216 219 219 92 92 289 289 287 287 286 286 285 285 207 207 284 284 168 168 167 167 208 208 169 169 176 176 167 167 175 175 205 205 176 176 181 181 180 180 205 205 172 172 174 174 180 180 173 173 206 206 174 174 204 204 203 203 206 206 177 177 179 179 203 203 178 178 185 185 179 179 186 186 202 202 185 185 184 184 183 183 202 202 182 182 191 191 183 183 190 190 198 198 191 191 192 192 193 193 198 198 152 152 154 154 193 193 153 153 170 170 154 154 201 201 197 197 171 171 199 199 195 195 200 200 201 201 200 200 197 197 196 196 189 189 194 194 199 199 196 196 195 195 188 188 187 187 282 282 194 194 189 189 188 188 281 281 283 283 209 209 282 282 187 187 283 283 290 290 89 89 53 53 94 94 48 48 95 95 65 65 64 64 70 70 49 49 291 291 292 292 293 293 291 291 294 294 96 96 100 100 97 97 295 295 293 293 294 294 294 294 296 296 295 295 296 296 31 31 297 297 31 31 30 30 297 297 218 218 219 219 216 216 216 216 297 297 217 217 217 217 297 297 30 30 296 296 297 297 295 295 293 293 292 292 291 291 292 292 50 50 49 49 50 50 52 52 51 51 52 52 290 290 53 53 89 89 88 88 53 53 90 90 91 91 88 88 85 85 84 84 91 91 83 83 298 298 84 84 86 86 87 87 298 298 86 86 298 298 83 83 81 81 80 80 87 87 54 54 56 56 80 80 55 55 82 82 56 56 75 75 76 76 82 82 60 60 62 62 76 76 61 61 73 73 62 62 72 72 74 74 73 73 69 69 71 71 74 74 70 70 64 64 71 71 68 68 63 63 65 65 66 66 58 58 67 67 68 68 67 67 63 63 59 59 77 77 57 57 66 66 59 59 58 58 79 79 78 78 46 46 57 57 77 77 79 79 48 48 47 47 95 95 46 46 78 78 47 47

- - - - -

299 299 300 300 301 301 302 302 303 303 304 304 305 305 306 306 307 307 308 308 309 309 310 310 311 311 312 312 313 313 314 314 315 315 316 316 317 317 318 318 319 319 320 320 321 321 322 322 305 305 323 323 320 320 324 324 325 325 326 326 325 325 327 327 328 328 329 329 330 330 331 331 332 332 330 330 333 333 334 334 335 335 336 336 337 337 338 338 339 339 340 340 338 338 329 329 341 341 342 342 343 343 344 344 345 345 341 341 346 346 347 347 348 348 349 349 347 347 337 337 350 350 345 345 351 351 352 352 353 353 354 354 346 346 355 355 356 356 355 355 346 346 348 348 357 357 358 358 359 359 360 360 361 361 362 362 363 363 364 364 365 365 356 356 355 355 363 363 342 342 366 366 367 367 368 368 369 369 366 366 363 363 365 365 356 356 365 365 364 364 370 370 368 368 371 371 372 372 373 373 374 374 350 350 375 375 370 370 364 364 370 370 375 375 376 376 377 377 378 378 379 379 370 370 376 376 380 380 347 347 349 349 348 348 381 381 382 382 383 383 340 340 339 339 338 338 337 337 339 339 349 349 332 332 331 331 330 330 329 329 331 331 340 340 333 333 324 324 326 326 333 333 326 326 332 332 328 328 327 327 306 306 327 327 325 325 324 324 321 321 384 384 322 322 328 328 306 306 305 305 385 385 386 386 384 384 385 385 387 387 386 386 388 388 389 389 390 390 387 387 389 389 388 388 391 391 392 392 393 393 390 390 391 391 388 388 390 390 392 392 391 391 394 394 381 381 383 383 392 392 394 394 393 393 395 395 382 382 396 396 381 381 396 396 382 382 395 395 396 396 397 397 398 398 319 319 318 318 387 387 385 385 389 389 393 393 394 394 383 383 320 320 323 323 321 321 384 384 386 386 322 322 323 323 399 399 400 400 317 317 400 400 318 318 401 401 402 402 403 403 401 401 403 403 398 398 404 404 405 405 406 406 402 402 404 404 406 406 405 405 407 407 408 408 409 409 407 407 314 314 408 408 406 406 405 405 410 410 411 411 412 412 411 411 316 316 315 315 411 411 315 315 412 412 413 413 410 410 412 412 409 409 314 314 316 316 410 410 413 413 414 414 415 415 416 416 417 417 416 416 415 415 414 414 418 418 415 415 417 417 419 419 418 418 417 417 419 419 417 417 420 420 421 421 422 422 423 423 409 409 408 408 407 407 413 413 416 416 414 414 319 319 398 398 403 403 404 404 402 402 401 401 317 317 323 323 400 400 424 424 425 425 426 426 425 425 424 424 399 399 427 427 428 428 429 429 429 429 428 428 430 430 310 310 309 309 431 431 432 432 433 433 434 434 435 435 436 436 437 437 438 438 302 302 439 439 440 440 441 441 311 311 442 442 443 443 444 444 445 445 446 446 439 439 447 447 448 448 449 449 304 304 450 450 444 444 451 451 449 449 452 452 432 432 453 453 433 433 454 454 448 448 455 455 456 456 434 434 457 457 458 458 459 459 460 460 461 461 462 462 463 463 464 464 457 457 454 454 465 465 443 443 466 466 467 467 452 452 465 465 468 468 469 469 470 470 445 445 441 441 471 471 472 472 312 312 473 473 474 474 437 437 436 436 475 475 308 308 310 310 436 436 435 435 475 475 431 431 427 427 429 429 309 309 427 427 431 431 430 430 476 476 426 426 430 430 428 428 476 476 399 399 477 477 425 425 426 426 476 476 424 424 323 323 305 305 477 477 478 478 479 479 480 480 481 481 482 482 483 483 484 484 480 480 479 479 485 485 481 481 486 486 485 485 482 482 481 481 486 486 487 487 488 488 485 485 486 486 488 488 489 489 490 490 491 491 491 491 490 490 488 488 492 492 490 490 489 489 493 493 492 492 494 494 495 495 496 496 493 493 489 489 494 494 492 492 497 497 496 496 498 498 493 493 494 494 495 495 497 497 499 499 500 500 499 499 497 497 498 498 501 501 500 500 499 499 482 482 502 502 503 503 469 469 504 504 505 505 501 501 504 504 500 500 470 470 469 469 505 505 502 502 479 479 506 506 507 507 506 506 478 478 507 507 508 508 509 509 502 502 506 506 503 503 505 505 504 504 501 501 495 495 498 498 496 496 482 482 503 503 483 483 487 487 491 491 488 488 510 510 511 511 512 512 513 513 514 514 515 515 516 516 517 517 518 518 519 519 507 507 513 513 507 507 519 519 506 506 517 517 516 516 520 520 508 508 507 507 478 478 521 521 520 520 516 516 520 520 521 521 522 522 523 523 522 522 521 521 508 508 510 510 509 509 524 524 522 522 523 523 525 525 526 526 527 527 523 523 528 528 524 524 509 509 510 510 529 529 510 510 512 512 529 529 299 299 530 530 300 300 514 514 518 518 531 531 517 517 531 531 518 518 515 515 519 519 513 513 515 515 514 514 531 531 299 299 301 301 511 511 512 512 511 511 301 301 532 532 533 533 534 534 299 299 535 535 530 530 535 535 526 526 530 530 527 527 526 526 535 535 525 525 527 527 536 536 537 537 538 538 539 539 540 540 536 536 537 537 541 541 542 542 543 543 543 543 544 544 541 541 377 377 545 545 542 542 543 543 542 542 545 545 377 377 379 379 545 545 546 546 547 547 548 548 538 538 541 541 544 544 537 537 539 539 540 540 538 538 544 544 539 539 536 536 540 540 525 525 549 549 550 550 551 551 551 551 550 550 552 552 534 534 550 550 532 532 533 533 532 532 553 553 554 554 555 555 556 556 553 553 557 557 533 533 558 558 559 559 557 557 560 560 559 559 558 558 561 561 554 554 562 562 477 477 563 563 484 484 506 506 479 479 478 478 557 557 553 553 558 558 550 550 534 534 552 552 564 564 549 549 565 565 566 566 564 564 565 565 564 564 566 566 567 567 568 568 567 567 566 566 569 569 570 570 571 571 572 572 573 573 371 371 574 574 572 572 575 575 576 576 577 577 335 335 578 578 579 579 336 336 437 437 474 474 580 580 580 580 581 581 582 582 583 583 472 472 473 473 475 475 435 435 308 308 584 584 585 585 583 583 586 586 585 585 584 584 587 587 588 588 586 586 484 484 588 588 587 587 587 587 477 477 484 484 477 477 399 399 323 323 563 563 559 559 560 560 563 563 560 560 480 480 588 588 585 585 586 586 584 584 583 583 473 473 312 312 472 472 313 313 311 311 313 313 440 440 441 441 440 440 471 471 445 445 471 471 446 446 439 439 446 446 438 438 302 302 438 438 303 303 304 304 303 303 450 450 444 444 450 450 442 442 443 443 442 442 466 466 465 465 466 466 467 467 452 452 467 467 451 451 449 449 451 451 447 447 448 448 447 447 455 455 454 454 455 455 464 464 457 457 464 464 456 456 434 434 456 456 432 432 459 459 433 433 453 453 458 458 460 460 422 422 459 459 453 453 460 460 421 421 423 423 461 461 458 458 422 422 421 421 462 462 582 582 463 463 423 423 462 462 461 461 580 580 474 474 581 581 582 582 581 581 463 463 589 589 555 555 578 578 567 567 568 568 570 570 546 546 374 374 547 547 561 561 590 590 591 591 592 592 593 593 591 591 565 565 549 549 551 551 594 594 593 593 592 592 593 593 594 594 595 595 595 595 596 596 307 307 307 307 596 596 305 305 484 484 563 563 480 480 563 563 477 477 596 596 477 477 305 305 596 596 595 595 594 594 596 596 592 592 591 591 590 590 590 590 561 561 562 562 562 562 554 554 556 556 556 556 555 555 589 589 578 578 555 555 579 579 336 336 579 579 334 334 335 335 334 334 576 576 577 577 576 576 597 597 575 575 597 597 574 574 575 575 577 577 597 597 572 572 574 574 573 573 371 371 573 573 372 372 368 368 372 372 369 369 366 366 369 369 367 367 342 342 367 367 343 343 341 341 343 343 344 344 345 345 344 344 351 351 350 350 351 351 373 373 374 374 373 373 547 547 357 357 546 546 548 548 359 359 358 358 354 354 357 357 548 548 358 358 353 353 352 352 362 362 359 359 354 354 353 353 360 360 569 569 361 361 352 352 360 360 362 362 570 570 568 568 571 571 569 569 571 571 361 361

- - - - -

598 598 599 599 600 600 601 601 599 599 602 602 599 599 601 601 600 600 603 603 604 604 602 602 601 601 602 602 604 604 603 603 605 605 606 606 606 606 604 604 603 603 607 607 605 605 608 608 605 605 607 607 606 606 609 609 610 610 608 608 607 607 608 608 610 610 609 609 611 611 612 612 612 612 610 610 609 609 613 613 611 611 614 614 611 611 613 613 612 612 615 615 616 616 614 614 613 613 614 614 616 616 617 617 616 616 615 615 618 618 598 598 600 600 618 618 619 619 620 620 620 620 598 598 618 618 621 621 619 619 622 622 619 619 621 621 620 620 623 623 624 624 622 622 621 621 622 622 624 624 623 623 625 625 626 626 626 626 624 624 623 623 627 627 625 625 628 628 625 625 627 627 626 626 629 629 630 630 628 628 627 627 628 628 630 630 629 629 631 631 632 632 632 632 630 630 629 629 633 633 631 631 634 634 631 631 633 633 632 632 633 633 634 634 635 635

- - - - -

636 636 637 637 638 638 639 639 640 640 641 641 642 642 643 643 644 644 645 645 646 646 647 647 648 648 649 649 650 650 651 651 652 652 653 653 654 654 655 655 656 656 655 655 654 654 657 657 656 656 658 658 659 659 659 659 654 654 656 656 660 660 661 661 658 658 659 659 658 658 661 661 657 657 648 648 650 650 657 657 650 650 655 655 653 653 649 649 651 651 651 651 649 649 648 648 643 643 652 652 644 644 643 643 653 653 652 652 642 642 645 645 647 647 642 642 644 644 645 645 646 646 636 636 638 638 647 647 646 646 638 638 640 640 639 639 637 637 636 636 640 640 637 637

- - - - -

662 662 663 663 664 664 662 662 665 665 663 663

- - - - -

666 666 667 667 668 668 666 666 669 669 667 667

- - - - -

670 670 671 671 672 672 670 670 673 673 671 671

- - - - -

674 674 675 675 676 676 677 677 678 678 679 679 680 680 681 681 682 682 683 683 684 684 685 685 686 686 687 687 688 688 689 689 690 690 691 691 692 692 693 693 694 694 695 695 696 696 691 691 691 691 690 690 695 695 697 697 696 696 698 698 695 695 698 698 696 696 699 699 697 697 698 698 692 692 694 694 689 689 689 689 694 694 690 690 683 683 693 693 684 684 684 684 693 693 692 692 687 687 685 685 688 688 687 687 683 683 685 685 686 686 677 677 679 679 686 686 688 688 677 677 678 678 680 680 682 682 679 679 678 678 682 682 674 674 676 676 681 681 680 680 674 674 681 681

- - - - -

700 700 701 701 702 702 702 702 703 703 700 700

- - - - -

704 704 705 705 706 706 704 704 707 707 705 705

- - - - -

708 708 709 709 710 710 710 710 711 711 708 708

- - - - -

712 712 713 713 714 714 715 715 716 716 717 717 718 718 719 719 720 720 721 721 722 722 723 723 724 724 725 725 726 726 727 727 728 728 729 729 730 730 731 731 732 732 731 731 730 730 733 733 732 732 734 734 735 735 735 735 730 730 732 732 736 736 737 737 734 734 735 735 734 734 737 737 733 733 724 724 726 726 733 733 726 726 731 731 729 729 725 725 727 727 727 727 725 725 724 724 719 719 728 728 720 720 719 719 729 729 728 728 718 718 721 721 723 723 718 718 720 720 721 721 722 722 712 712 714 714 723 723 722 722 714 714 716 716 715 715 713 713 712 712 716 716 713 713

- - - - -

738 738 739 739 740 740 738 738 741 741 739 739

- - - - -

742 742 743 743 744 744 742 742 745 745 743 743

- - - - -

746 746 747 747 748 748 746 746 749 749 747 747

- - - - -

750 750 751 751 752 752 753 753 754 754 755 755 756 756 757 757 758 758 759 759 760 760 761 761 762 762 763 763 764 764 765 765 766 766 767 767 768 768 769 769 770 770 771 771 772 772 767 767 767 767 766 766 771 771 773 773 772 772 774 774 771 771 774 774 772 772 775 775 773 773 774 774 768 768 770 770 765 765 765 765 770 770 766 766 759 759 769 769 760 760 760 760 769 769 768 768 763 763 761 761 764 764 763 763 759 759 761 761 762 762 753 753 755 755 762 762 764 764 753 753 754 754 756 756 758 758 755 755 754 754 758 758 750 750 752 752 757 757 756 756 750 750 757 757

- - - - -

776 776 777 777 778 778 779 779 780 780 778 778 776 776 778 778 780 780 779 779 781 781 782 782 782 782 780 780 779 779 783 783 781 781 784 784 781 781 783 783 782 782 785 785 786 786 784 784 783 783 784 784 786 786 785 785 787 787 788 788 788 788 786 786 785 785 789 789 787 787 790 790 787 787 789 789 788 788 791 791 792 792 790 790 789 789 790 790 792 792 791 791 793 793 794 794 794 794 792 792 791 791 793 793 795 795 794 794 796 796 777 777 776 776 796 796 797 797 798 798 798 798 777 777 796 796 799 799 797 797 800 800 797 797 799 799 798 798 801 801 802 802 800 800 799 799 800 800 802 802 801 801 803 803 804 804 804 804 802 802 801 801 805 805 803 803 806 806 803 803 805 805 804 804 807 807 808 808 806 806 805 805 806 806 808 808 807 807 809 809 810 810 810 810 808 808 807 807 811 811 809 809 812 812 809 809 811 811 810 810 811 811 812 812 813 813

- - - - -

814 814 815 815 816 816 817 817 818 818 819 819 820 820 821 821 822 822 823 823 824 824 825 825 826 826 827 827 828 828 829 829 830 830 831 831 832 832 833 833 834 834 833 833 832 832 835 835 834 834 836 836 837 837 837 837 832 832 834 834 838 838 839 839 836 836 837 837 836 836 839 839 835 835 826 826 828 828 835 835 828 828 833 833 831 831 827 827 829 829 829 829 827 827 826 826 821 821 830 830 822 822 821 821 831 831 830 830 820 820 823 823 825 825 820 820 822 822 823 823 824 824 814 814 816 816 825 825 824 824 816 816 818 818 817 817 815 815 814 814 818 818 815 815

- - - - -

840 840 841 841 842 842 840 840 843 843 841 841

- - - - -

844 844 845 845 846 846 844 844 847 847 845 845

- - - - -

848 848 849 849 850 850 848 848 851 851 849 849

- - - - -

852 852 853 853 854 854 855 855 856 856 857 857 858 858 859 859 860 860 861 861 862 862 863 863 864 864 865 865 866 866 867 867 862 862 868 868 861 861 868 868 862 862 869 869 867 867 868 868 866 866 865 865 863 863 865 865 861 861 863 863 864 864 855 855 857 857 864 864 866 866 855 855 856 856 858 858 860 860 857 857 856 856 860 860 852 852 854 854 859 859 858 858 852 852 859 859

- - - - -

870 870 871 871 872 872 870 870 873 873 871 871

- - - - -

874 874 875 875 876 876 876 876 877 877 874 874

- - - - -

878 878 879 879 880 880 878 878 881 881 879 879

- - - - -

882 882 883 883 884 884 885 885 886 886 887 887 888 888 889 889 890 890 891 891 892 892 893 893 894 894 895 895 896 896 896 896 897 897 894 894 898 898 899 899 895 895 896 896 895 895 899 899 897 897 890 890 889 889 889 889 894 894 897 897 888 888 891 891 893 893 888 888 890 890 891 891 892 892 882 882 884 884 893 893 892 892 884 884 886 886 885 885 883 883 882 882 886 886 883 883

- - - - -

900 900 901 901 902 902 900 900 903 903 901 901

- - - - -

904 904 905 905 906 906 904 904 907 907 905 905

- - - - -

908 908 909 909 910 910 908 908 911 911 909 909

- - - - -

912 912 913 913 914 914 915 915 916 916 917 917 918 918 919 919 920 920 921 921 922 922 923 923 924 924 925 925 926 926 927 927 928 928 929 929 930 930 931 931 932 932 933 933 934 934 929 929 929 929 928 928 933 933 935 935 934 934 936 936 933 933 936 936 934 934 937 937 935 935 936 936 930 930 932 932 927 927 927 927 932 932 928 928 921 921 931 931 922 922 922 922 931 931 930 930 925 925 923 923 926 926 925 925 921 921 923 923 924 924 915 915 917 917 924 924 926 926 915 915 916 916 918 918 920 920 917 917 916 916 920 920 912 912 914 914 919 919 918 918 912 912 919 919

- - - - -

938 938 939 939 940 940 941 941 942 942 943 943 944 944 945 945 939 939 940 940 939 939 945 945 946 946 944 944 947 947 944 944 946 946 945 945 947 947 948 948 949 949 949 949 946 946 947 947 950 950 951 951 948 948 949 949 948 948 951 951 952 952 950 950 953 953 950 950 952 952 951 951 953 953 954 954 955 955 955 955 952 952 953 953 956 956 957 957 954 954 955 955 954 954 957 957 958 958 956 956 959 959 956 956 958 958 957 957 960 960 958 958 959 959 960 960 959 959 961 961 940 940 962 962 938 938 963 963 962 962 964 964 962 962 963 963 938 938 964 964 965 965 966 966 966 966 963 963 964 964 967 967 968 968 965 965 966 966 965 965 968 968 969 969 967 967 970 970 967 967 969 969 968 968 970 970 971 971 972 972 972 972 969 969 970 970 973 973 974 974 971 971 972 972 971 971 974 974 975 975 973 973 976 976 973 973 975 975 974 974 976 976 977 977 978 978 978 978 975 975 976 976 978 978 977 977 943 943 979 979 980 980 981 981 977 977 941 941 943 943 982 982 983 983 984 984 985 985 986 986 987 987 988 988 989 989 990 990 991 991 992 992 993 993 994 994 995 995 996 996 997 997 998 998 999 999 1000 1000 1001 1001 1002 1002 1003 1003 1004 1004 1005 1005 1006 1006 1007 1007 1008 1008 1000 1000 1008 1008 1007 1007 1006 1006 1009 1009 1010 1010 1009 1009 1006 1006 1008 1008 1011 1011 1012 1012 1010 1010 1010 1010 1009 1009 1011 1011 961 961 1012 1012 1013 1013 1011 1011 1013 1013 1012 1012 960 960 961 961 1013 1013 1002 1002 1001 1001 1004 1004 1000 1000 1007 1007 1001 1001 1003 1003 1005 1005 996 996 1002 1002 1004 1004 1003 1003 994 994 997 997 995 995 1005 1005 994 994 996 996 998 998 989 989 999 999 997 997 999 999 995 995 993 993 988 988 990 990 990 990 989 989 998 998 982 982 992 992 991 991 992 992 988 988 993 993 984 984 983 983 986 986 982 982 991 991 983 983 985 985 987 987 979 979 984 984 986 986 985 985 980 980 942 942 981 981 987 987 980 980 979 979 941 941 981 981 942 942

- - - - -

1014 1014 1015 1015 1016 1016 1017 1017 1018 1018 1019 1019 1020 1020 1021 1021 1022 1022 1023 1023 1024 1024 1025 1025 1026 1026 1027 1027 1028 1028 1029 1029 1030 1030 1031 1031 1032 1032 1033 1033 1034 1034 1035 1035 1036 1036 1037 1037 1038 1038 1039 1039 1040 1040 1041 1041 1042 1042 1043 1043 1044 1044 1045 1045 1046 1046 1047 1047 1048 1048 1049 1049 1050 1050 1051 1051 1052 1052 1053 1053 1054 1054 1055 1055 1056 1056 1057 1057 1058 1058 1059 1059 1060 1060 1061 1061 1062 1062 1063 1063 1064 1064 1065 1065 1066 1066 1067 1067 1068 1068 1069 1069 1070 1070 1071 1071 1069 1069 1072 1072 1068 1068 1073 1073 1074 1074 1073 1073 1068 1068 1070 1070 1075 1075 1076 1076 1074 1074 1074 1074 1073 1073 1075 1075 1077 1077 1076 1076 1078 1078 1075 1075 1078 1078 1076 1076 1077 1077 1079 1079 1080 1080 1079 1079 1077 1077 1078 1078 1081 1081 1082 1082 1080 1080 1080 1080 1079 1079 1081 1081 1083 1083 1082 1082 1084 1084 1081 1081 1084 1084 1082 1082 1083 1083 1085 1085 1086 1086 1085 1085 1083 1083 1084 1084 1087 1087 1019 1019 1086 1086 1086 1086 1085 1085 1087 1087 1071 1071 1072 1072 1064 1064 1087 1087 1017 1017 1019 1019 1069 1069 1071 1071 1070 1070 1065 1065 1063 1063 1062 1062 1062 1062 1064 1064 1072 1072 1057 1057 1067 1067 1066 1066 1067 1067 1063 1063 1065 1065 1056 1056 1058 1058 1061 1061 1057 1057 1066 1066 1058 1058 1060 1060 1059 1059 1050 1050 1056 1056 1061 1061 1060 1060 1051 1051 1054 1054 1052 1052 1059 1059 1051 1051 1050 1050 1055 1055 1046 1046 1053 1053 1054 1054 1053 1053 1052 1052 1047 1047 1045 1045 1044 1044 1044 1044 1046 1046 1055 1055 1039 1039 1049 1049 1048 1048 1049 1049 1045 1045 1047 1047 1038 1038 1040 1040 1043 1043 1039 1039 1048 1048 1040 1040 1042 1042 1041 1041 1032 1032 1038 1038 1043 1043 1042 1042 1033 1033 1036 1036 1034 1034 1041 1041 1033 1033 1032 1032 1037 1037 1028 1028 1035 1035 1036 1036 1035 1035 1034 1034 1029 1029 1027 1027 1026 1026 1026 1026 1028 1028 1037 1037 1021 1021 1031 1031 1030 1030 1031 1031 1027 1027 1029 1029 1020 1020 1022 1022 1023 1023 1021 1021 1030 1030 1022 1022 1025 1025 1024 1024 1016 1016 1020 1020 1023 1023 1025 1025 1014 1014 1018 1018 1015 1015 1024 1024 1014 1014 1016 1016 1017 1017 1015 1015 1018 1018

- - - - -

1088 1088 1089 1089 1090 1090 1091 1091 1092 1092 1093 1093 1094 1094 1095 1095 1096 1096 1097 1097 1098 1098 1099 1099 1100 1100 1101 1101 1102 1102 1103 1103 1104 1104 1105 1105 1102 1102 1106 1106 1107 1107 1107 1107 1100 1100 1102 1102 1108 1108 1109 1109 1106 1106 1107 1107 1106 1106 1109 1109 1105 1105 1101 1101 1103 1103 1103 1103 1101 1101 1100 1100 1095 1095 1104 1104 1096 1096 1095 1095 1105 1105 1104 1104 1094 1094 1097 1097 1099 1099 1094 1094 1096 1096 1097 1097 1098 1098 1088 1088 1090 1090 1099 1099 1098 1098 1090 1090 1092 1092 1091 1091 1089 1089 1088 1088 1092 1092 1089 1089

- - - - -

1110 1110 1111 1111 1112 1112 1113 1113 1114 1114 1115 1115 1116 1116 1117 1117 1118 1118 1119 1119 1120 1120 1121 1121 1122 1122 1123 1123 1124 1124 1125 1125 1126 1126 1127 1127 1124 1124 1128 1128 1129 1129 1129 1129 1122 1122 1124 1124 1130 1130 1131 1131 1128 1128 1129 1129 1128 1128 1131 1131 1127 1127 1123 1123 1125 1125 1125 1125 1123 1123 1122 1122 1117 1117 1126 1126 1118 1118 1117 1117 1127 1127 1126 1126 1116 1116 1119 1119 1121 1121 1116 1116 1118 1118 1119 1119 1120 1120 1110 1110 1112 1112 1121 1121 1120 1120 1112 1112 1114 1114 1113 1113 1111 1111 1110 1110 1114 1114 1111 1111

- - - - -

1132 1132 1133 1133 1134 1134 1135 1135 1136 1136 1137 1137 1138 1138 1139 1139 1140 1140 1141 1141 1142 1142 1143 1143 1144 1144 1145 1145 1146 1146 1147 1147 1148 1148 1149 1149 1146 1146 1150 1150 1151 1151 1151 1151 1144 1144 1146 1146 1152 1152 1153 1153 1150 1150 1151 1151 1150 1150 1153 1153 1149 1149 1145 1145 1147 1147 1147 1147 1145 1145 1144 1144 1139 1139 1148 1148 1140 1140 1139 1139 1149 1149 1148 1148 1138 1138 1141 1141 1143 1143 1138 1138 1140 1140 1141 1141 1142 1142 1132 1132 1134 1134 1143 1143 1142 1142 1134 1134 1136 1136 1135 1135 1133 1133 1132 1132 1136 1136 1133 1133

- - - - -

1154 1154 1155 1155 1156 1156 1157 1157 1158 1158 1159 1159 1160 1160 1161 1161 1162 1162 1163 1163 1164 1164 1165 1165 1166 1166 1167 1167 1168 1168 1169 1169 1170 1170 1171 1171 1168 1168 1172 1172 1173 1173 1173 1173 1166 1166 1168 1168 1174 1174 1175 1175 1172 1172 1173 1173 1172 1172 1175 1175 1171 1171 1167 1167 1169 1169 1169 1169 1167 1167 1166 1166 1161 1161 1170 1170 1162 1162 1161 1161 1171 1171 1170 1170 1160 1160 1163 1163 1165 1165 1160 1160 1162 1162 1163 1163 1164 1164 1154 1154 1156 1156 1165 1165 1164 1164 1156 1156 1158 1158 1157 1157 1155 1155 1154 1154 1158 1158 1155 1155

- - - - -

1176 1176 1177 1177 1178 1178 1179 1179 1180 1180 1181 1181 1182 1182 1183 1183 1184 1184 1185 1185 1186 1186 1187 1187 1188 1188 1189 1189 1190 1190 1191 1191 1192 1192 1193 1193 1194 1194 1195 1195 1196 1196 1195 1195 1194 1194 1190 1190 1197 1197 1198 1198 1196 1196 1196 1196 1195 1195 1197 1197 1191 1191 1189 1189 1188 1188 1197 1197 1199 1199 1198 1198 1188 1188 1190 1190 1194 1194 1183 1183 1193 1193 1192 1192 1193 1193 1189 1189 1191 1191 1182 1182 1184 1184 1185 1185 1183 1183 1192 1192 1184 1184 1187 1187 1186 1186 1178 1178 1182 1182 1185 1185 1187 1187 1176 1176 1180 1180 1177 1177 1186 1186 1176 1176 1178 1178 1179 1179 1177 1177 1180 1180

- - - - -

1200 1200 1201 1201 1202 1202 1203 1203 1204 1204 1205 1205 1206 1206 1207 1207 1208 1208 1209 1209 1210 1210 1211 1211 1212 1212 1213 1213 1214 1214 1215 1215 1216 1216 1217 1217 1218 1218 1219 1219 1220 1220 1219 1219 1218 1218 1214 1214 1221 1221 1222 1222 1220 1220 1220 1220 1219 1219 1221 1221 1215 1215 1213 1213 1212 1212 1221 1221 1223 1223 1222 1222 1212 1212 1214 1214 1218 1218 1207 1207 1217 1217 1216 1216 1217 1217 1213 1213 1215 1215 1206 1206 1208 1208 1209 1209 1207 1207 1216 1216 1208 1208 1211 1211 1210 1210 1202 1202 1206 1206 1209 1209 1211 1211 1200 1200 1204 1204 1201 1201 1210 1210 1200 1200 1202 1202 1203 1203 1201 1201 1204 1204

- - - - -

1224 1224 1225 1225 1226 1226 1227 1227 1228 1228 1229 1229 1230 1230 1231 1231 1232 1232 1233 1233 1234 1234 1235 1235 1236 1236 1237 1237 1238 1238 1239 1239 1240 1240 1241 1241 1238 1238 1242 1242 1243 1243 1243 1243 1236 1236 1238 1238 1244 1244 1245 1245 1242 1242 1243 1243 1242 1242 1245 1245 1241 1241 1237 1237 1239 1239 1239 1239 1237 1237 1236 1236 1231 1231 1240 1240 1232 1232 1231 1231 1241 1241 1240 1240 1230 1230 1233 1233 1235 1235 1230 1230 1232 1232 1233 1233 1234 1234 1224 1224 1226 1226 1235 1235 1234 1234 1226 1226 1228 1228 1227 1227 1225 1225 1224 1224 1228 1228 1225 1225

- - - - -

1246 1246 1247 1247 1248 1248 1249 1249 1250 1250 1251 1251 1252 1252 1253 1253 1254 1254 1255 1255 1256 1256 1257 1257 1258 1258 1259 1259 1260 1260 1261 1261 1262 1262 1263 1263 1260 1260 1264 1264 1265 1265 1265 1265 1258 1258 1260 1260 1266 1266 1267 1267 1264 1264 1265 1265 1264 1264 1267 1267 1263 1263 1259 1259 1261 1261 1261 1261 1259 1259 1258 1258 1253 1253 1262 1262 1254 1254 1253 1253 1263 1263 1262 1262 1252 1252 1255 1255 1257 1257 1252 1252 1254 1254 1255 1255 1256 1256 1246 1246 1248 1248 1257 1257 1256 1256 1248 1248 1250 1250 1249 1249 1247 1247 1246 1246 1250 1250 1247 1247

- - - - - - - 32.4015 29.5641 16.6 31.8958 29.6485 16.6 32.4015 29.5641 0 35.7623 32.6579 16.6 35.7623 32.6579 0 35.7199 33.1688 0 30.9599 35.2568 16.6 31.4108 35.5008 16.6 30.9599 35.2568 0 31.8958 29.6485 0 31.4108 29.8149 16.6 31.4108 29.8149 0 30.5553 30.3739 16.6 30.9599 30.059 0 30.9599 30.059 16.6 30.5553 30.3739 0 30.2081 30.7511 16.6 29.9276 31.1803 16.6 29.9276 31.1803 0 30.2081 30.7511 0 29.7217 31.6499 16.6 29.7217 31.6499 0 29.5535 32.6579 16.6 29.5958 32.1469 0 29.5958 32.1469 16.6 29.5535 32.6579 0 32.9142 29.5641 0 32.9142 29.5641 16.6 33.42 29.6485 0 33.42 29.6485 16.6 33.9049 29.8149 0 33.9049 29.8149 16.6 34.3558 30.059 16.6 34.3558 30.059 0 34.7604 30.3739 0 34.7604 30.3739 16.6 35.1077 30.7511 0 35.1077 30.7511 16.6 35.3881 31.1803 16.6 35.3881 31.1803 0 35.5941 31.6499 0 35.5941 31.6499 16.6 35.7199 32.1469 0 35.7199 32.1469 16.6 35.5941 33.6659 16.6 35.7199 33.1688 16.6 35.5941 33.6659 0 34.7604 34.9418 16.6 35.1077 34.5646 16.6 34.7604 34.9418 0 35.3881 34.1354 16.6 35.3881 34.1354 0 35.1077 34.5646 0 33.9049 35.5008 16.6 33.42 35.6673 0 33.42 35.6673 16.6 34.3558 35.2568 0 33.9049 35.5008 0 34.3558 35.2568 16.6 31.8958 35.6673 0 31.8958 35.6673 16.6 32.4015 35.7517 16.6 32.4015 35.7517 0 32.9142 35.7517 16.6 32.9142 35.7517 0 30.5553 34.9418 16.6 30.5553 34.9418 0 31.4108 35.5008 0 29.9276 34.1354 0 30.2081 34.5646 16.6 30.2081 34.5646 0 29.7217 33.6659 0 29.9276 34.1354 16.6 29.7217 33.6659 16.6 29.5958 33.1688 0 29.5958 33.1688 16.6 35.7623 32.6579 16.6 31.8958 35.6673 16.6 31.4108 35.5008 16.6 33.9049 35.5008 16.6 35.1077 34.5646 16.6 34.7604 34.9418 16.6 34.3558 35.2568 16.6 33.42 35.6673 16.6 35.3881 34.1354 16.6 35.5941 33.6659 16.6 32.9142 35.7517 16.6 32.4015 35.7517 16.6 35.7199 33.1688 16.6 35.3881 31.1803 16.6 35.5941 31.6499 16.6 30.5553 34.9418 16.6 30.9599 35.2568 16.6 35.7199 32.1469 16.6 30.2081 34.5646 16.6 29.9276 34.1354 16.6 35.1077 30.7511 16.6 33.9049 29.8149 16.6 29.5958 33.1688 16.6 29.5535 32.6579 16.6 34.7604 30.3739 16.6 29.7217 33.6659 16.6 34.3558 30.059 16.6 29.7217 31.6499 16.6 29.9276 31.1803 16.6 32.4015 29.5641 16.6 29.5958 32.1469 16.6 32.9142 29.5641 16.6 33.42 29.6485 16.6 30.5553 30.3739 16.6 30.9599 30.059 16.6 31.4108 29.8149 16.6 31.8958 29.6485 16.6 30.2081 30.7511 16.6 35.7623 32.6579 0 31.4108 35.5008 0 31.8958 35.6673 0 33.9049 35.5008 0 34.7604 34.9418 0 35.1077 34.5646 0 34.3558 35.2568 0 35.3881 34.1354 0 33.42 35.6673 0 35.5941 33.6659 0 32.9142 35.7517 0 32.4015 35.7517 0 35.7199 33.1688 0 35.3881 31.1803 0 30.5553 34.9418 0 35.5941 31.6499 0 35.7199 32.1469 0 30.9599 35.2568 0 30.2081 34.5646 0 35.1077 30.7511 0 29.9276 34.1354 0 33.9049 29.8149 0 29.5535 32.6579 0 29.5958 33.1688 0 34.7604 30.3739 0 34.3558 30.059 0 29.7217 33.6659 0 29.7217 31.6499 0 32.4015 29.5641 0 29.9276 31.1803 0 29.5958 32.1469 0 33.42 29.6485 0 32.9142 29.5641 0 30.5553 30.3739 0 31.4108 29.8149 0 30.9599 30.059 0 30.2081 30.7511 0 31.8958 29.6485 0 - 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- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 2 2 1 1 0 0 3 3 2 2

- - - - -

4 4 6 6 5 5 4 4 7 7 6 6

- - - - -

8 8 10 10 9 9 9 9 11 11 8 8

- - - - -

12 12 14 14 13 13 13 13 15 15 12 12

- - - - -

16 16 18 18 17 17 17 17 19 19 16 16

- - - - -

20 20 22 22 21 21 20 20 21 21 23 23

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 4 4 5 5 6 6 2 2 7 7 1 1 7 7 2 2 8 8 9 9 6 6 6 6 7 7 8 8 9 9 10 10 11 11 10 10 9 9 8 8 12 12 11 11 13 13 10 10 13 13 11 11 14 14 15 15 12 12 12 12 13 13 14 14 15 15 16 16 17 17 16 16 15 15 14 14 18 18 17 17 19 19 16 16 19 19 17 17 20 20 21 21 18 18 18 18 19 19 20 20 22 22 21 21 20 20 22 22 23 23 21 21 1 1 0 0 24 24 25 25 26 26 24 24 24 24 0 0 25 25 26 26 27 27 28 28 27 27 26 26 25 25 29 29 28 28 30 30 27 27 30 30 28 28 31 31 32 32 29 29 29 29 30 30 31 31 32 32 33 33 34 34 33 33 32 32 31 31 35 35 34 34 36 36 33 33 36 36 34 34 37 37 38 38 35 35 35 35 36 36 37 37 38 38 39 39 40 40 39 39 38 38 37 37 39 39 4 4 40 40 41 41 42 42 43 43 40 40 4 4 3 3 44 44 45 45 46 46 47 47 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 62 62 70 70 69 69 68 68 71 71 72 72 72 72 69 69 68 68 73 73 71 71 74 74 71 71 73 73 72 72 23 23 75 75 74 74 73 73 74 74 75 75 22 22 75 75 23 23 63 63 67 67 64 64 62 62 64 64 70 70 65 65 57 57 66 66 63 63 65 65 67 67 56 56 58 58 59 59 66 66 57 57 56 56 61 61 60 60 52 52 59 59 58 58 60 60 54 54 51 51 50 50 51 51 61 61 52 52 44 44 53 53 55 55 55 55 54 54 50 50 45 45 49 49 46 46 44 44 46 46 53 53 47 47 41 41 48 48 45 45 47 47 49 49 43 43 42 42 5 5 48 48 41 41 43 43 3 3 5 5 42 42

- - - - -

76 76 77 77 78 78 79 79 80 80 81 81 81 81 82 82 79 79 80 80 83 83 84 84 83 83 80 80 79 79 85 85 84 84 86 86 83 83 86 86 84 84 87 87 88 88 85 85 85 85 86 86 87 87 88 88 77 77 76 76 77 77 88 88 87 87 89 89 90 90 91 91 78 78 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 111 111 112 112 113 113 104 104 113 113 112 112 113 113 109 109 111 111 105 105 104 104 112 112 106 106 103 103 107 107 107 107 103 103 105 105 97 97 99 99 108 108 108 108 99 99 106 106 102 102 101 101 98 98 97 97 102 102 98 98 100 100 96 96 95 95 101 101 100 100 95 95 94 94 89 89 91 91 94 94 96 96 89 89 92 92 90 90 93 93 92 92 91 91 90 90 93 93 76 76 78 78

- - - - -

114 114 115 115 116 116 117 117 118 118 119 119 118 118 117 117 120 120 119 119 121 121 122 122 122 122 117 117 119 119 123 123 124 124 121 121 122 122 121 121 124 124 125 125 123 123 126 126 123 123 125 125 124 124 126 126 114 114 116 116 116 116 125 125 126 126 127 127 128 128 129 129 115 115 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 148 148 149 149 148 148 150 150 151 151 143 143 151 151 150 150 150 150 148 148 147 147 142 142 151 151 143 143 144 144 146 146 141 141 146 146 142 142 141 141 135 135 145 145 136 136 145 145 144 144 136 136 139 139 137 137 140 140 135 135 137 137 139 139 138 138 134 134 133 133 140 140 134 134 138 138 132 132 128 128 127 127 132 132 127 127 133 133 131 131 130 130 129 129 131 131 129 129 128 128 130 130 115 115 114 114

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0 0 1 1 2 2 3 3 2 2 4 4 1 1 4 4 2 2 5 5 6 6 3 3 3 3 4 4 5 5 6 6 7 7 8 8 7 7 6 6 5 5 9 9 8 8 10 10 7 7 10 10 8 8 11 11 12 12 9 9 9 9 10 10 11 11 12 12 13 13 14 14 13 13 12 12 11 11 15 15 14 14 16 16 13 13 16 16 14 14 17 17 18 18 15 15 15 15 16 16 17 17 18 18 19 19 20 20 19 19 18 18 17 17 21 21 20 20 22 22 19 19 22 22 20 20 23 23 24 24 21 21 21 21 22 22 23 23 24 24 25 25 26 26 25 25 24 24 23 23 27 27 26 26 28 28 25 25 28 28 26 26 29 29 30 30 27 27 27 27 28 28 29 29 30 30 31 31 32 32 31 31 30 30 29 29 33 33 32 32 34 34 31 31 34 34 32 32 35 35 36 36 33 33 33 33 34 34 35 35 37 37 36 36 35 35 37 37 38 38 36 36 1 1 0 0 39 39 40 40 41 41 39 39 39 39 0 0 40 40 41 41 42 42 43 43 42 42 41 41 40 40 44 44 43 43 45 45 42 42 45 45 43 43 46 46 47 47 44 44 44 44 45 45 46 46 47 47 48 48 49 49 48 48 47 47 46 46 50 50 49 49 51 51 48 48 51 51 49 49 52 52 53 53 50 50 50 50 51 51 52 52 53 53 54 54 55 55 54 54 53 53 52 52 56 56 55 55 57 57 54 54 57 57 55 55 58 58 59 59 56 56 56 56 57 57 58 58 59 59 60 60 61 61 60 60 59 59 58 58 62 62 61 61 63 63 60 60 63 63 61 61 64 64 65 65 62 62 62 62 63 63 64 64 65 65 66 66 67 67 66 66 65 65 64 64 68 68 67 67 69 69 66 66 69 69 67 67 70 70 71 71 68 68 68 68 69 69 70 70 71 71 72 72 73 73 72 72 71 71 70 70 72 72 38 38 73 73 73 73 38 38 37 37

- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

- - - - -

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- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

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- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

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- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

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0 0 1 1 2 2 3 3 2 2 4 4 1 1 4 4 2 2 5 5 6 6 3 3 3 3 4 4 5 5 6 6 7 7 8 8 7 7 6 6 5 5 9 9 8 8 10 10 7 7 10 10 8 8 11 11 12 12 9 9 9 9 10 10 11 11 12 12 13 13 14 14 13 13 12 12 11 11 15 15 14 14 16 16 13 13 16 16 14 14 17 17 18 18 15 15 15 15 16 16 17 17 18 18 19 19 20 20 19 19 18 18 17 17 21 21 20 20 22 22 19 19 22 22 20 20 23 23 24 24 21 21 21 21 22 22 23 23 24 24 25 25 26 26 25 25 24 24 23 23 27 27 26 26 28 28 25 25 28 28 26 26 29 29 30 30 27 27 27 27 28 28 29 29 30 30 31 31 32 32 31 31 30 30 29 29 33 33 32 32 34 34 31 31 34 34 32 32 35 35 36 36 33 33 33 33 34 34 35 35 37 37 36 36 35 35 37 37 38 38 36 36 1 1 0 0 39 39 40 40 41 41 39 39 39 39 0 0 40 40 41 41 42 42 43 43 42 42 41 41 40 40 44 44 43 43 45 45 42 42 45 45 43 43 46 46 47 47 44 44 44 44 45 45 46 46 47 47 48 48 49 49 48 48 47 47 46 46 50 50 49 49 51 51 48 48 51 51 49 49 52 52 53 53 50 50 50 50 51 51 52 52 53 53 54 54 55 55 54 54 53 53 52 52 56 56 55 55 57 57 54 54 57 57 55 55 58 58 59 59 56 56 56 56 57 57 58 58 59 59 60 60 61 61 60 60 59 59 58 58 62 62 61 61 63 63 60 60 63 63 61 61 64 64 65 65 62 62 62 62 63 63 64 64 65 65 66 66 67 67 66 66 65 65 64 64 68 68 67 67 69 69 66 66 69 69 67 67 70 70 71 71 68 68 68 68 69 69 70 70 71 71 72 72 73 73 72 72 71 71 70 70 72 72 38 38 73 73 73 73 38 38 37 37

- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

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- - - - - - - - - - - - - -

0 0 1 1 2 2 3 3 2 2 4 4 1 1 4 4 2 2 5 5 6 6 3 3 3 3 4 4 5 5 6 6 7 7 8 8 7 7 6 6 5 5 9 9 8 8 10 10 7 7 10 10 8 8 11 11 12 12 9 9 9 9 10 10 11 11 12 12 13 13 14 14 13 13 12 12 11 11 15 15 14 14 16 16 13 13 16 16 14 14 17 17 18 18 15 15 15 15 16 16 17 17 18 18 19 19 20 20 19 19 18 18 17 17 21 21 20 20 22 22 19 19 22 22 20 20 23 23 24 24 21 21 21 21 22 22 23 23 24 24 25 25 26 26 25 25 24 24 23 23 27 27 26 26 28 28 25 25 28 28 26 26 29 29 30 30 27 27 27 27 28 28 29 29 30 30 31 31 32 32 31 31 30 30 29 29 33 33 32 32 34 34 31 31 34 34 32 32 35 35 36 36 33 33 33 33 34 34 35 35 37 37 36 36 35 35 37 37 38 38 36 36 1 1 0 0 39 39 40 40 41 41 39 39 39 39 0 0 40 40 41 41 42 42 43 43 42 42 41 41 40 40 44 44 43 43 45 45 42 42 45 45 43 43 46 46 47 47 44 44 44 44 45 45 46 46 47 47 48 48 49 49 48 48 47 47 46 46 50 50 49 49 51 51 48 48 51 51 49 49 52 52 53 53 50 50 50 50 51 51 52 52 53 53 54 54 55 55 54 54 53 53 52 52 56 56 55 55 57 57 54 54 57 57 55 55 58 58 59 59 56 56 56 56 57 57 58 58 59 59 60 60 61 61 60 60 59 59 58 58 62 62 61 61 63 63 60 60 63 63 61 61 64 64 65 65 62 62 62 62 63 63 64 64 65 65 66 66 67 67 66 66 65 65 64 64 68 68 67 67 69 69 66 66 69 69 67 67 70 70 71 71 68 68 68 68 69 69 70 70 71 71 72 72 73 73 72 72 71 71 70 70 72 72 38 38 73 73 73 73 38 38 37 37

- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

- - - - -

111 111 112 112 113 113 114 114 115 115 116 116 114 114 117 117 115 115 118 118 116 116 119 119 115 115 119 119 116 116 120 120 121 121 118 118 118 118 119 119 120 120 121 121 122 122 123 123 122 122 121 121 120 120 124 124 125 125 126 126 122 122 127 127 123 123 128 128 129 129 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 143 143 147 147 146 146 138 138 143 143 145 145 146 146 140 140 137 137 139 139 137 137 147 147 138 138 141 141 140 140 139 139 134 134 142 142 135 135 135 135 142 142 141 141 130 130 129 129 136 136 136 136 129 129 134 134 131 131 133 133 128 128 130 130 131 131 128 128 132 132 112 112 111 111 133 133 132 132 111 111 113 113 125 125 124 124 113 113 112 112 125 125 123 123 127 127 126 126 127 127 124 124 126 126

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- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

- - - - -

111 111 112 112 113 113 114 114 115 115 116 116 114 114 117 117 115 115 118 118 116 116 119 119 115 115 119 119 116 116 120 120 121 121 118 118 118 118 119 119 120 120 121 121 122 122 123 123 122 122 121 121 120 120 124 124 125 125 126 126 122 122 127 127 123 123 128 128 129 129 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 143 143 147 147 146 146 138 138 143 143 145 145 146 146 140 140 137 137 139 139 137 137 147 147 138 138 141 141 140 140 139 139 134 134 142 142 135 135 135 135 142 142 141 141 130 130 129 129 136 136 136 136 129 129 134 134 131 131 133 133 128 128 130 130 131 131 128 128 132 132 112 112 111 111 133 133 132 132 111 111 113 113 125 125 124 124 113 113 112 112 125 125 123 123 127 127 126 126 127 127 124 124 126 126

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0 0 1 1 2 2 3 3 2 2 4 4 1 1 4 4 2 2 5 5 6 6 3 3 3 3 4 4 5 5 6 6 7 7 8 8 7 7 6 6 5 5 9 9 8 8 10 10 7 7 10 10 8 8 11 11 12 12 9 9 9 9 10 10 11 11 12 12 13 13 14 14 13 13 12 12 11 11 15 15 14 14 16 16 13 13 16 16 14 14 17 17 18 18 15 15 15 15 16 16 17 17 18 18 19 19 20 20 19 19 18 18 17 17 21 21 20 20 22 22 19 19 22 22 20 20 23 23 24 24 21 21 21 21 22 22 23 23 24 24 25 25 26 26 25 25 24 24 23 23 27 27 26 26 28 28 25 25 28 28 26 26 29 29 30 30 27 27 27 27 28 28 29 29 30 30 31 31 32 32 31 31 30 30 29 29 33 33 32 32 34 34 31 31 34 34 32 32 35 35 36 36 33 33 33 33 34 34 35 35 37 37 36 36 35 35 37 37 38 38 36 36 1 1 0 0 39 39 40 40 41 41 39 39 39 39 0 0 40 40 41 41 42 42 43 43 42 42 41 41 40 40 44 44 43 43 45 45 42 42 45 45 43 43 46 46 47 47 44 44 44 44 45 45 46 46 47 47 48 48 49 49 48 48 47 47 46 46 50 50 49 49 51 51 48 48 51 51 49 49 52 52 53 53 50 50 50 50 51 51 52 52 53 53 54 54 55 55 54 54 53 53 52 52 56 56 55 55 57 57 54 54 57 57 55 55 58 58 59 59 56 56 56 56 57 57 58 58 59 59 60 60 61 61 60 60 59 59 58 58 62 62 61 61 63 63 60 60 63 63 61 61 64 64 65 65 62 62 62 62 63 63 64 64 65 65 66 66 67 67 66 66 65 65 64 64 68 68 67 67 69 69 66 66 69 69 67 67 70 70 71 71 68 68 68 68 69 69 70 70 71 71 72 72 73 73 72 72 71 71 70 70 72 72 38 38 73 73 73 73 38 38 37 37

- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

- - - - -

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0 0 1 1 2 2 3 3 2 2 4 4 1 1 4 4 2 2 5 5 6 6 3 3 3 3 4 4 5 5 6 6 7 7 8 8 7 7 6 6 5 5 9 9 8 8 10 10 7 7 10 10 8 8 11 11 12 12 9 9 9 9 10 10 11 11 12 12 13 13 14 14 13 13 12 12 11 11 15 15 14 14 16 16 13 13 16 16 14 14 17 17 18 18 15 15 15 15 16 16 17 17 18 18 19 19 20 20 19 19 18 18 17 17 21 21 20 20 22 22 19 19 22 22 20 20 23 23 24 24 21 21 21 21 22 22 23 23 24 24 25 25 26 26 25 25 24 24 23 23 27 27 26 26 28 28 25 25 28 28 26 26 29 29 30 30 27 27 27 27 28 28 29 29 30 30 31 31 32 32 31 31 30 30 29 29 33 33 32 32 34 34 31 31 34 34 32 32 35 35 36 36 33 33 33 33 34 34 35 35 37 37 36 36 35 35 37 37 38 38 36 36 1 1 0 0 39 39 40 40 41 41 39 39 39 39 0 0 40 40 41 41 42 42 43 43 42 42 41 41 40 40 44 44 43 43 45 45 42 42 45 45 43 43 46 46 47 47 44 44 44 44 45 45 46 46 47 47 48 48 49 49 48 48 47 47 46 46 50 50 49 49 51 51 48 48 51 51 49 49 52 52 53 53 50 50 50 50 51 51 52 52 53 53 54 54 55 55 54 54 53 53 52 52 56 56 55 55 57 57 54 54 57 57 55 55 58 58 59 59 56 56 56 56 57 57 58 58 59 59 60 60 61 61 60 60 59 59 58 58 62 62 61 61 63 63 60 60 63 63 61 61 64 64 65 65 62 62 62 62 63 63 64 64 65 65 66 66 67 67 66 66 65 65 64 64 68 68 67 67 69 69 66 66 69 69 67 67 70 70 71 71 68 68 68 68 69 69 70 70 71 71 72 72 73 73 72 72 71 71 70 70 72 72 38 38 73 73 73 73 38 38 37 37

- - - - -

74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

- - - - -

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74 74 75 75 76 76 77 77 78 78 79 79 77 77 79 79 80 80 81 81 82 82 78 78 79 79 78 78 82 82 83 83 81 81 84 84 81 81 83 83 82 82 84 84 85 85 86 86 86 86 83 83 84 84 87 87 88 88 89 89 86 86 85 85 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 100 100 101 101 102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 106 106 110 110 110 110 102 102 109 109 106 106 109 109 107 107 103 103 101 101 100 100 100 100 102 102 110 110 105 105 101 101 103 103 97 97 99 99 104 104 99 99 105 105 104 104 92 92 98 98 93 93 98 98 97 97 93 93 94 94 91 91 95 95 92 92 91 91 94 94 96 96 74 74 76 76 95 95 74 74 96 96 75 75 87 87 89 89 75 75 89 89 76 76 85 85 88 88 90 90 90 90 88 88 87 87

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111 111 112 112 113 113 114 114 115 115 116 116 114 114 117 117 115 115 118 118 116 116 119 119 115 115 119 119 116 116 120 120 121 121 118 118 118 118 119 119 120 120 121 121 122 122 123 123 122 122 121 121 120 120 124 124 125 125 126 126 122 122 127 127 123 123 128 128 129 129 130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 143 143 147 147 146 146 138 138 143 143 145 145 146 146 140 140 137 137 139 139 137 137 147 147 138 138 141 141 140 140 139 139 134 134 142 142 135 135 135 135 142 142 141 141 130 130 129 129 136 136 136 136 129 129 134 134 131 131 133 133 128 128 130 130 131 131 128 128 132 132 112 112 111 111 133 133 132 132 111 111 113 113 125 125 124 124 113 113 112 112 125 125 123 123 127 127 126 126 127 127 124 124 126 126

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20 20 21 21 22 22 20 20 23 23 21 21

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24 24 25 25 26 26 25 25 24 24 27 27

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28 28 29 29 30 30 29 29 28 28 31 31

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32 32 33 33 34 34 32 32 35 35 33 33

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36 36 37 37 38 38 36 36 39 39 37 37

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40 40 41 41 42 42 40 40 43 43 41 41

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44 44 45 45 46 46 44 44 47 47 45 45

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16 16 18 18 17 17 17 17 19 19 16 16

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20 20 22 22 21 21 20 20 21 21 23 23

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0 0 1 1 2 2 3 3 4 4 2 2 0 0 2 2 4 4 5 5 4 4 3 3 6 6 5 5 7 7 3 3 7 7 5 5 6 6 7 7 8 8 7 7 9 9 8 8 8 8 9 9 10 10 6 6 8 8 11 11 11 11 8 8 12 12

- - - - -

13 13 14 14 15 15 16 16 14 14 13 13 13 13 17 17 16 16

- - - - -

18 18 19 19 20 20 21 21 22 22 19 19 18 18 21 21 19 19

- - - - -

23 23 24 24 25 25 23 23 25 25 26 26 27 27 28 28 29 29 30 30 28 28 27 27 31 31 29 29 32 32 27 27 33 33 30 30 28 28 32 32 29 29 33 33 34 34 26 26 26 26 30 30 33 33 23 23 34 34 35 35 34 34 23 23 26 26 23 23 35 35 36 36

- - - - -

37 37 38 38 39 39 38 38 40 40 41 41 42 42 43 43 44 44 45 45 46 46 47 47 44 44 43 43 47 47 45 45 48 48 46 46 47 47 46 46 44 44 48 48 41 41 40 40 41 41 48 48 45 45 38 38 37 37 49 49 38 38 49 49 40 40 37 37 50 50 49 49

- - - - -

51 51 52 52 53 53 53 53 54 54 55 55 52 52 54 54 53 53 56 56 54 54 52 52 57 57 55 55 58 58 55 55 54 54 58 58

- - - - -

59 59 60 60 61 61 62 62 63 63 64 64 65 65 66 66 67 67 68 68 69 69 70 70 67 67 66 66 70 70 68 68 64 64 69 69 70 70 69 69 67 67 60 60 63 63 62 62 62 62 64 64 68 68 71 71 63 63 59 59 63 63 60 60 59 59

- - - - -

72 72 73 73 74 74 74 74 73 73 75 75 72 72 76 76 77 77 76 76 72 72 74 74 72 72 77 77 78 78 76 76 79 79 77 77

- - - - -

80 80 81 81 82 82 83 83 80 80 82 82 80 80 83 83 84 84 83 83 85 85 84 84

- - - - -

86 86 87 87 88 88 89 89 88 88 90 90 91 91 92 92 93 93 92 92 91 91 94 94 89 89 94 94 91 91 90 90 88 88 87 87 94 94 89 89 90 90 87 87 86 86 95 95

- - - - -

96 96 97 97 98 98 99 99 98 98 100 100 100 100 98 98 97 97 97 97 96 96 101 101

- - - - -

102 102 103 103 104 104 105 105 106 106 107 107 108 108 109 109 110 110 111 111 112 112 113 113 114 114 115 115 116 116 117 117 118 118 119 119 112 112 119 119 118 118 120 120 117 117 121 121 117 117 120 120 118 118 119 119 112 112 111 111 107 107 106 106 110 110 113 113 116 116 115 115 115 115 111 111 113 113 114 114 116 116 105 105 114 114 105 105 107 107 106 106 108 108 110 110 108 108 102 102 109 109 104 104 109 109 102 102

- - - - -

122 122 123 123 124 124 124 124 125 125 122 122

- - - - -

126 126 127 127 128 128 128 128 129 129 126 126

- - - - -

130 130 131 131 132 132 133 133 134 134 135 135 136 136 137 137 138 138 139 139 140 140 141 141 142 142 143 143 144 144 145 145 146 146 147 147 147 147 148 148 145 145 149 149 146 146 150 150 145 145 150 150 146 146 151 151 149 149 150 150 140 140 148 148 147 147 138 138 135 135 134 134 143 143 139 139 141 141 139 139 148 148 140 140 143 143 141 141 144 144 142 142 133 133 135 135 142 142 144 144 133 133 134 134 136 136 138 138 136 136 131 131 137 137 132 132 152 152 130 130 131 131 130 130 137 137

- - - - -

153 153 154 154 155 155 156 156 157 157 158 158 159 159 160 160 161 161 162 162 163 163 164 164 165 165 162 162 166 166 167 167 163 163 168 168 162 162 168 168 163 163 169 169 167 167 168 168 166 166 162 162 164 164 153 153 170 170 159 159 159 159 161 161 157 157 165 165 166 166 156 156 161 161 158 158 157 157 165 165 156 156 158 158 159 159 170 170 160 160 153 153 155 155 170 170

- - - - -

171 171 172 172 173 173 171 171 174 174 172 172 172 172 174 174 175 175 172 172 175 175 176 176 175 175 177 177 176 176

- - - - -

178 178 179 179 180 180 181 181 182 182 183 183 184 184 185 185 186 186 187 187 188 188 189 189 180 180 190 190 191 191 187 187 192 192 193 193 194 194 193 193 192 192 195 195 196 196 197 197 196 196 198 198 192 192 199 199 200 200 201 201 200 200 202 202 197 197 203 203 204 204 205 205 203 203 206 206 207 207 208 208 209 209 210 210 211 211 212 212 213 213 214 214 211 211 213 213 215 215 216 216 217 217 204 204 218 218 205 205 219 219 208 208 216 216 210 210 209 209 220 220 221 221 215 215 217 217 215 215 219 219 216 216 222 222 181 181 221 221 221 221 217 217 222 222 214 214 213 213 220 220 209 209 208 208 219 219 213 213 210 210 220 220 218 218 204 204 212 212 211 211 218 218 212 212 203 203 207 207 201 201 205 205 206 206 203 203 202 202 200 200 199 199 199 199 201 201 207 207 195 195 198 198 196 196 195 195 197 197 202 202 193 193 188 188 187 187 194 194 192 192 198 198 189 189 184 184 186 186 188 188 184 184 189 189 185 185 190 190 223 223 185 185 223 223 186 186 191 191 178 178 180 180 223 223 190 190 180 180 183 183 182 182 179 179 178 178 183 183 179 179 181 181 222 222 182 182

- - - - -

224 224 225 225 226 226 227 227 228 228 229 229 230 230 231 231 228 228 232 232 233 233 234 234 235 235 233 233 236 236 237 237 238 238 239 239 240 240 241 241 239 239 242 242 243 243 244 244 245 245 246 246 247 247 248 248 249 249 250 250 244 244 251 251 242 242 246 246 245 245 252 252 249 249 253 253 254 254 243 243 255 255 256 256 257 257 258 258 259 259 250 250 260 260 261 261 262 262 263 263 264 264 265 265 263 263 257 257 263 263 265 265 264 264 266 266 262 262 264 264 267 267 266 266 268 268 262 262 266 266 267 267 260 260 259 259 258 258 225 225 269 269 226 226 268 268 266 266 269 269 268 268 269 269 225 225 259 259 265 265 257 257 261 261 248 248 250 250 258 258 261 261 260 260 254 254 255 255 249 249 249 249 248 248 253 253 244 244 243 243 256 256 256 256 255 255 254 254 246 246 252 252 251 251 242 242 251 251 252 252 237 237 245 245 238 238 238 238 245 245 247 247 240 240 234 234 241 241 241 241 237 237 239 239 234 234 233 233 235 235 234 234 240 240 232 232 236 236 227 227 229 229 235 235 236 236 229 229 231 231 230 230 224 224 227 227 230 230 228 228 226 226 231 231 224 224

- - - - -

270 270 271 271 272 272 273 273 274 274 275 275 274 274 273 273 276 276 277 277 278 278 279 279 273 273 275 275 280 280 281 281 282 282 283 283 284 284 285 285 286 286 287 287 288 288 289 289 290 290 291 291 292 292 293 293 281 281 294 294 295 295 296 296 297 297 298 298 299 299 300 300 300 300 296 296 301 301 302 302 296 296 289 289 298 298 303 303 299 299 304 304 305 305 288 288 306 306 291 291 290 290 290 290 307 307 306 306 307 307 288 288 305 305 290 290 288 288 307 307 287 287 308 308 288 288 304 304 288 288 308 308 287 287 289 289 309 309 310 310 289 289 296 296 310 310 309 309 289 289 296 296 302 302 311 311 295 295 310 310 296 296 301 301 298 298 300 300 312 312 296 296 311 311 313 313 300 300 299 299 281 281 314 314 294 294 315 315 300 300 313 313 316 316 300 300 317 317 282 282 284 284 318 318 319 319 316 316 317 317 284 284 286 286 318 318 316 316 284 284 281 281 316 316 281 281 300 300 281 281 284 284 282 282 320 320 321 321 284 284 270 270 320 320 284 284 316 316 322 322 323 323 323 323 270 270 316 316 270 270 284 284 316 316 270 270 279 279 271 271 270 270 324 324 325 325 270 270 277 277 279 279 277 277 270 270 325 325 275 275 278 278 280 280 280 280 278 278 277 277 281 281 293 293 297 297 301 301 296 296 312 312 281 281 297 297 296 296 317 317 300 300 315 315 300 300 281 281 296 296 314 314 281 281 283 283 326 326 320 320 270 270 319 319 322 322 316 316 285 285 284 284 327 327 321 321 327 327 284 284 272 272 326 326 270 270 323 323 324 324 270 270

- - - - -

328 328 329 329 330 330 331 331 332 332 333 333 333 333 334 334 331 331 333 333 335 335 334 334 335 335 333 333 336 336 337 337 335 335 336 336 334 334 335 335 338 338 339 339 340 340 335 335 338 338 335 335 341 341 342 342 339 339 335 335 343 343 335 335 344 344 340 340 345 345 335 335 346 346 347 347 348 348 340 340 339 339 347 347 349 349 350 350 339 339 347 347 351 351 348 348 350 350 352 352 353 353 350 350 353 353 330 330 354 354 350 350 355 355 353 353 328 328 330 330 355 355 350 350 330 330 354 354 356 356 350 350 357 357 350 350 356 356 358 358 357 357 359 359 360 360 361 361 357 357 362 362 363 363 358 358 364 364 365 365 358 358 364 364 358 358 363 363 365 365 366 366 358 358 358 358 366 366 357 357 367 367 357 357 366 366 368 368 369 369 357 357 368 368 357 357 367 367 370 370 371 371 357 357 370 370 357 357 369 369 357 357 371 371 372 372 361 361 359 359 357 357 360 360 357 357 356 356 351 351 347 347 373 373 340 340 374 374 375 375 350 350 347 347 339 339 344 344 335 335 345 345 342 342 376 376 339 339 377 377 345 345 340 340 378 378 340 340 375 375 379 379 340 340 380 380 340 340 378 378 380 380 340 340 379 379 381 381 340 340 382 382 383 383 340 340 381 381 382 382 372 372 373 373 347 347 350 350 349 349 384 384 357 357 372 372 347 347 384 384 352 352 350 350 347 347 350 350 357 357 340 340 346 346 374 374 376 376 385 385 339 339 339 339 385 385 349 349 346 346 340 340 347 347 383 383 377 377 340 340 341 341 335 335 343 343 335 335 337 337 342 342

- - - - -

386 386 387 387 388 388 389 389 390 390 391 391 392 392 389 389 393 393 394 394 395 395 391 391 396 396 393 393 397 397 398 398 395 395 399 399 400 400 397 397 401 401 402 402 403 403 398 398 404 404 401 401 405 405 406 406 407 407 408 408 409 409 410 410 405 405 411 411 412 412 413 413 414 414 415 415 416 416 417 417 418 418 419 419 420 420 421 421 422 422 423 423 424 424 425 425 426 426 427 427 428 428 426 426 429 429 427 427 430 430 420 420 431 431 430 430 431 431 427 427 432 432 423 423 425 425 429 429 433 433 432 432 422 422 421 421 434 434 435 435 424 424 436 436 409 409 405 405 401 401 414 414 419 419 418 418 435 435 436 436 411 411 413 413 412 412 437 437 419 419 414 414 416 416 438 438 415 415 407 407 439 439 437 437 440 440 386 386 441 441 442 442 408 408 407 407 415 415 406 406 408 408 403 403 441 441 410 410 442 442 415 415 438 438 416 416 387 387 437 437 439 439 421 421 418 418 434 434 434 434 418 418 417 417 430 430 421 421 420 420 428 428 427 427 431 431 433 433 429 429 426 426 425 425 429 429 432 432 435 435 425 425 424 424 413 413 435 435 411 411 440 440 437 437 412 412 388 388 387 387 439 439 442 442 387 387 386 386 409 409 442 442 410 410 400 400 401 401 404 404 396 396 397 397 400 400 389 389 397 397 393 393 389 389 392 392 390 390 391 391 390 390 443 443 394 394 399 399 395 395 443 443 394 394 391 391 399 399 402 402 398 398 403 403 408 408 398 398

- - - - -

444 444 445 445 446 446 447 447 448 448 449 449 450 450 451 451 447 447 452 452 448 448 453 453 454 454 455 455 451 451 456 456 457 457 453 453 458 458 459 459 455 455 460 460 456 456 461 461 462 462 463 463 459 459 464 464 465 465 466 466 467 467 463 463 468 468 469 469 470 470 471 471 472 472 473 473 474 474 475 475 476 476 477 477 478 478 479 479 480 480 481 481 482 482 483 483 484 484 485 485 486 486 484 484 486 486 487 487 488 488 489 489 478 478 488 488 486 486 489 489 490 490 482 482 481 481 487 487 490 490 491 491 479 479 492 492 480 480 493 493 494 494 483 483 467 467 459 459 463 463 472 472 477 477 476 476 493 493 469 469 494 494 470 470 495 495 471 471 476 476 473 473 472 472 496 496 466 466 474 474 497 497 498 498 495 495 444 444 499 499 500 500 465 465 474 474 466 466 464 464 461 461 465 465 500 500 499 499 468 468 474 474 473 473 496 496 446 446 497 497 495 495 480 480 492 492 477 477 492 492 475 475 477 477 488 488 478 478 480 480 485 485 489 489 486 486 491 491 484 484 487 487 482 482 490 490 487 487 493 493 483 483 482 482 470 470 469 469 493 493 498 498 471 471 495 495 445 445 497 497 446 446 499 499 444 444 446 446 467 467 468 468 499 499 458 458 462 462 459 459 454 454 458 458 455 455 447 447 451 451 455 455 447 447 449 449 450 450 448 448 501 501 449 449 452 452 453 453 457 457 501 501 448 448 452 452 457 457 456 456 460 460 461 461 456 456 465 465

- - - - -

502 502 503 503 504 504 505 505 506 506 507 507 508 508 509 509 507 507 506 506 508 508 507 507 506 506 510 510 511 511 505 505 512 512 506 506 506 506 511 511 513 513 514 514 510 510 506 506 515 515 503 503 516 516 514 514 517 517 510 510 518 518 503 503 502 502 519 519 520 520 521 521 522 522 523 523 524 524 524 524 523 523 504 504 503 503 524 524 504 504 523 523 522 522 525 525 503 503 526 526 519 519 518 518 526 526 503 503 519 519 527 527 528 528 529 529 530 530 527 527 530 530 529 529 531 531 528 528 532 532 519 519 527 527 519 519 529 529 533 533 519 519 532 532 534 534 519 519 521 521 533 533 520 520 519 519 535 535 536 536 537 537 526 526 529 529 519 519 503 503 510 510 516 516 535 535 538 538 536 536 536 536 510 510 503 503 536 536 511 511 510 510 513 513 539 539 506 506 540 540 511 511 541 541 511 511 542 542 541 541 511 511 543 543 544 544 545 545 511 511 540 540 543 543 546 546 547 547 543 543 511 511 548 548 543 543 548 548 549 549 546 546 543 543 549 549 548 548 511 511 550 550 544 544 551 551 511 511 511 511 545 545 550 550 519 519 534 534 537 537 524 524 503 503 552 552 536 536 503 503 519 519 515 515 552 552 503 503 536 536 519 519 537 537 538 538 542 542 511 511 517 517 553 553 510 510 510 510 553 553 516 516 538 538 511 511 536 536 551 551 513 513 511 511 506 506 539 539 508 508 506 506 512 512 514 514

- - - - -

554 554 555 555 556 556 557 557 558 558 559 559 556 556 560 560 561 561 555 555 560 560 556 556 561 561 562 562 563 563 562 562 561 561 560 560 564 564 565 565 566 566 562 562 567 567 563 563 568 568 569 569 570 570 571 571 569 569 572 572 573 573 568 568 574 574 570 570 574 574 568 568 575 575 576 576 573 573 573 573 574 574 575 575 577 577 578 578 579 579 563 563 567 567 580 580 569 569 571 571 570 570 572 572 565 565 564 564 572 572 564 564 571 571 566 566 565 565 563 563 566 566 563 563 580 580 577 577 581 581 578 578 578 578 582 582 579 579 554 554 581 581 583 583 577 577 583 583 581 581 580 580 567 567 584 584 554 554 583 583 555 555 580 580 584 584 585 585 586 586 587 587 585 585 585 585 584 584 586 586 587 587 588 588 589 589 588 588 587 587 586 586 590 590 589 589 591 591 588 588 591 591 589 589 592 592 593 593 590 590 590 590 591 591 592 592 594 594 595 595 593 593 594 594 596 596 597 597 598 598 597 597 599 599 595 595 600 600 601 601 602 602 603 603 604 604 605 605 606 606 607 607 608 608 609 609 610 610 611 611 612 612 613 613 614 614 615 615 616 616 617 617 618 618 619 619 620 620 621 621 622 622 623 623 624 624 625 625 626 626 627 627 628 628 629 629 630 630 631 631 632 632 633 633 634 634 635 635 636 636 637 637 636 636 638 638 637 637 638 638 639 639 637 637 640 640 636 636 641 641 642 642 643 643 644 644 644 644 645 645 642 642 646 646 643 643 647 647 643 643 646 646 644 644 579 579 648 648 647 647 646 646 647 647 648 648 582 582 648 648 579 579 632 632 634 634 639 639 649 649 650 650 651 651 652 652 653 653 654 654 641 641 655 655 640 640 645 645 656 656 657 657 657 657 642 642 645 645 641 641 636 636 628 628 640 640 655 655 658 658 657 657 656 656 659 659 655 655 659 659 658 658 659 659 656 656 658 658 634 634 633 633 660 660 633 633 652 652 660 660 650 650 661 661 653 653 654 654 653 653 661 661 649 649 661 661 650 650 651 651 576 576 575 575 651 651 575 575 649 649 639 639 638 638 632 632 652 652 654 654 660 660 626 626 628 628 635 635 628 628 636 636 635 635 631 631 630 630 627 627 631 631 627 627 626 626 629 629 621 621 620 620 629 629 620 620 630 630 622 622 623 623 662 662 621 621 623 623 622 622 625 625 615 615 614 614 625 625 614 614 662 662 616 616 617 617 619 619 615 615 617 617 616 616 609 609 618 618 610 610 619 619 618 618 609 609 611 611 608 608 612 612 608 608 610 610 612 612 663 663 664 664 665 665 603 603 611 611 613 613 666 666 667 667 602 602 668 668 665 665 607 607 669 669 670 670 605 605 559 559 671 671 666 666 624 624 672 672 625 625 662 662 623 623 625 625 624 624 673 673 672 672 674 674 675 675 676 676 677 677 678 678 675 675 679 679 680 680 678 678 681 681 682 682 680 680 683 683 682 682 664 664 603 603 613 613 604 604 683 683 664 664 663 663 663 663 665 665 668 668 667 667 603 603 602 602 668 668 607 607 606 606 671 671 667 667 666 666 606 606 605 605 670 670 558 558 671 671 559 559 601 601 670 670 669 669 599 599 558 558 557 557 601 601 669 669 595 595 599 599 557 557 598 598 596 596 599 599 597 597 593 593 592 592 594 594 592 592 596 596 594 594 595 595 594 594 600 600 681 681 664 664 682 682 679 679 681 681 680 680 677 677 679 679 678 678 674 674 677 677 675 675 673 673 674 674 676 676 676 676 672 672 673 673

- - - - -

684 684 685 685 686 686 687 687 688 688 684 684 684 684 686 686 687 687 687 687 689 689 688 688 690 690 688 688 689 689 691 691 692 692 690 690 690 690 689 689 691 691 691 691 693 693 692 692

- - - - -

694 694 695 695 696 696 697 697 696 696 698 698 694 694 699 699 695 695 696 696 695 695 698 698

- - - - -

700 700 701 701 702 702 703 703 704 704 705 705 706 706 707 707 708 708 709 709 710 710 711 711 712 712 713 713 714 714 715 715 716 716 717 717 718 718 719 719 715 715 720 720 721 721 716 716 717 717 716 716 721 721 722 722 720 720 723 723 720 720 722 722 721 721 715 715 717 717 718 718 714 714 703 703 712 712 709 709 719 719 710 710 718 718 710 710 719 719 713 713 711 711 714 714 713 713 709 709 711 711 705 705 704 704 708 708 712 712 703 703 705 705 706 706 700 700 707 707 704 704 706 706 708 708 702 702 707 707 700 700

- - - - -

724 724 725 725 726 726 726 726 727 727 724 724

- - - - -

728 728 729 729 730 730 730 730 731 731 728 728

- - - - -

732 732 733 733 734 734 735 735 736 736 737 737 738 738 739 739 740 740 741 741 742 742 743 743 744 744 745 745 746 746 747 747 742 742 748 748 741 741 748 748 742 742 747 747 749 749 750 750 749 749 747 747 748 748 745 745 741 741 743 743 734 734 751 751 732 732 735 735 744 744 746 746 745 745 743 743 746 746 740 740 737 737 736 736 744 744 735 735 737 737 738 738 733 733 739 739 736 736 738 738 740 740 733 733 732 732 739 739

- - - - -

752 752 753 753 754 754 755 755 756 756 757 757 756 756 752 752 754 754 755 755 752 752 756 756

- - - - -

758 758 759 759 760 760 761 761 762 762 763 763 758 758 762 762 761 761 758 758 760 760 762 762

- - - - -

764 764 765 765 766 766 766 766 765 765 767 767 764 764 768 768 765 765 765 765 768 768 769 769 768 768 770 770 769 769

- - - - -

771 771 772 772 773 773 774 774 775 775 776 776 776 776 775 775 777 777 778 778 779 779 774 774 774 774 776 776 778 778 780 780 781 781 782 782 783 783 779 779 780 780 784 784 785 785 786 786 787 787 781 781 788 788 784 784 789 789 790 790 791 791 792 792 784 784 793 793 794 794 787 787 787 787 795 795 793 793 796 796 789 789 784 784 793 793 797 797 794 794 796 796 798 798 799 799 800 800 784 784 792 792 801 801 799 799 798 798 799 799 802 802 803 803 799 799 804 804 802 802 796 796 805 805 798 798 801 801 804 804 799 799 784 784 800 800 805 805 796 796 784 784 805 805 784 784 786 786 791 791 787 787 794 794 806 806 787 787 790 790 795 795 806 806 807 807 787 787 808 808 809 809 788 788 810 810 808 808 788 788 811 811 812 812 788 788 811 811 772 772 813 813 814 814 815 815 772 772 813 813 772 772 816 816 772 772 815 815 817 817 772 772 771 771 816 816 788 788 781 781 772 772 772 772 817 817 773 773 781 781 818 818 819 819 818 818 781 781 807 807 820 820 780 780 782 782 772 772 781 781 780 780 821 821 782 782 781 781 780 780 779 779 778 778 820 820 783 783 780 780 809 809 785 785 788 788 790 790 787 787 784 784 784 784 788 788 785 785 807 807 781 781 787 787 787 787 788 788 784 784 810 810 788 788 812 812 822 822 780 780 823 823 819 819 821 821 781 781 788 788 772 772 811 811 822 822 814 814 772 772 822 822 772 772 780 780 780 780 778 778 823 823

- - - - - - - - - - - 1 1 1 1 - - - 1 - - - - - - - - - - - 0.101961 0.101961 0.101961 1 - - - 1 - - - - - - - - - - - 0.898039 0.898039 0.898039 1 - - - 1 - - - - - - - - - - - 0.631373 0.658824 0.678431 1 - - - 1 - - - - - - - - - - - 0.968627 0.878431 0.6 1 - - - 1 - - - - - - - - - - - 0.109804 0.184314 0 1 - - - 1 - - - - - - - - - - - 0.792157 0.819608 0.933333 1 - - - 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -8.88178e-015 -9.81308e-018 -1 -0.703947 -9.81308e-018 -1 9.81308e-018 4.82341 -1 9.81308e-018 8.88178e-015 -0.640698 0 0 0 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 -9.81308e-018 -9.81308e-018 -0.703947 -9.81308e-018 9.81308e-018 -1 4.22341 9.81308e-018 1 9.81308e-018 -0.640698 0 0 0 1 - - - - - - - - - - - - -7.46625e-015 -1 9.81308e-018 -0.703947 -9.81308e-018 9.81308e-018 1 -5.39659 -1 7.46625e-015 -9.81308e-018 -0.640698 0 0 0 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -0.959406 0 0.282028 -11.2194 0 1 0 1.70341 -0.282028 0 -0.959406 -45.9898 0 0 0 1 - - - - - - - - - - - - 0.144807 0 -0.98946 38.4702 0 1 0 1.70341 0.98946 0 0.144807 76.5429 0 0 0 1 - - - - - - - - - - - - 1 0 0 11.6382 0 1 0 1.70341 0 0 1 32.0172 0 0 0 1 - - - - - - - - - - - - -0.00822618 0 0.999966 -33.732 0 1 0 1.70341 -0.999966 0 -0.00822618 -78.297 0 0 0 1 - - - - - - - - - - - - - - - - - diff --git a/multi_uav_simulator/config/simulation.rviz b/multi_uav_simulator/config/simulation.rviz deleted file mode 100644 index 6c69e16..0000000 --- a/multi_uav_simulator/config/simulation.rviz +++ /dev/null @@ -1,312 +0,0 @@ -Panels: - - Class: rviz/Displays - Help Height: 78 - Name: Displays - Property Tree Widget: - Expanded: ~ - Splitter Ratio: 0.6470588445663452 - Tree Height: 557 - - Class: rviz/Selection - Name: Selection - - Class: rviz/Tool Properties - Expanded: - - /2D Pose Estimate1 - - /2D Nav Goal1 - - /Publish Point1 - Name: Tool Properties - Splitter Ratio: 0.5886790156364441 - - Class: rviz/Views - Expanded: - - /Current View1 - Name: Views - Splitter Ratio: 0.5 - - Class: rviz/Time - Experimental: false - Name: Time - SyncMode: 0 - SyncSource: "" -Preferences: - PromptSaveOnExit: true -Toolbars: - toolButtonStyle: 2 -Visualization Manager: - Class: "" - Displays: - - Alpha: 0.5 - Cell Size: 1 - Class: rviz/Grid - Color: 160; 160; 164 - Enabled: true - Line Style: - Line Width: 0.029999999329447746 - Value: Lines - Name: Grid - Normal Cell Count: 0 - Offset: - X: 0 - Y: 0 - Z: 0 - Plane: XY - Plane Cell Count: 20 - Reference Frame: - Value: true - - Alpha: 1 - Class: rviz/RobotModel - Collision Enabled: false - Enabled: true - Links: - All Links Enabled: true - Expand Joint Details: false - Expand Link Details: false - Expand Tree: false - Link Tree Style: Links in Alphabetic Order - base_link1: - Alpha: 1 - Show Axes: false - Show Trail: false - Value: true - Name: RobotModel - Robot Description: robot1 - TF Prefix: "" - Update Interval: 0 - Value: true - Visual Enabled: true - - Alpha: 1 - Class: rviz/Axes - Enabled: true - Length: 0.5 - Name: Axes - Radius: 0.05000000074505806 - Reference Frame: map - Show Trail: false - Value: true - - Alpha: 1 - Class: rviz/RobotModel - Collision Enabled: false - Enabled: true - Links: - All Links Enabled: true - Expand Joint Details: false - Expand Link Details: false - Expand Tree: false - Link Tree Style: Links in Alphabetic Order - base_link2: - Alpha: 1 - Show Axes: false - Show Trail: false - Value: true - Name: RobotModel - Robot Description: robot2 - TF Prefix: "" - Update Interval: 0 - Value: true - Visual Enabled: true - - Alpha: 1 - Class: rviz/RobotModel - Collision Enabled: false - Enabled: true - Links: - All Links Enabled: true - Expand Joint Details: false - Expand Link Details: false - Expand Tree: false - Link Tree Style: Links in Alphabetic Order - base_link3: - Alpha: 1 - Show Axes: false - Show Trail: false - Value: true - Name: RobotModel - Robot Description: robot3 - TF Prefix: "" - Update Interval: 0 - Value: true - Visual Enabled: true - - Alpha: 1 - Class: rviz/RobotModel - Collision Enabled: false - Enabled: true - Links: - All Links Enabled: true - Expand Joint Details: false - Expand Link Details: false - Expand Tree: false - Link Tree Style: Links in Alphabetic Order - base_link4: - Alpha: 1 - Show Axes: false - Show Trail: false - Value: true - Name: RobotModel - Robot Description: robot4 - TF Prefix: "" - Update Interval: 0 - Value: true - Visual Enabled: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link2/path - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link4/path - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link3/path - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link1/path - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Alpha: 1 - Class: rviz/RobotModel - Collision Enabled: false - Enabled: true - Links: - All Links Enabled: true - Expand Joint Details: false - Expand Link Details: false - Expand Tree: false - Link Tree Style: Links in Alphabetic Order - base_link5: - Alpha: 1 - Show Axes: false - Show Trail: false - Value: true - Name: RobotModel - Robot Description: robot5 - TF Prefix: "" - Update Interval: 0 - Value: true - Visual Enabled: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link5/path - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link1/goal - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link2/goal - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link3/goal - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link4/goal - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - - Class: rviz/Marker - Enabled: true - Marker Topic: /base_link5/goal - Name: Marker - Namespaces: - "": true - Queue Size: 100 - Value: true - Enabled: true - Global Options: - Background Color: 255; 255; 255 - Default Light: true - Fixed Frame: map - Frame Rate: 10 - Name: root - Tools: - - Class: rviz/Interact - Hide Inactive Objects: true - - Class: rviz/MoveCamera - - Class: rviz/Select - - Class: rviz/FocusCamera - - Class: rviz/Measure - - Class: rviz/SetInitialPose - Theta std deviation: 0.2617993950843811 - Topic: /initialpose - X std deviation: 0.5 - Y std deviation: 0.5 - - Class: rviz/SetGoal - Topic: /move_base_simple/goal - - Class: rviz/PublishPoint - Single click: true - Topic: /clicked_point - Value: true - Views: - Current: - Class: rviz/Orbit - Distance: 8.682811737060547 - Enable Stereo Rendering: - Stereo Eye Separation: 0.05999999865889549 - Stereo Focal Distance: 1 - Swap Stereo Eyes: false - Value: false - Field of View: 0.7853981852531433 - Focal Point: - X: 0.24857836961746216 - Y: -0.6647985577583313 - Z: 0.5124149322509766 - Focal Shape Fixed Size: false - Focal Shape Size: 0.05000000074505806 - Invert Z Axis: false - Name: Current View - Near Clip Distance: 0.009999999776482582 - Pitch: 0.6653982996940613 - Target Frame: - Yaw: 2.915405035018921 - Saved: ~ -Window Geometry: - Displays: - collapsed: true - Height: 1015 - Hide Left Dock: true - Hide Right Dock: false - QMainWindow State: 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 - Selection: - collapsed: true - Time: - collapsed: false - Tool Properties: - collapsed: false - Views: - collapsed: false - Width: 1267 - X: 2413 - Y: 156 diff --git a/multi_uav_simulator/include/multi_uav_simulator/Quadrotor.h b/multi_uav_simulator/include/multi_uav_simulator/Quadrotor.h deleted file mode 100644 index 0771d2f..0000000 --- a/multi_uav_simulator/include/multi_uav_simulator/Quadrotor.h +++ /dev/null @@ -1,95 +0,0 @@ -#ifndef PROJECT_QUADROTOR_H -#define PROJECT_QUADROTOR_H - -#include -#include -#include -#include -#include "DynamicsProvider.h" -#include "tf/tf.h" -#include -#include "ros/ros.h" -#include "simulator_utils/Waypoint.h" -#include "Trajectory_t.h" - -#include -#include - -#ifndef state -#define state -enum State { - Idle, - TakingOff, - Landing, - Hover, - Autonomous -}; -#endif - -using namespace Eigen; -using namespace std; -#include "std_msgs/Float32MultiArray.h" - - -class Quadrotor { -public: - Quadrotor(int robot_id, double frequency, ros::NodeHandle &n); - void move(const desired_state_t &d_state); - void setState(State m_state); - State getState(); - - bool initialize(double dt); - - void desired_pos_cb(const geometry_msgs::Point &pt); - - void iteration(const ros::TimerEvent &e); - void run(); - -private: - - State m_state; - double sim_time, tau, dt, frequency; - int robot_id; - std::string worldframe, localframe, robot_link_name; - gains_t gains; - std::vector traj_piece; - int xd_it; - Vector3d u, target_pos; - state_space_t x0, xd0; - - bool set_init_target; - geometry_msgs::Point target_next; - bool set_next_target = false; - // Vector3d ; - mav_trajectory_generation::Trajectory traj; - // mav_trajectory_generation::Trajectory traj_temp; - - ControllerImpl *controller; - state_space_t state_space; - ros::NodeHandle nh; - - DynamicsProvider *dynamics; - params_t params; - init_vals_t init_vals; - - ros::Publisher marker_pub, goal_pub, state_pub; - visualization_msgs::Marker m, g; - std::vector points; - ros::Subscriber desired_state_sub; - vector positions; - - bool quad_initialized = false; - // Vector3d xd; - - void do_rhp(); - void initPaths(); - void set_state_space(); - bool load_params(); - bool load_init_vals(); - void send_transform(); - void publish_path(); - void publish_state(); - static mav_trajectory_generation::Trajectory get_opt_traj(const opt_t &ps, const Vector3d& pe); -}; - -#endif diff --git a/multi_uav_simulator/include/multi_uav_simulator/cfSimUtils.h b/multi_uav_simulator/include/multi_uav_simulator/cfSimUtils.h deleted file mode 100755 index b8516f6..0000000 --- a/multi_uav_simulator/include/multi_uav_simulator/cfSimUtils.h +++ /dev/null @@ -1,42 +0,0 @@ -// -// Created by malintha on 2/27/18. -// - -#ifndef PROJECT_CFSIMUTILS_H -#define PROJECT_CFSIMUTILS_H - -#include -#include -#include "ros/ros.h" -#include -#include -#include -#include -#include "tf/tf.h" - -using namespace Eigen; - -namespace cfSimUtils { - /** - * @param gamma roll - * @param beta pitch - * @param alpha yaw - */ - - struct node { - int id, cluster; - float x, y, z; - std::string type; - node(int id, int cluster, float x, float y, float z, std::string type):id(id), cluster(cluster), x(x), y(y), - z(z), type(type) {}; - }; - - Matrix3d getR(double gamma, double beta, double alpha); - double getTargetPWM(double targetThrust); - Vector3d transformtoRPY(tf::Transform transform); - std::vector > retrievePaths(); - std::vector retrieveTopologyConfig(); - -} - -#endif diff --git a/multi_uav_simulator/package.xml b/multi_uav_simulator/package.xml deleted file mode 100755 index 1dbae14..0000000 --- a/multi_uav_simulator/package.xml +++ /dev/null @@ -1,70 +0,0 @@ - - - multi_uav_simulator - 0.0.0 - The cf_simulator package - - - - - malintha fernando - - - - - - MIT - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - catkin - roscpp - std_msgs - geo_controller - roscpp - std_msgs - roscpp - std_msgs - geo_controller - mav_trajectory_generation - simulator_utils - - - - - - - - - diff --git a/multi_uav_simulator/src/Quadrotor.cpp b/multi_uav_simulator/src/Quadrotor.cpp deleted file mode 100644 index 03abe9b..0000000 --- a/multi_uav_simulator/src/Quadrotor.cpp +++ /dev/null @@ -1,353 +0,0 @@ -// -// Created by malintha on 8/22/18. -// -#include "Quadrotor.h" -#include -#include -#include -#include "simulator_utils/simulator_utils.h" - -mav_trajectory_generation::Trajectory Quadrotor::get_opt_traj(const opt_t &ps, const Vector3d& pe) { - mav_trajectory_generation::Vertex::Vector vertices; - mav_trajectory_generation::Vertex v_s(3), v_e(3); - const int derivative_to_optimize = mav_trajectory_generation::derivative_order::JERK; - - v_s.addConstraint(mav_trajectory_generation::derivative_order::POSITION, ps.position); - v_s.addConstraint(mav_trajectory_generation::derivative_order::VELOCITY, ps.velocity); - v_s.addConstraint(mav_trajectory_generation::derivative_order::ACCELERATION, ps.acceleration); - - v_e.makeStartOrEnd(pe, derivative_to_optimize); - - vertices.push_back(v_s); - vertices.push_back(v_e); - - mav_trajectory_generation::PolynomialOptimization<8> opt(3); - std::vector segment_times; - const double v_max = 1; - const double a_max = 4; - segment_times = estimateSegmentTimes(vertices, v_max, a_max); - ROS_DEBUG_STREAM("segement times: "<dt = 1/frequency; - this->initialize(1 / frequency); - this->u << 0,0,0; - - while (marker_pub.getNumSubscribers() < 1) { - ROS_INFO("Waiting for subscriber"); - ros::Duration(1).sleep(); - } -} - -bool Quadrotor::initialize(double dt_) { - m_state = State::Idle; - // load quad params - if (!load_params()) { - ROS_ERROR_STREAM("Could not load the drone parameters"); - return false; - } - // load init params - if (!load_init_vals()) { - ROS_ERROR_STREAM("Could not load the drone initial values"); - return false; - } - - stringstream ss; - ss << localframe << to_string(robot_id); - robot_link_name = ss.str(); - - // set initial values - state_space.position = init_vals.position; - state_space.velocity = init_vals.velocity; - state_space.R = init_vals.R; - state_space.omega = init_vals.omega; - - dynamics = new DynamicsProvider(params, init_vals); - controller = new ControllerImpl(params, init_vals, gains, dt_); - - this->setState(State::Autonomous); - initPaths(); - - desired_state_sub = nh.subscribe("desired_state", 10, &Quadrotor::desired_pos_cb, this); - state_pub = nh.advertise("current_state", 10); - ROS_DEBUG_STREAM("Drone initialized " << robot_id); - ROS_INFO_STREAM("Desired state subscriber topic: " << "robot_"<set_init_target = false; - return true; -} - -void Quadrotor::initPaths() { - marker_pub = nh.advertise( - ros::names::append(robot_link_name, "path"), 10); - - goal_pub = nh.advertise( - ros::names::append(robot_link_name, "goal"), 10); - g.header.stamp = m.header.stamp = ros::Time::now(); - g.header.frame_id = m.header.frame_id = worldframe; - m.type = visualization_msgs::Marker::LINE_STRIP; - - m.action = visualization_msgs::Marker::ADD; - m.id = this->robot_id; - m.color.r = 1; - m.color.g = 0.0; - m.color.b = 0.0; - m.color.a = 1; - m.scale.x = 0.05; - m.pose.orientation.w = 1.0; - - g.id = this->robot_id + 20; - g.type = visualization_msgs::Marker::CUBE; - g.action = visualization_msgs::Marker::ADD; - g.color.r = 1; - g.color.g = 0; - g.color.b = 0; - g.color.a = 0.5; - g.scale.x = 0.1; - g.scale.y = 0.1; - g.scale.z = 0.1; - -} - -void Quadrotor::setState(State m_state_) { - this->m_state = m_state_; -} - -void Quadrotor::move(const desired_state_t &d_state) { - control_out_t control = controller->get_control(dynamics->get_state(), d_state); - dynamics->update(control, sim_time); - - // updating the model on rviz - set_state_space(); - send_transform(); - dynamics->reset_dynamics(); - sim_time += dt; -} - -/** - * converts the dynamics state_space (NED) to NWU and stores for the quadrotor - * This is for broadcasting the transformation -*/ -void Quadrotor::set_state_space() { - state_space_t ss = dynamics->get_state(); - state_space.position = simulator_utils::ned_nwu_rotation(ss.position); - state_space.R = simulator_utils::ned_nwu_rotation(ss.R); - state_space.velocity = simulator_utils::ned_nwu_rotation(ss.velocity); - state_space.omega = simulator_utils::ned_nwu_rotation(ss.omega); -} - -void Quadrotor::send_transform() { - static tf::TransformBroadcaster br; - tf::Transform transform; - Vector3d position = state_space.position; - Matrix3d R = state_space.R; - Vector3d rpy = simulator_utils::R2RPY(R); - transform.setOrigin(tf::Vector3(position[0], position[1], -position[2])); - tf::Quaternion q; - q.setRPY(rpy[0], rpy[1], rpy[2]); - transform.setRotation(q); - if(quad_initialized && !isnan(q.x())) - br.sendTransform(tf::StampedTransform(transform, ros::Time::now(), worldframe, robot_link_name)); -} - -State Quadrotor::getState() { - return this->m_state; -} - -bool Quadrotor::load_params() { - stringstream ss; - ss << "/robot_" << to_string(this->robot_id); - string robot_name = ss.str(); - double temp; - if (!nh.getParam(ros::names::append(robot_name, "drone/model/gravity"), params.gravity)) return false; - // = temp; - vector J_; - if (!nh.getParam(ros::names::append(robot_name, "drone/model/J"), J_)) return false; - // Matrix3d J; - params.J << J_[0], 0, 0, - 0, J_[1], 0, - 0, 0, J_[2]; - params.J_inv = params.J.inverse(); - if (!nh.getParam(ros::names::append(robot_name, "drone/model/m"), params.mass)) return false; - // = temp; - params.F = 0; - Vector3d M(0, 0, 0); - params.M = M; - vector gains_; - if (!nh.getParam(ros::names::append(robot_name, "drone/controller/gains"), gains_)) return false; - this->gains = {gains_[0], gains_[1], gains_[2], gains_[3]}; - - ROS_DEBUG_STREAM("Loaded control parameters"); - return true; -} - -bool Quadrotor::load_init_vals() { - vector position, vel, R, omega; - stringstream ss; - ss << "/robot_" << to_string(this->robot_id); - string robot_name = ss.str(); - if (!nh.getParam(ros::names::append(robot_name, "position"), position)) return false; - if (!nh.getParam(ros::names::append(robot_name, "velocity"), vel)) return false; - if (!nh.getParam(ros::names::append(robot_name, "rotation"), R)) return false; - if (!nh.getParam(ros::names::append(robot_name, "omega"), omega)) return false; - if (!nh.getParam("/frame/fixed", worldframe)) return false; - if (!nh.getParam("/frame/prefix", localframe)) return false; - init_vals.position = Vector3d(position.data()); - init_vals.velocity = Vector3d(vel.data()); - init_vals.R = Matrix3d(R.data()); - init_vals.omega = Vector3d(omega.data()); - - this->x0.position = simulator_utils::ned_nwu_rotation(init_vals.position); - this->x0.velocity = simulator_utils::ned_nwu_rotation(init_vals.velocity); - this->xd0.position = this->x0.position; - this->target_pos = simulator_utils::ned_nwu_rotation(init_vals.position); - ROS_DEBUG_STREAM("Loaded the drone initialization values"); - return true; -} - -void Quadrotor::desired_pos_cb(const geometry_msgs::Point &pt) { - Vector3d p1 = {pt.x, pt.y, pt.z}; - Vector3d p2 = target_pos; - if((p2 - p1).norm() >= 0.2) { - if(!set_init_target) { - set_init_target = true; - // set init trajectory - Vector3d init_z = {0,0,0}; - opt_t ps = {target_pos, init_z, init_z, init_z}; - Vector3d pe = {pt.x, pt.y, pt.z}; - this->traj = get_opt_traj(ps, pe); - this->target_pos = pe; - ROS_DEBUG_STREAM(robot_id<<" Set init trajectory"); - } - else { - this->target_next = pt; - this->target_pos = {pt.x, pt.y, pt.z}; - this->set_next_target = true; - ROS_DEBUG_STREAM(robot_id<<" Set new target"); - } - } -} - -// if there is another target available, calculate a new trajectory -void Quadrotor::do_rhp() { - - if (set_next_target) { - Vector3d pt = {target_next.x, target_next.y, target_next.z}; - Vector3d ps, vel(0,0,0), acc(0,0,0); - // changing to a new trajectory midway - ROS_DEBUG_STREAM("calculating a new trajectory"); - ps = this->dynamics->get_state().position; - vel = this->dynamics->get_state().velocity; - acc = this->dynamics->get_state().acceleration; - - opt_t wp = {ps, vel, acc}; - - this->traj = get_opt_traj(wp, pt); - ROS_DEBUG_STREAM("Setting a new trajectory of length: "<set_next_target = false; - tau = 0; - }; -} - -// xd should be in NED frame and so does dynamics and controller. -void Quadrotor::iteration(const ros::TimerEvent &e) { - // compute the next desired state using incoming control signal and current state - Vector3d b1d(1, 0, 0); - Vector3d xd = simulator_utils::ned_nwu_rotation(init_vals.position); - - // use traj optimization to navigate to the desired state - if(this->set_init_target) { - if(set_next_target) { - do_rhp(); - } - xd = traj.evaluate(tau, mav_trajectory_generation::derivative_order::POSITION); - - if(abs(tau - traj.getMaxTime()) >= dt) { - tau = tau + dt; - } - } - - desired_state_t dss = {xd, b1d}; - this->move(dss); - this->publish_path(); - this->publish_state(); -} - -void Quadrotor::publish_path() { - constexpr int arrowLength = 0.05; - Vector3d x = this->dynamics->get_state().position; - x[1] = -x[1]; - geometry_msgs::Point p; - if(!isnan(x[0]) && !isnan(x[1])) { - p.x = x[0]; - p.y = x[1]; - p.z = x[2]; - quad_initialized = true; - } - else - { - p.x = 0; - p.y = 0; - p.z = 0; - } - - m.points.push_back(p); - if (m.points.size() > 1000) - m.points.erase(m.points.begin()); - - g.pose.position.x = this->target_pos[0]; - g.pose.position.y = -this->target_pos[1]; - g.pose.position.z = this->target_pos[2]; - g.pose.orientation.x = 0.0; - g.pose.orientation.y = 0.0; - g.pose.orientation.z = 0.0; - g.pose.orientation.w = 1.0; - - goal_pub.publish(g); - marker_pub.publish(m); -} - -void Quadrotor::run() { - ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration, this); - ros::spin(); -} - -void Quadrotor::publish_state() { - simulator_utils::Waypoint wp; - geometry_msgs::Point p,v; - state_space_t ned_state = this->dynamics->get_state(); - p.x = ned_state.position[0]; - p.y = ned_state.position[1]; - p.z = ned_state.position[2]; - v.x = ned_state.velocity[0]; - v.y = ned_state.velocity[1]; - v.z = ned_state.velocity[2]; - wp.position = p; - wp.velocity = v; - wp.acceleration.x = wp.acceleration.y = wp.acceleration.z = 0; - this->state_pub.publish(wp); -} - -int main(int argc, char **argv) { - - int robot_id = std::atoi(argv[1]); - double frequency = (double)std::atof(argv[2]); - - ROS_DEBUG_STREAM("initializing : " << robot_id << endl); - ros::init(argc, argv, "~"); - ros::NodeHandle n; - Quadrotor quad(robot_id, frequency, n); - quad.run(); - - return 0; -} \ No newline at end of file diff --git a/package.xml b/package.xml new file mode 100644 index 0000000..4a5600c --- /dev/null +++ b/package.xml @@ -0,0 +1,27 @@ + + + + mavswarm2 + 0.0.0 + TODO: Package description + parallels + TODO: License declaration + + ament_cmake + + rclcpp + simulator_interfaces + simulator_utils + controller + std_msgs + geometry_msgs + sensor_msgs + visualization_msgs + + ament_lint_auto + ament_lint_common + + + ament_cmake + + diff --git a/rosinstall/dependencies.rosinstall b/rosinstall/dependencies.rosinstall deleted file mode 100644 index 6d22a50..0000000 --- a/rosinstall/dependencies.rosinstall +++ /dev/null @@ -1,8 +0,0 @@ -- git: {local-name: mav_trajectory_generation, uri: 'https://github.com/ethz-asl/mav_trajectory_generation'} -- git: {local-name: catkin_simple, uri: 'https://github.com/catkin/catkin_simple.git'} -- git: {local-name: eigen_catkin, uri: 'https://github.com/ethz-asl/eigen_catkin.git'} -- git: {local-name: eigen_checks, uri: 'https://github.com/ethz-asl/eigen_checks.git'} -- git: {local-name: glog_catkin, uri: 'https://github.com/ethz-asl/glog_catkin.git'} -- git: {local-name: mav_comm, uri: 'https://github.com/ethz-asl/mav_comm.git'} -- git: {local-name: nlopt, uri: 'https://github.com/ethz-asl/nlopt.git'} - diff --git a/simulator_utils/CMakeLists.txt b/simulator_utils/CMakeLists.txt deleted file mode 100644 index 17746f9..0000000 --- a/simulator_utils/CMakeLists.txt +++ /dev/null @@ -1,210 +0,0 @@ -cmake_minimum_required(VERSION 2.8.3) -project(simulator_utils) - -## Compile as C++11, supported in ROS Kinetic and newer -# add_compile_options(-std=c++11) - -## Find catkin macros and libraries -## if COMPONENTS list like find_package(catkin REQUIRED COMPONENTS xyz) -## is used, also find other catkin packages -find_package(catkin REQUIRED COMPONENTS - roscpp - std_msgs - message_generation - geometry_msgs - ) - -## System dependencies are found with CMake's conventions -# find_package(Boost REQUIRED COMPONENTS system) - - -## Uncomment this if the package has a setup.py. This macro ensures -## modules and global scripts declared therein get installed -## See http://ros.org/doc/api/catkin/html/user_guide/setup_dot_py.html -# catkin_python_setup() - -################################################ -## Declare ROS messages, services and actions ## -################################################ - -## To declare and build messages, services or actions from within this -## package, follow these steps: -## * Let MSG_DEP_SET be the set of packages whose message types you use in -## your messages/services/actions (e.g. std_msgs, actionlib_msgs, ...). -## * In the file package.xml: -## * add a build_depend tag for "message_generation" -## * add a build_depend and a exec_depend tag for each package in MSG_DEP_SET -## * If MSG_DEP_SET isn't empty the following dependency has been pulled in -## but can be declared for certainty nonetheless: -## * add a exec_depend tag for "message_runtime" -## * In this file (CMakeLists.txt): -## * add "message_generation" and every package in MSG_DEP_SET to -## find_package(catkin REQUIRED COMPONENTS ...) -## * add "message_runtime" and every package in MSG_DEP_SET to -## catkin_package(CATKIN_DEPENDS ...) -## * uncomment the add_*_files sections below as needed -## and list every .msg/.srv/.action file to be processed -## * uncomment the generate_messages entry below -## * add every package in MSG_DEP_SET to generate_messages(DEPENDENCIES ...) - -## Generate messages in the 'msg' folder -add_message_files( - FILES - Waypoint.msg -) - -## Generate services in the 'srv' folder -# add_service_files( -# FILES -# Service1.srv -# Service2.srv -# ) - -## Generate actions in the 'action' folder -# add_action_files( -# FILES -# Action1.action -# Action2.action -# ) - -## Generate added messages and services with any dependencies listed here -generate_messages( - DEPENDENCIES - std_msgs - geometry_msgs -) - -################################################ -## Declare ROS dynamic reconfigure parameters ## -################################################ - -## To declare and build dynamic reconfigure parameters within this -## package, follow these steps: -## * In the file package.xml: -## * add a build_depend and a exec_depend tag for "dynamic_reconfigure" -## * In this file (CMakeLists.txt): -## * add "dynamic_reconfigure" to -## find_package(catkin REQUIRED COMPONENTS ...) -## * uncomment the "generate_dynamic_reconfigure_options" section below -## and list every .cfg file to be processed - -## Generate dynamic reconfigure parameters in the 'cfg' folder -# generate_dynamic_reconfigure_options( -# cfg/DynReconf1.cfg -# cfg/DynReconf2.cfg -# ) - -################################### -## catkin specific configuration ## -################################### -## The catkin_package macro generates cmake config files for your package -## Declare things to be passed to dependent projects -## INCLUDE_DIRS: uncomment this if your package contains header files -## LIBRARIES: libraries you create in this project that dependent projects also need -## CATKIN_DEPENDS: catkin_packages dependent projects also need -## DEPENDS: system dependencies of this project that dependent projects also need -catkin_package( - INCLUDE_DIRS include - LIBRARIES simulator_utils - CATKIN_DEPENDS message_runtime - # CATKIN_DEPENDS roscpp std_msgs - # DEPENDS system_lib -) - -########### -## Build ## -########### - -## Specify additional locations of header files -## Your package locations should be listed before other locations -include_directories( - include/${PROJECT_NAME} - ${catkin_INCLUDE_DIRS} -) - -## Declare a C++ library -add_library(${PROJECT_NAME} - include/${PROJECT_NAME} - src/simulator_utils.cpp - src/Drone.cpp -) - -## Add cmake target dependencies of the library -## as an example, code may need to be generated before libraries -## either from message generation or dynamic reconfigure -# add_dependencies(${PROJECT_NAME} ${${PROJECT_NAME}_EXPORTED_TARGETS} ${catkin_EXPORTED_TARGETS}) - -## Declare a C++ executable -## With catkin_make all packages are built within a single CMake context -## The recommended prefix ensures that target names across packages don't collide -# add_executable(${PROJECT_NAME}_node src/simulator_utils_node.cpp) - -## Rename C++ executable without prefix -## The above recommended prefix causes long target names, the following renames the -## target back to the shorter version for ease of user use -## e.g. "rosrun someones_pkg node" instead of "rosrun someones_pkg someones_pkg_node" -# set_target_properties(${PROJECT_NAME}_node PROPERTIES OUTPUT_NAME node PREFIX "") - -## Add cmake target dependencies of the executable -## same as for the library above -# add_dependencies(${PROJECT_NAME}_node ${${PROJECT_NAME}_EXPORTED_TARGETS} ${catkin_EXPORTED_TARGETS}) - -## Specify libraries to link a library or executable target against -# target_link_libraries(${PROJECT_NAME}_node -# ${catkin_LIBRARIES} -# ) - -############# -## Install ## -############# - -# all install targets should use catkin DESTINATION variables -# See http://ros.org/doc/api/catkin/html/adv_user_guide/variables.html - -## Mark executable scripts (Python etc.) for installation -## in contrast to setup.py, you can choose the destination -# catkin_install_python(PROGRAMS -# scripts/my_python_script -# DESTINATION ${CATKIN_PACKAGE_BIN_DESTINATION} -# ) - -## Mark executables for installation -## See http://docs.ros.org/melodic/api/catkin/html/howto/format1/building_executables.html -# install(TARGETS ${PROJECT_NAME}_node -# RUNTIME DESTINATION ${CATKIN_PACKAGE_BIN_DESTINATION} -# ) - -## Mark libraries for installation -## See http://docs.ros.org/melodic/api/catkin/html/howto/format1/building_libraries.html -# install(TARGETS ${PROJECT_NAME} -# ARCHIVE DESTINATION ${CATKIN_PACKAGE_LIB_DESTINATION} -# LIBRARY DESTINATION ${CATKIN_PACKAGE_LIB_DESTINATION} -# RUNTIME DESTINATION ${CATKIN_GLOBAL_BIN_DESTINATION} -# ) - -## Mark cpp header files for installation -# install(DIRECTORY include/${PROJECT_NAME}/ -# DESTINATION ${CATKIN_PACKAGE_INCLUDE_DESTINATION} -# FILES_MATCHING PATTERN "*.h" -# PATTERN ".svn" EXCLUDE -# ) - -## Mark other files for installation (e.g. launch and bag files, etc.) -# install(FILES -# # myfile1 -# # myfile2 -# DESTINATION ${CATKIN_PACKAGE_SHARE_DESTINATION} -# ) - -############# -## Testing ## -############# - -## Add gtest based cpp test target and link libraries -# catkin_add_gtest(${PROJECT_NAME}-test test/test_simulator_utils.cpp) -# if(TARGET ${PROJECT_NAME}-test) -# target_link_libraries(${PROJECT_NAME}-test ${PROJECT_NAME}) -# endif() - -## Add folders to be run by python nosetests -# catkin_add_nosetests(test) diff --git a/simulator_utils/include/simulator_utils/Drone.h b/simulator_utils/include/simulator_utils/Drone.h deleted file mode 100644 index b666ff9..0000000 --- a/simulator_utils/include/simulator_utils/Drone.h +++ /dev/null @@ -1,28 +0,0 @@ -// -// Created by malintha on 10/14/20. -// -#ifndef SIMULATOR_UTILS_DRONE_H -#define SIMULATOR_UTILS_DRONE_H - -//#include -#include "ros/ros.h" -#include "simulator_utils/Waypoint.h" -#include "ros/console.h" - -//using namespace std; - -class Drone { - ros::Subscriber state_sub; - ros::NodeHandle nh; - void state_cb(const simulator_utils::WaypointConstPtr& wp); - -public: - int id; - simulator_utils::Waypoint state; - Drone(int id, const ros::NodeHandle &n); - simulator_utils::Waypoint get_state() const; - - -}; - -#endif \ No newline at end of file diff --git a/simulator_utils/include/simulator_utils/simulator_utils.h b/simulator_utils/include/simulator_utils/simulator_utils.h deleted file mode 100644 index 16f2e98..0000000 --- a/simulator_utils/include/simulator_utils/simulator_utils.h +++ /dev/null @@ -1,64 +0,0 @@ -#pragma once - -#include - -using namespace Eigen; - -typedef struct { - Vector3d position; - Matrix3d R; - Vector3d omega; - Vector3d velocity; - double h; -} init_vals_t; - -typedef struct { - double gravity; - double mass; - Matrix3d J; - Matrix3d J_inv; - double F; - Vector3d M; -} params_t; - -typedef struct { - Vector3d position; - Vector3d velocity; - Vector3d acceleration; - Matrix3d R; - Vector3d omega; -} state_space_t; - -typedef struct { - Vector3d x; - Vector3d b1; -} desired_state_t; - -typedef struct -{ - double kx; - double kv; - double kr; - double komega; -} gains_t; - -typedef struct { - double F; - Vector3d M; -} control_out_t; - -typedef struct { - Vector3d position; - Vector3d velocity; - Vector3d acceleration; - Vector3d jerk; -} opt_t; - -namespace simulator_utils { - Matrix3d hat(Vector3d v); - Vector3d R2RPY(Matrix3d R); - Vector3d ned_nwu_rotation(Vector3d v); - Matrix3d ned_nwu_rotation(Matrix3d m); - Vector3d vee(Matrix3d mat); - -} diff --git a/simulator_utils/msg/Waypoint.msg b/simulator_utils/msg/Waypoint.msg deleted file mode 100644 index 90e3c87..0000000 --- a/simulator_utils/msg/Waypoint.msg +++ /dev/null @@ -1,4 +0,0 @@ -# A waypoint message type for the drones to follow -geometry_msgs/Point position -geometry_msgs/Point velocity -geometry_msgs/Point acceleration \ No newline at end of file diff --git a/simulator_utils/package.xml b/simulator_utils/package.xml deleted file mode 100644 index ee70fa7..0000000 --- a/simulator_utils/package.xml +++ /dev/null @@ -1,66 +0,0 @@ - - - simulator_utils - 0.0.0 - The simulator_utils package - - - - - malintha - - - - - - TODO - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - catkin - roscpp - std_msgs - roscpp - std_msgs - roscpp - std_msgs - message_generation - message_runtime - - - - - - - diff --git a/simulator_utils/src/Drone.cpp b/simulator_utils/src/Drone.cpp deleted file mode 100644 index 8ecf9e4..0000000 --- a/simulator_utils/src/Drone.cpp +++ /dev/null @@ -1,31 +0,0 @@ -// -// Created by malintha on 10/14/20. -// -#include -#include "Drone.h" - -using namespace std; - -simulator_utils::Waypoint Drone::get_state() const { - // ROS_DEBUG_STREAM("Robot: "<state.position.x<<" " << this->state.position.y); - return this->state; -} - -void Drone::state_cb(const simulator_utils::WaypointConstPtr &wp) { - this->state.position = wp->position; - this->state.velocity = wp->velocity; - this->state.acceleration = wp->acceleration; -} - -// TODO: pass the topic prefix as a parameter -Drone::Drone(int id, const ros::NodeHandle &n):id(id), nh(n) { - - stringstream ss; - ss << "/robot_"<state_sub = nh.subscribe(ss.str(), 10, - &Drone::state_cb, - this); - - ROS_DEBUG_STREAM("Robot: "<id<<" Waiting for quadrotor states."); - ros::topic::waitForMessage(ss.str(), ros::Duration(3)); -} \ No newline at end of file diff --git a/simulator_utils/src/simulator_utils.cpp b/simulator_utils/src/simulator_utils.cpp deleted file mode 100644 index 548d576..0000000 --- a/simulator_utils/src/simulator_utils.cpp +++ /dev/null @@ -1,45 +0,0 @@ -#include "simulator_utils.h" -#include - -Matrix3d simulator_utils::hat(Vector3d v) -{ - Matrix3d hat_map(3, 3); - hat_map << 0, -v(2), v(1), - v(2), 0, -v(0), - -v(1), v(0), 0; - return hat_map; -} - -Vector3d simulator_utils::vee(Matrix3d mat) -{ - Vector3d vee_vec(mat(2, 1), mat(0, 2),mat(1, 0)); - return vee_vec; -} - -Vector3d simulator_utils::R2RPY(Matrix3d R) -{ - Vector3d rpy; - rpy << atan2(R(2, 1), R(2, 2)), - atan2(-R(2, 0), sqrt(R(2, 1) * R(2, 1) + R(2, 2) * R(2, 2))), - atan2(R(1, 0), R(0, 0)); - return rpy; -} - -Vector3d simulator_utils::ned_nwu_rotation(Vector3d v) -{ - Matrix3d rot; - rot << 1, 0, 0, - 0, -1, 0, - 0, 0, -1; - return rot * v; -} - -Matrix3d simulator_utils::ned_nwu_rotation(Matrix3d m) -{ - Matrix3d rot; - rot << 1, 0, 0, - 0, -1, 0, - 0, 0, -1; - return rot * m; -} - diff --git a/multi_uav_simulator/src/DynamicsProvider.cpp b/src/dynamics_provider.cpp similarity index 86% rename from multi_uav_simulator/src/DynamicsProvider.cpp rename to src/dynamics_provider.cpp index 5958df6..33540a3 100644 --- a/multi_uav_simulator/src/DynamicsProvider.cpp +++ b/src/dynamics_provider.cpp @@ -1,11 +1,25 @@ -// -// Created by malintha on 7/31/18. -// +/* -#include "DynamicsProvider.h" +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. + +*/ + +#include "dynamics_provider.h" #include #include -#include +// #include "rcutils/logging.h" /** * The equations and state_space use NED inertial frame. Therefore, the initial values are needed to be diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp new file mode 100644 index 0000000..a4f325d --- /dev/null +++ b/src/quadrotor.cpp @@ -0,0 +1,257 @@ +/* +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. +*/ + +#include "quadrotor.h" +#include +#include +#include "rclcpp/logging.hpp" +#include "simulator_utils/simulator_utils.h" + + +void Quadrotor::move(const desired_state_t &d_state) { + control_out_t control = controller->get_control(dynamics->get_state(), d_state); + dynamics->update(control, sim_time); + + // updating the model on rviz + set_state_space(); + send_transform(); + dynamics->reset_dynamics(); + sim_time += dt; +} + +/** + * converts the dynamics state_space (NED) to NWU and stores for the quadrotor + * This is for broadcasting the transformation +*/ +void Quadrotor::set_state_space() { + state_space_t ss = dynamics->get_state(); + state_space.position = simulator_utils::ned_nwu_rotation(ss.position); + state_space.R = simulator_utils::ned_nwu_rotation(ss.R); + state_space.velocity = simulator_utils::ned_nwu_rotation(ss.velocity); + state_space.omega = simulator_utils::ned_nwu_rotation(ss.omega); +} + +// void Quadrotor::send_transform() { +// static tf::TransformBroadcaster br; +// tf::Transform transform; +// Vector3d position = state_space.position; +// Matrix3d R = state_space.R; +// Vector3d rpy = simulator_utils::R2RPY(R); +// transform.setOrigin(tf::Vector3(position[0], position[1], -position[2])); +// tf::Quaternion q; +// q.setRPY(rpy[0], rpy[1], rpy[2]); +// transform.setRotation(q); +// if(quad_initialized && !isnan(q.x())) +// br.sendTransform(tf::StampedTransform(transform, ros::Time::now(), worldframe, robot_link_name)); +// } + +State Quadrotor::getState() { + return this->m_state; +} + +bool Quadrotor::load_params() { + stringstream ss; + ss << "/robot_" << to_string(this->robot_id); + string robot_name = ss.str(); + double temp; + if (!nh.getParam(ros::names::append(robot_name, "drone/model/gravity"), params.gravity)) return false; + // = temp; + vector J_; + if (!nh.getParam(ros::names::append(robot_name, "drone/model/J"), J_)) return false; + // Matrix3d J; + params.J << J_[0], 0, 0, + 0, J_[1], 0, + 0, 0, J_[2]; + params.J_inv = params.J.inverse(); + if (!nh.getParam(ros::names::append(robot_name, "drone/model/m"), params.mass)) return false; + // = temp; + params.F = 0; + Vector3d M(0, 0, 0); + params.M = M; + vector gains_; + if (!nh.getParam(ros::names::append(robot_name, "drone/controller/gains"), gains_)) return false; + this->gains = {gains_[0], gains_[1], gains_[2], gains_[3]}; + + ROS_DEBUG_STREAM("Loaded control parameters"); + return true; +} + +bool Quadrotor::load_init_vals() { + vector position, vel, R, omega; + stringstream ss; + ss << "/robot_" << to_string(this->robot_id); + string robot_name = ss.str(); + if (!nh.getParam(ros::names::append(robot_name, "position"), position)) return false; + if (!nh.getParam(ros::names::append(robot_name, "velocity"), vel)) return false; + if (!nh.getParam(ros::names::append(robot_name, "rotation"), R)) return false; + if (!nh.getParam(ros::names::append(robot_name, "omega"), omega)) return false; + if (!nh.getParam("/frame/fixed", worldframe)) return false; + if (!nh.getParam("/frame/prefix", localframe)) return false; + init_vals.position = Vector3d(position.data()); + init_vals.velocity = Vector3d(vel.data()); + init_vals.R = Matrix3d(R.data()); + init_vals.omega = Vector3d(omega.data()); + + this->x0.position = simulator_utils::ned_nwu_rotation(init_vals.position); + this->x0.velocity = simulator_utils::ned_nwu_rotation(init_vals.velocity); + this->xd0.position = this->x0.position; + this->target_pos = simulator_utils::ned_nwu_rotation(init_vals.position); + ROS_DEBUG_STREAM("Loaded the drone initialization values"); + return true; +} + +void Quadrotor::desired_pos_cb(const geometry_msgs::Point &pt) { + Vector3d xd = {pt.x, pt.y, pt.z}; + Vector3d b1d(1, 0, 0); + this->dss = {xd, b1d}; + +} + + +// xd should be in NED frame and so does dynamics and controller. +void Quadrotor::iteration(const ros::TimerEvent &e) { + this->move(this->dss); + this->publish_path(); + this->publish_state(); +} + +// void Quadrotor::publish_path() { +// constexpr int arrowLength = 0.05; +// Vector3d x = this->dynamics->get_state().position; +// x[1] = -x[1]; +// geometry_msgs::Point p; +// if(!isnan(x[0]) && !isnan(x[1])) { +// p.x = x[0]; +// p.y = x[1]; +// p.z = x[2]; +// quad_initialized = true; +// } +// else +// { +// p.x = 0; +// p.y = 0; +// p.z = 0; +// } + +// m.points.push_back(p); +// if (m.points.size() > 1000) +// m.points.erase(m.points.begin()); + +// g.pose.position.x = this->target_pos[0]; +// g.pose.position.y = -this->target_pos[1]; +// g.pose.position.z = this->target_pos[2]; +// g.pose.orientation.x = 0.0; +// g.pose.orientation.y = 0.0; +// g.pose.orientation.z = 0.0; +// g.pose.orientation.w = 1.0; + +// goal_pub.publish(g); +// marker_pub.publish(m); +// } + +void Quadrotor::run() { + ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration_rhp, this); + ros::spin(); +} + +// void Quadrotor::publish_state() { +// simulator_utils::Waypoint wp; +// geometry_msgs::Point p,v; +// state_space_t ned_state = this->dynamics->get_state(); +// p.x = ned_state.position[0]; +// p.y = ned_state.position[1]; +// p.z = ned_state.position[2]; +// v.x = ned_state.velocity[0]; +// v.y = ned_state.velocity[1]; +// v.z = ned_state.velocity[2]; +// wp.position = p; +// wp.velocity = v; +// wp.acceleration.x = wp.acceleration.y = wp.acceleration.z = 0; +// this->state_pub.publish(wp); +// } + +// bool Quadrotor::initialize(double dt_) { +// m_state = State::Idle; +// // load drone params +// if (!load_params()) { +// RCLCPP_ERROR(this->get_logger(), "Could not load the drone parameters"); +// return false; +// } +// // load init params +// if (!load_init_vals()) { +// RCLCPP_ERROR(this->get_logger(), "Could not load the drone initial values"); +// return false; +// } + +// std::stringstream ss; +// ss << localframe << robot_id; +// robot_link_name = ss.str(); + +// // set initial values +// state_space.position = init_vals.position; +// state_space.velocity = init_vals.velocity; +// state_space.R = init_vals.R; +// state_space.omega = init_vals.omega; + +// dynamics = new DynamicsProvider(params, init_vals); +// controller = new ControllerImpl(params, init_vals, gains, dt_); + +// this->setState(State::Autonomous); +// initPaths(); + +// desired_state_sub = this->create_subscription( +// "desired_state", 10, std::bind(&Quadrotor::desired_pos_cb, this, std::placeholders::_1)); +// state_pub = this->create_publisher("current_state", 10); +// RCLCPP_INFO(this->get_logger(), "Drone initialized %d", robot_id); +// RCLCPP_INFO(this->get_logger(), "Desired state subscriber topic: robot_%d/desired_state", robot_id); +// RCLCPP_INFO(this->get_logger(), "State publisher topic: robot_%d/current_state", robot_id); + +// this->set_init_target = false; +// return true; +// } + +void Quadrotor::setState(State m_state_) { + this->m_state = m_state_; +} + +Quadrotor::Quadrotor(int robot_id, double frequency) + : Node("quadrotor_" + std::to_string(robot_id)), robot_id(robot_id), frequency(frequency) { + sim_time = 0; + this->dt = 1 / frequency; + // this->initialize(1 / frequency); + this->u << 0, 0, 0; + + // while (marker_pub->get_subscription_count() < 1) { + // RCLCPP_INFO(this->get_logger(), "Waiting for subscriber"); + // std::this_thread::sleep_for(std::chrono::seconds(1)); + // } +} + +int main(int argc, char **argv) { + + int robot_id = std::atoi(argv[1]); + double frequency = (double)std::atof(argv[2]); + + RCLCPP_DEBUG_STREAM("initializing : " << robot_id << endl); + rclcpp::init(argc, argv); + stringstream ss; + // ss << "robot_"<(ss.str()); + Quadrotor quad(robot_id, frequency); + quad.run(); + + return 0; +} \ No newline at end of file From 9df7c36aa90fb5ff9fbcb3e05a0e1ef1bcbd1b90 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Tue, 4 Jun 2024 17:16:09 +0530 Subject: [PATCH 02/24] move quadrotor code to quadrotor.hpp --- .../mavswarm2/{quadrotor.h => quadrotor.hpp} | 55 ++++- include/mavswarm2/trajectory_t.h | 1 - readme.md | 2 +- src/quadrotor.cpp | 192 ++++++++---------- 4 files changed, 131 insertions(+), 119 deletions(-) rename include/mavswarm2/{quadrotor.h => quadrotor.hpp} (64%) diff --git a/include/mavswarm2/quadrotor.h b/include/mavswarm2/quadrotor.hpp similarity index 64% rename from include/mavswarm2/quadrotor.h rename to include/mavswarm2/quadrotor.hpp index 2e9aa11..5e8b827 100644 --- a/include/mavswarm2/quadrotor.h +++ b/include/mavswarm2/quadrotor.hpp @@ -47,17 +47,50 @@ using namespace std; class Quadrotor : public rclcpp::Node { public: - Quadrotor(int robot_id, double frequency, std::shared_ptr); - void move(const desired_state_t &d_state); - void setState(State m_state); - State getState(); - - bool initialize(double dt); - - void desired_pos_cb(const geometry_msgs::msg::Point &pt); - - void iteration(); - void run(); + Quadrotor::Quadrotor(int robot_id, double frequency) + : robot_id(robot_id), frequency(frequency), nh(n) { + sim_time = 0; + this->dt = 1/frequency; + // this->initialize(1 / frequency); + this->u << 0,0,0; + + // while (marker_pub.getNumSubscribers() < 1) { + // RCLCPP_INFO("Waiting for subscriber"); + // ros::Duration(1).sleep(); + // } +} + + void Quadrotor::move(const desired_state_t &d_state) { + control_out_t control = controller->get_control(dynamics->get_state(), d_state); + dynamics->update(control, sim_time); + + // updating the model on rviz + set_state_space(); + send_transform(); + dynamics->reset_dynamics(); + sim_time += dt; +} + void Quadrotor::setState(State m_state_) { + this->m_state = m_state_; +} + + // State getState(); + + // bool initialize(double dt); + + // void desired_pos_cb(const geometry_msgs::msg::Point &pt); + + // xd should be in NED frame and so does dynamics and controller. + void Quadrotor::iteration(const ros::TimerEvent &e) { + this->move(this->dss); + // this->publish_path(); + // this->publish_state(); + } + + void Quadrotor::run() { + // ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration, this); + ros::spin(); + } private: diff --git a/include/mavswarm2/trajectory_t.h b/include/mavswarm2/trajectory_t.h index 02a8be3..18823df 100644 --- a/include/mavswarm2/trajectory_t.h +++ b/include/mavswarm2/trajectory_t.h @@ -21,7 +21,6 @@ limitations under the License. #include #include "std_msgs/msg/float32_multi_array.hpp" - using namespace std; using namespace Eigen; diff --git a/readme.md b/readme.md index a35633a..ac41a3f 100644 --- a/readme.md +++ b/readme.md @@ -1,4 +1,4 @@ -# Mavswarm: A Lightweight Multi-Aerial Vehicle Simulator +# Mavswarm2: Under Development... Mavswarm is a lightweight and fast Multi-Aerial Vehicle simulator based on ROS (Robot Operating System). It supports simulating heterogenous quadrotor swarms of upto 10 robots on a single desktop with physics. Mavswarm also supports quadrotor control, trajectory optimization and receding horizon planning (RHP). Currently, the internal controller uses the Lee's geometric tracking controller [3] and it is tuned for two different quadrotor models out of the box. In addition you can extend the swarm simulation with more quadrotor models by simply adding the new quadrotor model parameters through a yaml configuration file. diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index a4f325d..00b0155 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -14,35 +14,26 @@ See the License for the specific language governing permissions and limitations under the License. */ -#include "quadrotor.h" -#include -#include +#include "quadrotor.hpp" +#include "rclcpp/rclcpp.hpp" +// #include +// #include #include "rclcpp/logging.hpp" -#include "simulator_utils/simulator_utils.h" +// #include "simulator_utils/simulator_utils.h" -void Quadrotor::move(const desired_state_t &d_state) { - control_out_t control = controller->get_control(dynamics->get_state(), d_state); - dynamics->update(control, sim_time); - - // updating the model on rviz - set_state_space(); - send_transform(); - dynamics->reset_dynamics(); - sim_time += dt; -} /** * converts the dynamics state_space (NED) to NWU and stores for the quadrotor * This is for broadcasting the transformation */ -void Quadrotor::set_state_space() { - state_space_t ss = dynamics->get_state(); - state_space.position = simulator_utils::ned_nwu_rotation(ss.position); - state_space.R = simulator_utils::ned_nwu_rotation(ss.R); - state_space.velocity = simulator_utils::ned_nwu_rotation(ss.velocity); - state_space.omega = simulator_utils::ned_nwu_rotation(ss.omega); -} +// void Quadrotor::set_state_space() { +// state_space_t ss = dynamics->get_state(); +// state_space.position = simulator_utils::ned_nwu_rotation(ss.position); +// state_space.R = simulator_utils::ned_nwu_rotation(ss.R); +// state_space.velocity = simulator_utils::ned_nwu_rotation(ss.velocity); +// state_space.omega = simulator_utils::ned_nwu_rotation(ss.omega); +// } // void Quadrotor::send_transform() { // static tf::TransformBroadcaster br; @@ -58,75 +49,75 @@ void Quadrotor::set_state_space() { // br.sendTransform(tf::StampedTransform(transform, ros::Time::now(), worldframe, robot_link_name)); // } -State Quadrotor::getState() { - return this->m_state; -} +// State Quadrotor::getState() { +// return this->m_state; +// } -bool Quadrotor::load_params() { - stringstream ss; - ss << "/robot_" << to_string(this->robot_id); - string robot_name = ss.str(); - double temp; - if (!nh.getParam(ros::names::append(robot_name, "drone/model/gravity"), params.gravity)) return false; - // = temp; - vector J_; - if (!nh.getParam(ros::names::append(robot_name, "drone/model/J"), J_)) return false; - // Matrix3d J; - params.J << J_[0], 0, 0, - 0, J_[1], 0, - 0, 0, J_[2]; - params.J_inv = params.J.inverse(); - if (!nh.getParam(ros::names::append(robot_name, "drone/model/m"), params.mass)) return false; - // = temp; - params.F = 0; - Vector3d M(0, 0, 0); - params.M = M; - vector gains_; - if (!nh.getParam(ros::names::append(robot_name, "drone/controller/gains"), gains_)) return false; - this->gains = {gains_[0], gains_[1], gains_[2], gains_[3]}; - - ROS_DEBUG_STREAM("Loaded control parameters"); - return true; -} - -bool Quadrotor::load_init_vals() { - vector position, vel, R, omega; - stringstream ss; - ss << "/robot_" << to_string(this->robot_id); - string robot_name = ss.str(); - if (!nh.getParam(ros::names::append(robot_name, "position"), position)) return false; - if (!nh.getParam(ros::names::append(robot_name, "velocity"), vel)) return false; - if (!nh.getParam(ros::names::append(robot_name, "rotation"), R)) return false; - if (!nh.getParam(ros::names::append(robot_name, "omega"), omega)) return false; - if (!nh.getParam("/frame/fixed", worldframe)) return false; - if (!nh.getParam("/frame/prefix", localframe)) return false; - init_vals.position = Vector3d(position.data()); - init_vals.velocity = Vector3d(vel.data()); - init_vals.R = Matrix3d(R.data()); - init_vals.omega = Vector3d(omega.data()); - - this->x0.position = simulator_utils::ned_nwu_rotation(init_vals.position); - this->x0.velocity = simulator_utils::ned_nwu_rotation(init_vals.velocity); - this->xd0.position = this->x0.position; - this->target_pos = simulator_utils::ned_nwu_rotation(init_vals.position); - ROS_DEBUG_STREAM("Loaded the drone initialization values"); - return true; -} - -void Quadrotor::desired_pos_cb(const geometry_msgs::Point &pt) { - Vector3d xd = {pt.x, pt.y, pt.z}; - Vector3d b1d(1, 0, 0); - this->dss = {xd, b1d}; - -} +// bool Quadrotor::load_params() { +// stringstream ss; +// ss << "/robot_" << to_string(this->robot_id); +// string robot_name = ss.str(); +// double temp; +// if (!nh.getParam(ros::names::append(robot_name, "drone/model/gravity"), params.gravity)) return false; +// // = temp; +// vector J_; +// if (!nh.getParam(ros::names::append(robot_name, "drone/model/J"), J_)) return false; +// // Matrix3d J; +// params.J << J_[0], 0, 0, +// 0, J_[1], 0, +// 0, 0, J_[2]; +// params.J_inv = params.J.inverse(); +// if (!nh.getParam(ros::names::append(robot_name, "drone/model/m"), params.mass)) return false; +// // = temp; +// params.F = 0; +// Vector3d M(0, 0, 0); +// params.M = M; +// vector gains_; +// if (!nh.getParam(ros::names::append(robot_name, "drone/controller/gains"), gains_)) return false; +// this->gains = {gains_[0], gains_[1], gains_[2], gains_[3]}; + +// ROS_DEBUG_STREAM(this->logger, "Loaded control parameters"); +// return true; +// } + +// bool Quadrotor::load_init_vals() { +// vector position, vel, R, omega; +// stringstream ss; +// ss << "/robot_" << to_string(this->robot_id); +// string robot_name = ss.str(); +// if (!nh.getParam(ros::names::append(robot_name, "position"), position)) return false; +// if (!nh.getParam(ros::names::append(robot_name, "velocity"), vel)) return false; +// if (!nh.getParam(ros::names::append(robot_name, "rotation"), R)) return false; +// if (!nh.getParam(ros::names::append(robot_name, "omega"), omega)) return false; +// if (!nh.getParam("/frame/fixed", worldframe)) return false; +// if (!nh.getParam("/frame/prefix", localframe)) return false; +// init_vals.position = Vector3d(position.data()); +// init_vals.velocity = Vector3d(vel.data()); +// init_vals.R = Matrix3d(R.data()); +// init_vals.omega = Vector3d(omega.data()); + +// this->x0.position = simulator_utils::ned_nwu_rotation(init_vals.position); +// this->x0.velocity = simulator_utils::ned_nwu_rotation(init_vals.velocity); +// this->xd0.position = this->x0.position; +// this->target_pos = simulator_utils::ned_nwu_rotation(init_vals.position); +// ROS_DEBUG_STREAM(this->logger, "Loaded the drone initialization values"); +// return true; +// } + +// void Quadrotor::desired_pos_cb(const geometry_msgs::Point &pt) { +// Vector3d xd = {pt.x, pt.y, pt.z}; +// Vector3d b1d(1, 0, 0); +// this->dss = {xd, b1d}; + +// } // xd should be in NED frame and so does dynamics and controller. -void Quadrotor::iteration(const ros::TimerEvent &e) { - this->move(this->dss); - this->publish_path(); - this->publish_state(); -} +// void Quadrotor::iteration(const ros::TimerEvent &e) { +// this->move(this->dss); +// this->publish_path(); +// this->publish_state(); +// } // void Quadrotor::publish_path() { // constexpr int arrowLength = 0.05; @@ -162,10 +153,10 @@ void Quadrotor::iteration(const ros::TimerEvent &e) { // marker_pub.publish(m); // } -void Quadrotor::run() { - ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration_rhp, this); - ros::spin(); -} +// void Quadrotor::run() { +// ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration_rhp, this); +// ros::spin(); +// } // void Quadrotor::publish_state() { // simulator_utils::Waypoint wp; @@ -223,29 +214,18 @@ void Quadrotor::run() { // return true; // } -void Quadrotor::setState(State m_state_) { - this->m_state = m_state_; -} +// void Quadrotor::setState(State m_state_) { +// this->m_state = m_state_; +// } -Quadrotor::Quadrotor(int robot_id, double frequency) - : Node("quadrotor_" + std::to_string(robot_id)), robot_id(robot_id), frequency(frequency) { - sim_time = 0; - this->dt = 1 / frequency; - // this->initialize(1 / frequency); - this->u << 0, 0, 0; - // while (marker_pub->get_subscription_count() < 1) { - // RCLCPP_INFO(this->get_logger(), "Waiting for subscriber"); - // std::this_thread::sleep_for(std::chrono::seconds(1)); - // } -} int main(int argc, char **argv) { int robot_id = std::atoi(argv[1]); double frequency = (double)std::atof(argv[2]); - - RCLCPP_DEBUG_STREAM("initializing : " << robot_id << endl); + + RCLCPP_DEBUG_STREAM(this->logger, "initializing : " << robot_id << endl); rclcpp::init(argc, argv); stringstream ss; // ss << "robot_"< Date: Wed, 5 Jun 2024 11:58:12 +0530 Subject: [PATCH 03/24] ros2 building the single drone boilerplate --- include/mavswarm2/dynamics_provider.h | 2 +- include/mavswarm2/quadrotor.hpp | 75 ++++++++++++++------------- include/mavswarm2/trajectory_t.h | 12 ++--- src/quadrotor.cpp | 7 +-- 4 files changed, 51 insertions(+), 45 deletions(-) diff --git a/include/mavswarm2/dynamics_provider.h b/include/mavswarm2/dynamics_provider.h index 918348c..d98e7e3 100644 --- a/include/mavswarm2/dynamics_provider.h +++ b/include/mavswarm2/dynamics_provider.h @@ -19,7 +19,7 @@ limitations under the License. #include // #include "tf2/transform_datatypes.h" -#include "simulator_utils/simulator_utils.h" +#include "simulator_utils/types.h" #include using namespace Eigen; diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 5e8b827..376dcb1 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -47,8 +47,8 @@ using namespace std; class Quadrotor : public rclcpp::Node { public: - Quadrotor::Quadrotor(int robot_id, double frequency) - : robot_id(robot_id), frequency(frequency), nh(n) { + Quadrotor(int robot_id, double frequency) + :Node("robot_"+to_string(robot_id)), frequency(frequency),robot_id(robot_id) { sim_time = 0; this->dt = 1/frequency; // this->initialize(1 / frequency); @@ -60,17 +60,7 @@ class Quadrotor : public rclcpp::Node { // } } - void Quadrotor::move(const desired_state_t &d_state) { - control_out_t control = controller->get_control(dynamics->get_state(), d_state); - dynamics->update(control, sim_time); - - // updating the model on rviz - set_state_space(); - send_transform(); - dynamics->reset_dynamics(); - sim_time += dt; -} - void Quadrotor::setState(State m_state_) { + void setState(State m_state_) { this->m_state = m_state_; } @@ -81,16 +71,11 @@ class Quadrotor : public rclcpp::Node { // void desired_pos_cb(const geometry_msgs::msg::Point &pt); // xd should be in NED frame and so does dynamics and controller. - void Quadrotor::iteration(const ros::TimerEvent &e) { - this->move(this->dss); - // this->publish_path(); - // this->publish_state(); - } - void Quadrotor::run() { - // ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration, this); - ros::spin(); - } + // void run() { + // // ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration, this); + // ros::spin(); + // } private: @@ -116,23 +101,43 @@ class Quadrotor : public rclcpp::Node { params_t params; init_vals_t init_vals; - rclcpp::Publisher::SharedPtr marker_pub, goal_pub, state_pub; - visualization_msgs::msg::Marker m, g; - std::vector points; - rclcpp::Subscription::SharedPtr desired_state_sub; - vector positions; + // rclcpp::Publisher::SharedPtr marker_pub, goal_pub, state_pub; + // visualization_msgs::msg::Marker m, g; + // std::vector points; + // rclcpp::Subscription::SharedPtr desired_state_sub; + // vector positions; - bool quad_initialized = false; + // bool quad_initialized = false; // rclcpp::TimerBase::SharedPtr timer; - void initPaths(); - void set_state_space(); - bool load_params(); - bool load_init_vals(); - void send_transform(); - void publish_path(); - void publish_state(); + // void initPaths(); + // void set_state_space(); + // bool load_params(); + // bool load_init_vals(); + // void send_transform(); + // void publish_path(); + // void publish_state(); + + void move(const desired_state_t &d_state) { + control_out_t control = controller->get_control(dynamics->get_state(), d_state); + // dynamics->update(control, sim_time); + RCLCPP_DEBUG(this->get_logger(), "got control: "); + // updating the model on rviz + // set_state_space(); + // send_transform(); + // dynamics->reset_dynamics(); + sim_time += dt; +} + + void iteration() { + Vector3d xd = simulator_utils::ned_nwu_rotation(Vector3d{0,0,0}); + Vector3d b1d(1, 0, 0); + desired_state_t dss = {xd, b1d}; + this->move(dss); + // this->publish_path(); + // this->publish_state(); + } }; diff --git a/include/mavswarm2/trajectory_t.h b/include/mavswarm2/trajectory_t.h index 18823df..d24dbbb 100644 --- a/include/mavswarm2/trajectory_t.h +++ b/include/mavswarm2/trajectory_t.h @@ -32,7 +32,7 @@ struct Trajectory_t { vector yc; vector zc; int D; - Trajectory_t(const std_msgs::Float32MultiArrayConstPtr& coeffs); + Trajectory_t(const std_msgs::msg::Float32MultiArray& coeffs); Trajectory_t(); Vector3d eval(double d); @@ -40,12 +40,12 @@ struct Trajectory_t { Trajectory_t::Trajectory_t() = default; -Trajectory_t::Trajectory_t(const std_msgs::Float32MultiArrayConstPtr& coeffs) { - this->D = coeffs->data.size()/3; +Trajectory_t::Trajectory_t(const std_msgs::msg::Float32MultiArray& coeffs) { + this->D = coeffs.data.size()/3; for(int j=0;jdata[j]); - yc.push_back(coeffs->data[j+ D]); - zc.push_back(coeffs->data[j+ 2*D]); + xc.push_back(coeffs.data[j]); + yc.push_back(coeffs.data[j+ D]); + zc.push_back(coeffs.data[j+ 2*D]); } } diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 00b0155..8b7f1d1 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -224,14 +224,15 @@ int main(int argc, char **argv) { int robot_id = std::atoi(argv[1]); double frequency = (double)std::atof(argv[2]); - - RCLCPP_DEBUG_STREAM(this->logger, "initializing : " << robot_id << endl); + auto logger = rclcpp::get_logger("logger"); + + RCLCPP_DEBUG(logger, "initializing : "); rclcpp::init(argc, argv); stringstream ss; // ss << "robot_"<(ss.str()); Quadrotor quad(robot_id, frequency); - quad.run(); + // quad.run(); return 0; } \ No newline at end of file From d771501b400480797c48a37011c83954bee33aba Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Thu, 6 Jun 2024 22:22:03 +0530 Subject: [PATCH 04/24] causing controllerImpl.h not found --- CMakeLists.txt | 1 + include/mavswarm2/quadrotor.hpp | 2 +- 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/CMakeLists.txt b/CMakeLists.txt index e40f539..74e4ae4 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -25,6 +25,7 @@ add_library(${PROJECT_NAME} SHARED src/quadrotor.cpp ) +add_executable(quadrotor_main src/quadrotor.cpp) ament_target_dependencies(mavswarm2 rclcpp simulator_utils diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 376dcb1..7d92a10 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -19,7 +19,7 @@ limitations under the License. #ifndef PROJECT_QUADROTOR_H #define PROJECT_QUADROTOR_H -#include +#include "controller/controllerImpl.h" #include #include #include From 8d528242d640fe29a563080ba67a5eea63003fc4 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Thu, 6 Jun 2024 21:59:33 +0530 Subject: [PATCH 05/24] adding all dependencies to package itself --- CMakeLists.txt | 41 ++--- .../mavswarm2/controller/controllerImpl.hpp | 140 +++++++++++++++++ include/mavswarm2/definitions.hpp | 83 ++++++++++ include/mavswarm2/dynamics_provider.h | 52 ------- .../mavswarm2/dynamics_provider.hpp | 144 +++++++++++------- include/mavswarm2/quadrotor.hpp | 13 +- .../{trajectory_t.h => trajectory_t.hpp} | 0 include/mavswarm2/{utils.h => utils.hpp} | 0 src/quadrotor.cpp | 4 +- 9 files changed, 344 insertions(+), 133 deletions(-) create mode 100644 include/mavswarm2/controller/controllerImpl.hpp create mode 100644 include/mavswarm2/definitions.hpp delete mode 100644 include/mavswarm2/dynamics_provider.h rename src/dynamics_provider.cpp => include/mavswarm2/dynamics_provider.hpp (80%) rename include/mavswarm2/{trajectory_t.h => trajectory_t.hpp} (100%) rename include/mavswarm2/{utils.h => utils.hpp} (100%) diff --git a/CMakeLists.txt b/CMakeLists.txt index 74e4ae4..0c13c07 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -12,7 +12,7 @@ find_package(ament_cmake REQUIRED) find_package(rclcpp REQUIRED) find_package(simulator_interfaces REQUIRED) find_package(simulator_utils REQUIRED) -find_package(controller REQUIRED) +# find_package(controller REQUIRED) find_package(std_msgs REQUIRED) find_package(geometry_msgs REQUIRED) find_package(sensor_msgs REQUIRED) @@ -27,17 +27,18 @@ add_library(${PROJECT_NAME} SHARED add_executable(quadrotor_main src/quadrotor.cpp) ament_target_dependencies(mavswarm2 - rclcpp - simulator_utils - simulator_interfaces - controller - tf2 - tf2_ros - visualization_msgs - geometry_msgs - std_msgs - ) +rclcpp +simulator_utils +simulator_interfaces +# controller +tf2 +tf2_ros +visualization_msgs +geometry_msgs +std_msgs +) +add_executable(quadrotor src/quadrotor.cpp ) # if(BUILD_TESTING) # find_package(ament_lint_auto REQUIRED) @@ -49,16 +50,18 @@ ament_target_dependencies(mavswarm2 # find_package(message_runtime REQUIRED) +install( + TARGETS ${PROJECT_NAME} + DESTINATION lib/${PROJECT_NAME} + + # EXPORT ${PROJECT_NAME} + # LIBRARY DESTINATION lib + # ARCHIVE DESTINATION lib + # RUNTIME DESTINATION bin + # INCLUDES DESTINATION include +) ament_package() -# install( -# TARGETS ${PROJECT_NAME} -# EXPORT ${PROJECT_NAME} -# LIBRARY DESTINATION lib -# ARCHIVE DESTINATION lib -# RUNTIME DESTINATION bin -# INCLUDES DESTINATION include -# ) # install( # DIRECTORY include/ diff --git a/include/mavswarm2/controller/controllerImpl.hpp b/include/mavswarm2/controller/controllerImpl.hpp new file mode 100644 index 0000000..ce5dada --- /dev/null +++ b/include/mavswarm2/controller/controllerImpl.hpp @@ -0,0 +1,140 @@ + +#ifndef GEOMETRIC_CONTROLLER +#define GEOMETRIC_CONTROLLER + +#pragma once + +#include +#include "simulator_utils/types.h" +#include "definitions.h" +#include + +using namespace Eigen; + +namespace su = simulator_utils; + +class ControllerImpl +{ + +public: + +ControllerImpl(params_t params_, init_vals_t init_vals_, gains_t gains_, double dt_) + :params(std::move(params_)), init_vals(std::move(init_vals_)), gains(gains_), dt(dt_) +{ + // initialize derivative operators + dxdt_ = dxdt(0.05, dt, 1); + d2xdt = dxdt(0.05, dt, 2); + d3xdt = dxdt(0.05, dt, 3); + d4xdt = dxdt(0.05, dt, 4); + + db1dt = dxdt(0.05, dt, 1); + d2b1dt = dxdt(0.05, dt, 2); + + dvdt = dxdt(0.05, dt, 1); + d2vdt = dxdt(0.05, dt, 2); +} + +control_out_t get_control(state_space_t ss, const desired_state_t& desired_s) +{ + // compute the derivatives of desired state + derivatives_t derivatives = get_derivatives(desired_s, ss); + + Vector3d ex = ss.position - desired_s.x; + Vector3d ev = ss.velocity - derivatives.d_xd; + Vector3d ea = derivatives.dv - derivatives.d2_xd; + Vector3d ej = derivatives.d2v - derivatives.d3_xd; + Vector3d e3(0,0,1); + Vector3d A = -gains.kx * ex - gains.kv * ev - params.mass * params.gravity * e3 + + params.mass * derivatives.d2_xd; + + double f = -A.dot(ss.R*e3); + double nA = A.norm(); + + Vector3d b3c = -A/nA; + Vector3d C = b3c.cross(desired_s.b1); + Vector3d b1c = -(1/C.norm())*b3c.cross(C); + Vector3d b2c = C/C.norm(); + Matrix3d Rc; + Rc << b1c, b2c, b3c; + + double nC = C.norm(); + + Vector3d A_1dot = -gains.kx*ev - gains.kv*ea + params.mass*derivatives.d3_xd; + Vector3d b3c_1dot = -A_1dot / nA + (A.dot(A_1dot)/pow(nA,3))*A; + + Vector3d C_1dot = b3c_1dot.cross(desired_s.b1) + b3c.cross(derivatives.db1); + Vector3d b2c_1dot = C/nC - C.dot(C_1dot)/(pow(nC,3))*C; + Vector3d b1c_1dot = b2c_1dot.cross(b3c) + b2c.cross(b3c_1dot); + + Vector3d A_2dot = -gains.kx*ea -gains.kv*ej + params.mass*derivatives.d4_xd; + Vector3d b3c_2dot = -A_2dot/nA + (2.0/pow(nA,3))*A.dot(A_1dot)*A_1dot + + (pow(A_1dot.norm(),2) + A.dot(A_2dot)/(pow(nA,3)))*A - (3.0/pow(nA,5))*(pow(A.dot(A_1dot),2))*A; + + Vector3d C_2dot = b3c_2dot.cross(desired_s.b1) + (b3c.cross(derivatives.d2b1)) + 2*b3c_1dot.cross(derivatives.db1); + + Vector3d b2c_2dot = C_2dot/nC - 2.0/(pow(nC,3))*C.dot(C_1dot)*C_1dot - (((pow(C_2dot.norm(),2) + C.dot(C_2dot)))/pow(nC,3))*C + + (3.0/pow(nC,5))*(pow(C.dot(C_1dot),2))*C; + + Vector3d b1c_2dot = b2c_2dot.cross(b3c) + b2c.cross(b3c_2dot) + 2.0*b2c_1dot.cross(b3c_1dot); + Matrix3d Rc_1dot, Rc_2dot; + Rc_1dot << b1c_1dot, b2c_1dot, b3c_1dot; + Rc_2dot << b1c_2dot, b2c_2dot, b3c_2dot; + + Vector3d omegac = su::vee(Rc.transpose()*Rc_1dot); + Vector3d omegac_1dot = su::vee(Rc.transpose()*Rc_2dot - + su::hat(omegac)*su::hat(omegac)); + + Vector3d er = 2.0*su::vee(Rc.transpose()*ss.R - ss.R.transpose()*Rc); + Vector3d eomega = ss.omega - ss.R.transpose()*Rc*omegac; + + Vector3d M = -gains.kr*er - gains.komega*eomega + ss.omega.cross(params.J*ss.omega) + - params.J*(su::hat(ss.omega)*ss.R.transpose()*Rc*omegac - ss.R.transpose()*Rc*omegac_1dot); + +// ROS_DEBUG_STREAM("\n eR \n"< + +using namespace Eigen; + +// compute the derivative of a signal +struct dxdt { + double tau; + double ts; + double a1; + double a2; + int order; + Vector3d dot; + Vector3d x_d1; + int it = 1; + +dxdt(double tau_, double ts_, int order_) : tau(tau_), ts(ts_), order(order_) +{ + a1 = (2 * tau - ts) / (2 * tau + ts); + a2 = 2 / (2 * tau + ts); + dot = Vector3d(0, 0, 0); + x_d1 = Vector3d(0, 0, 0); +} + +dxdt() {} + +Vector3d calculate(const Vector3d &x) +{ + if (it > order) + { + dot = a1 * dot + a2 * (x - x_d1); + } + it++; + x_d1 = x; + return dot; +} + +}; + +typedef struct +{ + Vector3d ex; + Vector3d ev; + Vector3d ea; + Vector3d ej; + Vector3d er; + Vector3d eomega; +} err_t; + +typedef struct { + // derivatives of desired states + Vector3d d_xd; + Vector3d d2_xd; + Vector3d d3_xd; + Vector3d d4_xd; + Vector3d db1; + Vector3d d2b1; + + // derivatives of current velocity + Vector3d dv; + Vector3d d2v; + +} derivatives_t; + + + diff --git a/include/mavswarm2/dynamics_provider.h b/include/mavswarm2/dynamics_provider.h deleted file mode 100644 index d98e7e3..0000000 --- a/include/mavswarm2/dynamics_provider.h +++ /dev/null @@ -1,52 +0,0 @@ -/* -Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) - -Licensed under the Apache License, Version 2.0 (the "License"); -you may not use this file except in compliance with the License. -You may obtain a copy of the License at - - http://www.apache.org/licenses/LICENSE-2.0 - -Unless required by applicable law or agreed to in writing, software -distributed under the License is distributed on an "AS IS" BASIS, -WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -See the License for the specific language governing permissions and -limitations under the License. -*/ - -#ifndef CF_SIMULATOR_DYNAMICSPROVIDER_H -#define CF_SIMULATOR_DYNAMICSPROVIDER_H - -#include -// #include "tf2/transform_datatypes.h" -#include "simulator_utils/types.h" -#include - -using namespace Eigen; - -class DynamicsProvider { - -public: - DynamicsProvider(params_t params, init_vals_t init_vals); - std::vector getCurrentState(); - state_space_t get_state(); - void update(control_out_t control, double sim_time); - void reset_dynamics(); - -private: - const size_t DIMENSIONS = 18; - const gsl_odeiv2_step_type *T = gsl_odeiv2_step_rkf45; - // Check if GSL is compatible with ROS 2, otherwise use alternatives - bool state_set = false; - state_space_t state_space; - params_t params; - init_vals_t init_vals; - double sim_time, t_start; - static int step(double t, const double* y, double* f, void *params); - gsl_odeiv2_step* s; - gsl_odeiv2_control *c; - gsl_odeiv2_evolve *e; - -}; - -#endif diff --git a/src/dynamics_provider.cpp b/include/mavswarm2/dynamics_provider.hpp similarity index 80% rename from src/dynamics_provider.cpp rename to include/mavswarm2/dynamics_provider.hpp index 33540a3..92e8695 100644 --- a/src/dynamics_provider.cpp +++ b/include/mavswarm2/dynamics_provider.hpp @@ -16,11 +16,20 @@ limitations under the License. */ -#include "dynamics_provider.h" +#ifndef CF_SIMULATOR_DYNAMICSPROVIDER_H +#define CF_SIMULATOR_DYNAMICSPROVIDER_H + +#include +// #include "tf2/transform_datatypes.h" +#include "simulator_utils/types.h" +#include + +// #include "dynamics_provider.h" #include #include // #include "rcutils/logging.h" +using namespace Eigen; /** * The equations and state_space use NED inertial frame. Therefore, the initial values are needed to be * converted from map frame (NWU) to NED frame. And convert them back to map frame before broadcasting. @@ -28,7 +37,11 @@ limitations under the License. * Note: the drone is already started upside down in the xacro, matching to the NED. * So no need to convert the rotation matrix and omega. */ -DynamicsProvider::DynamicsProvider(params_t params, init_vals_t init_vals) +class DynamicsProvider { + +public: + +DynamicsProvider(params_t params, init_vals_t init_vals) { this->params = params; this->init_vals = init_vals; @@ -47,57 +60,8 @@ DynamicsProvider::DynamicsProvider(params_t params, init_vals_t init_vals) } -/** - * ODE step for updating the quad state Dynamic equations are obtained from - * Geometric Tracking Control of a Quadrotor UAV on SE(3), Lee et al, (2010) -*/ -int DynamicsProvider::step(double t, const double *y, double *f, void *params) -{ - auto *param = reinterpret_cast(params); - (void) (t); - // copy R values from y - double R_temp[9]; - for (int i = 6, k = 0; i < 15; i++, k++) - { - R_temp[k] = y[i]; - } - Matrix3d R(R_temp); - - Vector3d omega(y[15], y[16], y[17]); - - // velocity for the next timestep eq(3) - Vector3d e3(0, 0, 1); - Vector3d v = param->gravity * e3 - (1 / param->mass) * (param->F * R * e3); - - // Rdot for next timestep eq(4) - Matrix3d Rdot = R * simulator_utils::hat(omega); - // Omegadot for the next timestep eq(5) - Vector3d Omegadot = param->J_inv * (param->M - omega.cross(param->J * omega)); - - // writing values to f - // position of next timestep eq(2) - int k = 0; - for (int i = 3; i < 6; i++, k++) - { - f[k] = y[i]; - } - for (int i = 0; i < 3; i++, k++) - { - f[k] = v[i]; - } - for (int i = 0; i < 9; i++, k++) - { - f[k] = Rdot.data()[i]; - } - for (int i = 0; i < 3; i++, k++) - { - f[k] = Omegadot[i]; - } - return GSL_SUCCESS; -} - -void DynamicsProvider::update(control_out_t control, double sim_time_) +void update(control_out_t control, double sim_time_) { t_start = sim_time; double t_stop = sim_time_; @@ -129,7 +93,7 @@ void DynamicsProvider::update(control_out_t control, double sim_time_) y[k] = state_space.omega[i]; } - gsl_odeiv2_system sys = {DynamicsProvider::step, nullptr, DIMENSIONS, ¶ms}; + gsl_odeiv2_system sys = {step, nullptr, DIMENSIONS, ¶ms}; double t = t_start; double h = 1e-5; while (t < t_stop) @@ -173,11 +137,81 @@ void DynamicsProvider::update(control_out_t control, double sim_time_) sim_time = t_stop; } -state_space_t DynamicsProvider::get_state() +state_space_t get_state() { return this->state_space; } -void DynamicsProvider::reset_dynamics() { +void reset_dynamics() { gsl_odeiv2_evolve_reset(this->e); } + +private: + const size_t DIMENSIONS = 18; + const gsl_odeiv2_step_type *T = gsl_odeiv2_step_rkf45; + // Check if GSL is compatible with ROS 2, otherwise use alternatives + bool state_set = false; + state_space_t state_space; + params_t params; + init_vals_t init_vals; + double sim_time, t_start; + // static int step(double t, const double* y, double* f, void *params); + gsl_odeiv2_step* s; + gsl_odeiv2_control *c; + gsl_odeiv2_evolve *e; + +/** + * ODE step for updating the quad state Dynamic equations are obtained from + * Geometric Tracking Control of a Quadrotor UAV on SE(3), Lee et al, (2010) +*/ +int step(double t, const double *y, double *f, void *params) +{ + auto *param = reinterpret_cast(params); + (void) (t); + // copy R values from y + double R_temp[9]; + for (int i = 6, k = 0; i < 15; i++, k++) + { + R_temp[k] = y[i]; + } + Matrix3d R(R_temp); + + Vector3d omega(y[15], y[16], y[17]); + + // velocity for the next timestep eq(3) + Vector3d e3(0, 0, 1); + Vector3d v = param->gravity * e3 - (1 / param->mass) * (param->F * R * e3); + + // Rdot for next timestep eq(4) + Matrix3d Rdot = R * simulator_utils::hat(omega); + + // Omegadot for the next timestep eq(5) + Vector3d Omegadot = param->J_inv * (param->M - omega.cross(param->J * omega)); + + // writing values to f + // position of next timestep eq(2) + int k = 0; + for (int i = 3; i < 6; i++, k++) + { + f[k] = y[i]; + } + for (int i = 0; i < 3; i++, k++) + { + f[k] = v[i]; + } + for (int i = 0; i < 9; i++, k++) + { + f[k] = Rdot.data()[i]; + } + for (int i = 0; i < 3; i++, k++) + { + f[k] = Omegadot[i]; + } + return GSL_SUCCESS; +} + + +}; + + +#endif diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 7d92a10..c172706 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -19,7 +19,7 @@ limitations under the License. #ifndef PROJECT_QUADROTOR_H #define PROJECT_QUADROTOR_H -#include "controller/controllerImpl.h" +#include "controller/geometric_controller.hpp" #include #include #include @@ -28,9 +28,8 @@ limitations under the License. #include "rclcpp/rclcpp.hpp" #include "simulator_interfaces/msg/waypoint.hpp" #include "trajectory_t.h" - #include "std_msgs/msg/float32_multi_array.hpp" - +using namespace std::chrono_literals; #ifndef STATE_H #define STATE_H enum State { @@ -44,6 +43,7 @@ enum State { using namespace Eigen; using namespace std; +using namespace std::chrono_literals; class Quadrotor : public rclcpp::Node { public: @@ -53,7 +53,7 @@ class Quadrotor : public rclcpp::Node { this->dt = 1/frequency; // this->initialize(1 / frequency); this->u << 0,0,0; - + timer_ = this->create_wall_timer(500ms, std::bind(&Quadrotor::iteration, this)); // while (marker_pub.getNumSubscribers() < 1) { // RCLCPP_INFO("Waiting for subscriber"); // ros::Duration(1).sleep(); @@ -100,6 +100,7 @@ class Quadrotor : public rclcpp::Node { DynamicsProvider *dynamics; params_t params; init_vals_t init_vals; + rclcpp::TimerBase::SharedPtr timer_; // rclcpp::Publisher::SharedPtr marker_pub, goal_pub, state_pub; // visualization_msgs::msg::Marker m, g; @@ -120,9 +121,9 @@ class Quadrotor : public rclcpp::Node { // void publish_state(); void move(const desired_state_t &d_state) { - control_out_t control = controller->get_control(dynamics->get_state(), d_state); + // control_out_t control = controller->get_control(dynamics->get_state(), d_state); // dynamics->update(control, sim_time); - RCLCPP_DEBUG(this->get_logger(), "got control: "); + RCLCPP_DEBUG(this->get_logger(), "IN MOVE"); // updating the model on rviz // set_state_space(); // send_transform(); diff --git a/include/mavswarm2/trajectory_t.h b/include/mavswarm2/trajectory_t.hpp similarity index 100% rename from include/mavswarm2/trajectory_t.h rename to include/mavswarm2/trajectory_t.hpp diff --git a/include/mavswarm2/utils.h b/include/mavswarm2/utils.hpp similarity index 100% rename from include/mavswarm2/utils.h rename to include/mavswarm2/utils.hpp diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 8b7f1d1..e52ee9d 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -232,7 +232,9 @@ int main(int argc, char **argv) { // ss << "robot_"<(ss.str()); Quadrotor quad(robot_id, frequency); - // quad.run(); + rclcpp::init(argc, argv); + rclcpp::spin(std::make_shared(0, 500)); + rclcpp::shutdown(); return 0; } \ No newline at end of file From a047130b448135db27886c4cbe554f09d5f7ad61 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Fri, 7 Jun 2024 18:50:52 +0530 Subject: [PATCH 06/24] fixing the executable vs library build issue --- CMakeLists.txt | 93 ++++++----- ...ollerImpl.hpp => geometric_controller.hpp} | 21 ++- include/mavswarm2/dynamics_provider.hpp | 4 +- include/mavswarm2/quadrotor.hpp | 13 +- include/mavswarm2/types.hpp | 124 +++++++++++++++ package.xml | 5 +- src/quadrotor.cpp | 144 +++++++++++++++++- 7 files changed, 341 insertions(+), 63 deletions(-) rename include/mavswarm2/controller/{controllerImpl.hpp => geometric_controller.hpp} (86%) create mode 100644 include/mavswarm2/types.hpp diff --git a/CMakeLists.txt b/CMakeLists.txt index 0c13c07..3a70919 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -3,63 +3,62 @@ project(mavswarm2) if(CMAKE_COMPILER_IS_GNUCXX OR CMAKE_CXX_COMPILER_ID MATCHES "Clang") add_compile_options(-Wall -Wextra -Wpedantic) -endif() - -# find dependencies -find_package(Armadillo REQUIRED) -find_package(GSL REQUIRED) -find_package(ament_cmake REQUIRED) -find_package(rclcpp REQUIRED) -find_package(simulator_interfaces REQUIRED) -find_package(simulator_utils REQUIRED) -# find_package(controller REQUIRED) -find_package(std_msgs REQUIRED) -find_package(geometry_msgs REQUIRED) -find_package(sensor_msgs REQUIRED) -find_package(visualization_msgs REQUIRED) -find_package(tf2_ros REQUIRED) + endif() + + + # find dependencies + # find_package(Armadillo REQUIRED) + # find_package(GSL REQUIRED) + find_package(ament_cmake REQUIRED) + find_package(rclcpp REQUIRED) + find_package(simulator_interfaces REQUIRED) + # # find_package(simulator_utils REQUIRED) + # # find_package(controller REQUIRED) + find_package(std_msgs REQUIRED) + # find_package(turtlesim REQUIRED) + find_package(geometry_msgs REQUIRED) + # find_package(sensor_msgs REQUIRED) + find_package(visualization_msgs REQUIRED) + find_package(tf2_ros REQUIRED) + + +# add_library(${PROJECT_NAME} SHARED +# src/quadrotor.cpp +# ) -add_library(${PROJECT_NAME} SHARED - src/dynamics_provider.cpp - src/quadrotor.cpp -) +add_executable(mavswarm2 src/quadrotor.cpp) -add_executable(quadrotor_main src/quadrotor.cpp) -ament_target_dependencies(mavswarm2 -rclcpp -simulator_utils -simulator_interfaces -# controller -tf2 -tf2_ros -visualization_msgs -geometry_msgs -std_msgs +ament_target_dependencies(${PROJECT_NAME} + geometry_msgs + rclcpp + tf2 + tf2_ros + visualization_msgs + simulator_interfaces + # turtlesim ) -add_executable(quadrotor src/quadrotor.cpp ) -# if(BUILD_TESTING) -# find_package(ament_lint_auto REQUIRED) - -# set(ament_cmake_copyright_FOUND TRUE) -# set(ament_cmake_cpplint_FOUND TRUE) -# ament_lint_auto_find_test_dependencies() -# endif() - -# find_package(message_runtime REQUIRED) - +# ament_target_dependencies(mavswarm2 +# rclcpp +# geometry_msgs +# visualization_msgs +# std_msgs +# tf2 +# tf2_ros +# simulator_interfaces +# ) install( TARGETS ${PROJECT_NAME} DESTINATION lib/${PROJECT_NAME} - - # EXPORT ${PROJECT_NAME} - # LIBRARY DESTINATION lib - # ARCHIVE DESTINATION lib - # RUNTIME DESTINATION bin - # INCLUDES DESTINATION include ) +# # EXPORT ${PROJECT_NAME} +# # LIBRARY DESTINATION lib +# # ARCHIVE DESTINATION lib +# # RUNTIME DESTINATION bin +# # INCLUDES DESTINATION include +# ) ament_package() diff --git a/include/mavswarm2/controller/controllerImpl.hpp b/include/mavswarm2/controller/geometric_controller.hpp similarity index 86% rename from include/mavswarm2/controller/controllerImpl.hpp rename to include/mavswarm2/controller/geometric_controller.hpp index ce5dada..4748302 100644 --- a/include/mavswarm2/controller/controllerImpl.hpp +++ b/include/mavswarm2/controller/geometric_controller.hpp @@ -1,3 +1,20 @@ +/* + +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. + +*/ #ifndef GEOMETRIC_CONTROLLER #define GEOMETRIC_CONTROLLER @@ -5,8 +22,8 @@ #pragma once #include -#include "simulator_utils/types.h" -#include "definitions.h" +#include "types.hpp" +#include "definitions.hpp" #include using namespace Eigen; diff --git a/include/mavswarm2/dynamics_provider.hpp b/include/mavswarm2/dynamics_provider.hpp index 92e8695..222f67d 100644 --- a/include/mavswarm2/dynamics_provider.hpp +++ b/include/mavswarm2/dynamics_provider.hpp @@ -21,7 +21,7 @@ limitations under the License. #include // #include "tf2/transform_datatypes.h" -#include "simulator_utils/types.h" +#include "types.hpp" #include // #include "dynamics_provider.h" @@ -164,7 +164,7 @@ void reset_dynamics() { * ODE step for updating the quad state Dynamic equations are obtained from * Geometric Tracking Control of a Quadrotor UAV on SE(3), Lee et al, (2010) */ -int step(double t, const double *y, double *f, void *params) +static int step(double t, const double *y, double *f, void *params) { auto *param = reinterpret_cast(params); (void) (t); diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index c172706..60c80d7 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -19,16 +19,17 @@ limitations under the License. #ifndef PROJECT_QUADROTOR_H #define PROJECT_QUADROTOR_H -#include "controller/geometric_controller.hpp" -#include #include -#include -#include "dynamics_provider.h" #include #include "rclcpp/rclcpp.hpp" -#include "simulator_interfaces/msg/waypoint.hpp" -#include "trajectory_t.h" +#include "trajectory_t.hpp" #include "std_msgs/msg/float32_multi_array.hpp" +#include "tf2_ros/transform_listener.h" +#include "visualization_msgs/msg/marker.hpp" +#include "dynamics_provider.hpp" +#include "controller/geometric_controller.hpp" +#include "simulator_interfaces/msg/waypoint.hpp" + using namespace std::chrono_literals; #ifndef STATE_H #define STATE_H diff --git a/include/mavswarm2/types.hpp b/include/mavswarm2/types.hpp new file mode 100644 index 0000000..4d367b5 --- /dev/null +++ b/include/mavswarm2/types.hpp @@ -0,0 +1,124 @@ +/* + +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. + +*/ + +#pragma once + +#include + +using namespace Eigen; + +typedef struct { + Vector3d position; + Matrix3d R; + Vector3d omega; + Vector3d velocity; + double h; +} init_vals_t; + +typedef struct { + double gravity; + double mass; + Matrix3d J; + Matrix3d J_inv; + double F; + Vector3d M; +} params_t; + +typedef struct { + Vector3d position; + Vector3d velocity; + Vector3d acceleration; + Matrix3d R; + Vector3d omega; +} state_space_t; + +typedef struct { + Vector3d x; + Vector3d b1; +} desired_state_t; + +typedef struct +{ + double kx; + double kv; + double kr; + double komega; +} gains_t; + +typedef struct { + double F; + Vector3d M; +} control_out_t; + +typedef struct { + Vector3d position; + Vector3d velocity; + Vector3d acceleration; + Vector3d jerk; +} opt_t; + +namespace simulator_utils { + Matrix3d hat(Vector3d v); + Vector3d R2RPY(Matrix3d R); + Vector3d ned_nwu_rotation(Vector3d v); + Matrix3d ned_nwu_rotation(Matrix3d m); + Vector3d vee(Matrix3d mat); + +} + +Matrix3d simulator_utils::hat(Vector3d v) +{ + Matrix3d hat_map(3, 3); + hat_map << 0, -v(2), v(1), + v(2), 0, -v(0), + -v(1), v(0), 0; + return hat_map; +} + +Vector3d simulator_utils::vee(Matrix3d mat) +{ + Vector3d vee_vec(mat(2, 1), mat(0, 2),mat(1, 0)); + return vee_vec; +} + +Vector3d simulator_utils::R2RPY(Matrix3d R) +{ + Vector3d rpy; + rpy << atan2(R(2, 1), R(2, 2)), + atan2(-R(2, 0), sqrt(R(2, 1) * R(2, 1) + R(2, 2) * R(2, 2))), + atan2(R(1, 0), R(0, 0)); + return rpy; +} + +Vector3d simulator_utils::ned_nwu_rotation(Vector3d v) +{ + Matrix3d rot; + rot << 1, 0, 0, + 0, -1, 0, + 0, 0, -1; + return rot * v; +} + +Matrix3d simulator_utils::ned_nwu_rotation(Matrix3d m) +{ + Matrix3d rot; + rot << 1, 0, 0, + 0, -1, 0, + 0, 0, -1; + return rot * m; +} \ No newline at end of file diff --git a/package.xml b/package.xml index 4a5600c..352882d 100644 --- a/package.xml +++ b/package.xml @@ -11,12 +11,13 @@ rclcpp simulator_interfaces - simulator_utils - controller + + std_msgs geometry_msgs sensor_msgs visualization_msgs + tf2 ament_lint_auto ament_lint_common diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index e52ee9d..69f84d0 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -229,12 +229,148 @@ int main(int argc, char **argv) { RCLCPP_DEBUG(logger, "initializing : "); rclcpp::init(argc, argv); stringstream ss; - // ss << "robot_"<(ss.str()); + ss << "robot_"<(ss.str()); Quadrotor quad(robot_id, frequency); rclcpp::init(argc, argv); - rclcpp::spin(std::make_shared(0, 500)); + // rclcpp::spin(std::make_shared(0, 500)); rclcpp::shutdown(); return 0; -} \ No newline at end of file +} + +// #include +// #include +// #include +// #include + +// #include "geometry_msgs/msg/transform_stamped.hpp" +// #include "geometry_msgs/msg/twist.hpp" +// #include "rclcpp/rclcpp.hpp" +// #include "tf2/exceptions.h" +// #include "tf2_ros/transform_listener.h" +// #include "tf2_ros/buffer.h" +// #include "turtlesim/srv/spawn.hpp" + +// using namespace std::chrono_literals; + +// class FrameListener : public rclcpp::Node +// { +// public: +// FrameListener() +// : Node("turtle_tf2_frame_listener"), +// turtle_spawning_service_ready_(false), +// turtle_spawned_(false) +// { +// // Declare and acquire `target_frame` parameter +// target_frame_ = this->declare_parameter("target_frame", "turtle1"); + +// tf_buffer_ = +// std::make_unique(this->get_clock()); +// tf_listener_ = +// std::make_shared(*tf_buffer_); + +// // Create a client to spawn a turtle +// spawner_ = +// this->create_client("spawn"); + +// // Create turtle2 velocity publisher +// publisher_ = +// this->create_publisher("turtle2/cmd_vel", 1); + +// // Call on_timer function every second +// timer_ = this->create_wall_timer( +// 1s, std::bind(&FrameListener::on_timer, this)); +// } + +// private: +// void on_timer() +// { +// // Store frame names in variables that will be used to +// // compute transformations +// std::string fromFrameRel = target_frame_.c_str(); +// std::string toFrameRel = "turtle2"; + +// if (turtle_spawning_service_ready_) { +// if (turtle_spawned_) { +// geometry_msgs::msg::TransformStamped t; + +// // Look up for the transformation between target_frame and turtle2 frames +// // and send velocity commands for turtle2 to reach target_frame +// try { +// t = tf_buffer_->lookupTransform( +// toFrameRel, fromFrameRel, +// tf2::TimePointZero); +// } catch (const tf2::TransformException & ex) { +// RCLCPP_INFO( +// this->get_logger(), "Could not transform %s to %s: %s", +// toFrameRel.c_str(), fromFrameRel.c_str(), ex.what()); +// return; +// } + +// geometry_msgs::msg::Twist msg; + +// static const double scaleRotationRate = 1.0; +// msg.angular.z = scaleRotationRate * atan2( +// t.transform.translation.y, +// t.transform.translation.x); + +// static const double scaleForwardSpeed = 0.5; +// msg.linear.x = scaleForwardSpeed * sqrt( +// pow(t.transform.translation.x, 2) + +// pow(t.transform.translation.y, 2)); + +// publisher_->publish(msg); +// } else { +// RCLCPP_INFO(this->get_logger(), "Successfully spawned"); +// turtle_spawned_ = true; +// } +// } else { +// // Check if the service is ready +// if (spawner_->service_is_ready()) { +// // Initialize request with turtle name and coordinates +// // Note that x, y and theta are defined as floats in turtlesim/srv/Spawn +// auto request = std::make_shared(); +// request->x = 4.0; +// request->y = 2.0; +// request->theta = 0.0; +// request->name = "turtle2"; + +// // Call request +// using ServiceResponseFuture = +// rclcpp::Client::SharedFuture; +// auto response_received_callback = [this](ServiceResponseFuture future) { +// auto result = future.get(); +// if (strcmp(result->name.c_str(), "turtle2") == 0) { +// turtle_spawning_service_ready_ = true; +// } else { +// RCLCPP_ERROR(this->get_logger(), "Service callback result mismatch"); +// } +// }; +// auto result = spawner_->async_send_request(request, response_received_callback); +// } else { +// RCLCPP_INFO(this->get_logger(), "Service is not ready"); +// } +// } +// } + +// // Boolean values to store the information +// // if the service for spawning turtle is available +// bool turtle_spawning_service_ready_; +// // if the turtle was successfully spawned +// bool turtle_spawned_; +// rclcpp::Client::SharedPtr spawner_{nullptr}; +// rclcpp::TimerBase::SharedPtr timer_{nullptr}; +// rclcpp::Publisher::SharedPtr publisher_{nullptr}; +// std::shared_ptr tf_listener_{nullptr}; +// std::unique_ptr tf_buffer_; +// std::string target_frame_; +// }; + +// int main(int argc, char * argv[]) +// { +// rclcpp::init(argc, argv); +// rclcpp::spin(std::make_shared()); +// rclcpp::shutdown(); +// return 0; +// } \ No newline at end of file From 609a40ccf39cef19a67cc1e387fe7d375ac988e4 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Mon, 10 Jun 2024 17:06:28 +0530 Subject: [PATCH 07/24] add ros2 launch file --- config/crazyflie_params.yaml | 14 ++++-- config/initial_conditions_2.yaml | 27 ++++++++++++ include/mavswarm2/quadrotor.hpp | 76 +++++++++++++++++++++++++++----- launch/quadrotor.launch | 14 ++++++ src/quadrotor.cpp | 11 +++-- 5 files changed, 121 insertions(+), 21 deletions(-) create mode 100644 config/initial_conditions_2.yaml create mode 100644 launch/quadrotor.launch diff --git a/config/crazyflie_params.yaml b/config/crazyflie_params.yaml index 98642bb..053e084 100644 --- a/config/crazyflie_params.yaml +++ b/config/crazyflie_params.yaml @@ -1,10 +1,16 @@ controller: - gains: [1, 0.5, 0.0015, 0.00075] + gains: + kx: 1 + kv: 0.5 + kr: 0.0015 + komega: 0.00075 -# model parameters for crazyflie drone model: - J: [2.3951e-5, 2.3951e-5, 3.2347e-5] + J: + jxx: 2.3951e-5 + jyy: 2.3951e-5 + jzz: 3.2347e-5 m: 0.032 d: 0.08 ctf: 0.0037 - gravity: 9.81 \ No newline at end of file + gravity: 9.81 diff --git a/config/initial_conditions_2.yaml b/config/initial_conditions_2.yaml new file mode 100644 index 0000000..785d9e8 --- /dev/null +++ b/config/initial_conditions_2.yaml @@ -0,0 +1,27 @@ +# define the initial positions of each robot in NWU frame +# change the initial rotation matrix to [1, 0, 0, 0, 1, 0, 0, 0, 1] for initialing the +# drones right side up. +robot_1: + ros__parameters: + position: + x: 2 + y: 2 + z: -2 + velocity: + x: 0 + y: 0 + z: 0 + rotation: + - 1 + - 0 + - 0 + - 0 + - -0.9995 + - -0.0314 + - 0 + - 0.0314 + - -0.9995 + omega: + r: 0 + p: 0 + y: 0 \ No newline at end of file diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 60c80d7..0e84545 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -22,6 +22,8 @@ limitations under the License. #include #include #include "rclcpp/rclcpp.hpp" +#include "rclcpp/logging.hpp" + #include "trajectory_t.hpp" #include "std_msgs/msg/float32_multi_array.hpp" #include "tf2_ros/transform_listener.h" @@ -53,14 +55,33 @@ class Quadrotor : public rclcpp::Node { sim_time = 0; this->dt = 1/frequency; // this->initialize(1 / frequency); + m_state = State::Idle; + this->u << 0,0,0; timer_ = this->create_wall_timer(500ms, std::bind(&Quadrotor::iteration, this)); + + if (!load_params()) { + RCLCPP_ERROR(this->get_logger(), "Could not load the drone parameters"); + rclcpp::shutdown(); + } + // // load init params + // if (!load_init_vals()) { + // RCLCPP_ERROR(this->get_logger(), "Could not load the drone initial values"); + // return false; + // } + + // logger = this->get_logger(); // while (marker_pub.getNumSubscribers() < 1) { - // RCLCPP_INFO("Waiting for subscriber"); + // RCLCPP_INFO(logger, "Waiting for subscriber"); // ros::Duration(1).sleep(); // } -} + // controller = std::make_shared(params, init_vals, gains, dt); + + + + +} void setState(State m_state_) { this->m_state = m_state_; } @@ -85,7 +106,7 @@ class Quadrotor : public rclcpp::Node { double sim_time, tau, dt, frequency; int robot_id; std::string worldframe, localframe, robot_link_name; - gains_t gains; + gains_t gains_; std::vector traj_piece; int xd_it; Vector3d u, target_pos; @@ -95,11 +116,11 @@ class Quadrotor : public rclcpp::Node { geometry_msgs::msg::Point target_next; bool set_next_target = false; - ControllerImpl *controller; + std::shared_ptr controller; state_space_t state_space; - - DynamicsProvider *dynamics; - params_t params; + // rclcpp::Logger logger; + std::shared_ptr dynamics_; + params_t params_; init_vals_t init_vals; rclcpp::TimerBase::SharedPtr timer_; @@ -115,16 +136,47 @@ class Quadrotor : public rclcpp::Node { // void initPaths(); // void set_state_space(); - // bool load_params(); - // bool load_init_vals(); + +bool load_params() { + stringstream ss; + ss << "/robot_" << to_string(this->robot_id); + string robot_name = ss.str(); + + vector gains(4); + this->get_parameter(robot_name + ".drone.model.gravity", params_.gravity); + this->get_parameter(robot_name + ".drone.model.m", params_.mass); + + this->gains_ = {gains[0], gains[1], gains[2], gains[3]}; + this->get_parameter(robot_name + ".drone.controller.gains.kx", gains[0]); + this->get_parameter(robot_name + ".drone.controller.gains.kv", gains[1]); + this->get_parameter(robot_name + ".drone.controller.gains.kr", gains[2]); + this->get_parameter(robot_name + ".drone.controller.gains.komega", gains[3]); + + vector J_(3); + this->get_parameter(robot_name + ".drone.model.J.jxx", J_[0]); + this->get_parameter(robot_name + ".drone.model.J.jyy", J_[1]); + this->get_parameter(robot_name + ".drone.model.J.jzz", J_[2]); + + params_.J << J_[0], 0, 0, + 0, J_[1], 0, + 0, 0, J_[2]; + params_.J_inv = params_.J.inverse(); + + // Load mass + params_.F = 0; + params_.M = Vector3d(0, 0, 0); + + RCLCPP_DEBUG(this->get_logger(), "Loaded control parameters"); + return true; +} // void send_transform(); // void publish_path(); // void publish_state(); void move(const desired_state_t &d_state) { - // control_out_t control = controller->get_control(dynamics->get_state(), d_state); + control_out_t control = controller->get_control(dynamics_->get_state(), d_state); // dynamics->update(control, sim_time); - RCLCPP_DEBUG(this->get_logger(), "IN MOVE"); + RCLCPP_INFO(this->get_logger(), "IN MOVE"); // updating the model on rviz // set_state_space(); // send_transform(); @@ -137,6 +189,8 @@ class Quadrotor : public rclcpp::Node { Vector3d b1d(1, 0, 0); desired_state_t dss = {xd, b1d}; this->move(dss); + RCLCPP_INFO(this->get_logger(), "Iteration: "); + // this->publish_path(); // this->publish_state(); } diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch new file mode 100644 index 0000000..ca20617 --- /dev/null +++ b/launch/quadrotor.launch @@ -0,0 +1,14 @@ + + + + + + + + + + \ No newline at end of file diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 69f84d0..69c772b 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -18,7 +18,6 @@ limitations under the License. #include "rclcpp/rclcpp.hpp" // #include // #include -#include "rclcpp/logging.hpp" // #include "simulator_utils/simulator_utils.h" @@ -218,22 +217,22 @@ limitations under the License. // this->m_state = m_state_; // } - - +/* +ros2 run mavswarm2 mavswarm2 0 50 --ros-args --log-level DEBUG +*/ int main(int argc, char **argv) { int robot_id = std::atoi(argv[1]); double frequency = (double)std::atof(argv[2]); auto logger = rclcpp::get_logger("logger"); - RCLCPP_DEBUG(logger, "initializing : "); + RCLCPP_INFO(logger, "Initialing drone: %s", to_string(robot_id).c_str()); rclcpp::init(argc, argv); stringstream ss; ss << "robot_"<(ss.str()); Quadrotor quad(robot_id, frequency); - rclcpp::init(argc, argv); - // rclcpp::spin(std::make_shared(0, 500)); + rclcpp::spin(std::make_shared(0, frequency)); rclcpp::shutdown(); return 0; From f38300a3615fe21742297ac243b42a74f275b497 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Tue, 11 Jun 2024 09:35:27 +0530 Subject: [PATCH 08/24] add launch file --- CMakeLists.txt | 4 ++++ config/crazyflie_params.yaml | 32 +++++++++++++++++--------------- include/mavswarm2/quadrotor.hpp | 16 +++++++++++----- launch/quadrotor.launch | 9 ++++++--- src/quadrotor.cpp | 2 +- 5 files changed, 39 insertions(+), 24 deletions(-) diff --git a/CMakeLists.txt b/CMakeLists.txt index 3a70919..a939232 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -53,6 +53,10 @@ install( TARGETS ${PROJECT_NAME} DESTINATION lib/${PROJECT_NAME} ) +install( + DIRECTORY launch config + DESTINATION share/${PROJECT_NAME}/ +) # # EXPORT ${PROJECT_NAME} # # LIBRARY DESTINATION lib # # ARCHIVE DESTINATION lib diff --git a/config/crazyflie_params.yaml b/config/crazyflie_params.yaml index 053e084..9c36d2f 100644 --- a/config/crazyflie_params.yaml +++ b/config/crazyflie_params.yaml @@ -1,16 +1,18 @@ -controller: - gains: - kx: 1 - kv: 0.5 - kr: 0.0015 - komega: 0.00075 +robot_0: + ros__parameters: + controller: + gains: + kx: 1 + kv: 0.5 + kr: 0.0015 + komega: 0.00075 -model: - J: - jxx: 2.3951e-5 - jyy: 2.3951e-5 - jzz: 3.2347e-5 - m: 0.032 - d: 0.08 - ctf: 0.0037 - gravity: 9.81 + model: + J: + jxx: 2.3951e-5 + jyy: 2.3951e-5 + jzz: 3.2347e-5 + m: 0.032 + d: 0.08 + ctf: 0.0037 + gravity: 9.81 diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 0e84545..60af90b 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -59,11 +59,14 @@ class Quadrotor : public rclcpp::Node { this->u << 0,0,0; timer_ = this->create_wall_timer(500ms, std::bind(&Quadrotor::iteration, this)); + + RCLCPP_INFO(this->get_logger(), "Loading parameters"); if (!load_params()) { RCLCPP_ERROR(this->get_logger(), "Could not load the drone parameters"); rclcpp::shutdown(); } + // // load init params // if (!load_init_vals()) { // RCLCPP_ERROR(this->get_logger(), "Could not load the drone initial values"); @@ -141,11 +144,14 @@ bool load_params() { stringstream ss; ss << "/robot_" << to_string(this->robot_id); string robot_name = ss.str(); + RCLCPP_INFO(this->get_logger(), robot_name.c_str()); vector gains(4); - this->get_parameter(robot_name + ".drone.model.gravity", params_.gravity); - this->get_parameter(robot_name + ".drone.model.m", params_.mass); - + this->get_parameter("/robot_0.model.gravity", params_.gravity); + this->get_parameter("model.m", params_.mass); + RCLCPP_INFO(this->get_logger(), to_string(params_.gravity).c_str()); + RCLCPP_INFO(this->get_logger(), to_string(params_.mass).c_str()); + this->gains_ = {gains[0], gains[1], gains[2], gains[3]}; this->get_parameter(robot_name + ".drone.controller.gains.kx", gains[0]); this->get_parameter(robot_name + ".drone.controller.gains.kv", gains[1]); @@ -166,7 +172,7 @@ bool load_params() { params_.F = 0; params_.M = Vector3d(0, 0, 0); - RCLCPP_DEBUG(this->get_logger(), "Loaded control parameters"); + RCLCPP_INFO(this->get_logger(), "Loaded control parameters"); return true; } // void send_transform(); @@ -188,7 +194,7 @@ bool load_params() { Vector3d xd = simulator_utils::ned_nwu_rotation(Vector3d{0,0,0}); Vector3d b1d(1, 0, 0); desired_state_t dss = {xd, b1d}; - this->move(dss); + // this->move(dss); RCLCPP_INFO(this->get_logger(), "Iteration: "); // this->publish_path(); diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index ca20617..44951ea 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -1,14 +1,17 @@ - + + + - + + + \ No newline at end of file diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 69c772b..5185fb0 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -229,7 +229,7 @@ int main(int argc, char **argv) { RCLCPP_INFO(logger, "Initialing drone: %s", to_string(robot_id).c_str()); rclcpp::init(argc, argv); stringstream ss; - ss << "robot_"<(ss.str()); Quadrotor quad(robot_id, frequency); rclcpp::spin(std::make_shared(0, frequency)); From 559a2469c4014f7aab3bf59d001fc557c3834ef7 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Tue, 11 Jun 2024 14:25:15 +0530 Subject: [PATCH 09/24] Passing ros2 params --- CMakeLists.txt | 2 +- config/crazyflie_params.yaml | 19 ++--- .../controller/geometric_controller.hpp | 8 +- include/mavswarm2/quadrotor.hpp | 77 ++++++++----------- launch/quadrotor.launch | 3 +- src/quadrotor.cpp | 6 +- 6 files changed, 52 insertions(+), 63 deletions(-) diff --git a/CMakeLists.txt b/CMakeLists.txt index a939232..4115f98 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -39,7 +39,7 @@ ament_target_dependencies(${PROJECT_NAME} # turtlesim ) -# ament_target_dependencies(mavswarm2 +# ament_target_dependencies(mavswarm2 # rclcpp # geometry_msgs # visualization_msgs diff --git a/config/crazyflie_params.yaml b/config/crazyflie_params.yaml index 9c36d2f..4d3a829 100644 --- a/config/crazyflie_params.yaml +++ b/config/crazyflie_params.yaml @@ -1,18 +1,15 @@ -robot_0: +/**: ros__parameters: - controller: - gains: - kx: 1 - kv: 0.5 - kr: 0.0015 - komega: 0.00075 + controller_gains: [1.0, 0.5, 0.015, 0.00075] + # kx: 1 + # kv: 0.5 + # kr: 0.0015 + # komega: 0.00075 model: - J: - jxx: 2.3951e-5 - jyy: 2.3951e-5 - jzz: 3.2347e-5 + J: [2.3951e-5, 2.3951e-5, 3.2347e-5] m: 0.032 d: 0.08 ctf: 0.0037 gravity: 9.81 + diff --git a/include/mavswarm2/controller/geometric_controller.hpp b/include/mavswarm2/controller/geometric_controller.hpp index 4748302..ccae68f 100644 --- a/include/mavswarm2/controller/geometric_controller.hpp +++ b/include/mavswarm2/controller/geometric_controller.hpp @@ -30,14 +30,15 @@ using namespace Eigen; namespace su = simulator_utils; -class ControllerImpl +class Geometric_Controller { public: -ControllerImpl(params_t params_, init_vals_t init_vals_, gains_t gains_, double dt_) - :params(std::move(params_)), init_vals(std::move(init_vals_)), gains(gains_), dt(dt_) +Geometric_Controller(params_t params_, gains_t gains_, double dt_) + :params(std::move(params_)), gains(gains_), dt(dt_) { + // initialize derivative operators dxdt_ = dxdt(0.05, dt, 1); d2xdt = dxdt(0.05, dt, 2); @@ -49,6 +50,7 @@ ControllerImpl(params_t params_, init_vals_t init_vals_, gains_t gains_, double dvdt = dxdt(0.05, dt, 1); d2vdt = dxdt(0.05, dt, 2); + } control_out_t get_control(state_space_t ss, const desired_state_t& desired_s) diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 60af90b..420f092 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -21,7 +21,7 @@ limitations under the License. #include #include -#include "rclcpp/rclcpp.hpp" + #include "rclcpp/logging.hpp" #include "trajectory_t.hpp" @@ -51,7 +51,7 @@ using namespace std::chrono_literals; class Quadrotor : public rclcpp::Node { public: Quadrotor(int robot_id, double frequency) - :Node("robot_"+to_string(robot_id)), frequency(frequency),robot_id(robot_id) { + :Node("robot_"+to_string(robot_id)), frequency(frequency), robot_id(robot_id) { sim_time = 0; this->dt = 1/frequency; // this->initialize(1 / frequency); @@ -67,18 +67,13 @@ class Quadrotor : public rclcpp::Node { rclcpp::shutdown(); } - // // load init params - // if (!load_init_vals()) { - // RCLCPP_ERROR(this->get_logger(), "Could not load the drone initial values"); - // return false; - // } - + // logger = this->get_logger(); // while (marker_pub.getNumSubscribers() < 1) { // RCLCPP_INFO(logger, "Waiting for subscriber"); // ros::Duration(1).sleep(); // } - // controller = std::make_shared(params, init_vals, gains, dt); + controller = std::make_shared(params_, gains_, dt); @@ -119,7 +114,7 @@ class Quadrotor : public rclcpp::Node { geometry_msgs::msg::Point target_next; bool set_next_target = false; - std::shared_ptr controller; + std::shared_ptr controller; state_space_t state_space; // rclcpp::Logger logger; std::shared_ptr dynamics_; @@ -141,37 +136,31 @@ class Quadrotor : public rclcpp::Node { // void set_state_space(); bool load_params() { - stringstream ss; - ss << "/robot_" << to_string(this->robot_id); - string robot_name = ss.str(); - RCLCPP_INFO(this->get_logger(), robot_name.c_str()); - - vector gains(4); - this->get_parameter("/robot_0.model.gravity", params_.gravity); - this->get_parameter("model.m", params_.mass); - RCLCPP_INFO(this->get_logger(), to_string(params_.gravity).c_str()); - RCLCPP_INFO(this->get_logger(), to_string(params_.mass).c_str()); - - this->gains_ = {gains[0], gains[1], gains[2], gains[3]}; - this->get_parameter(robot_name + ".drone.controller.gains.kx", gains[0]); - this->get_parameter(robot_name + ".drone.controller.gains.kv", gains[1]); - this->get_parameter(robot_name + ".drone.controller.gains.kr", gains[2]); - this->get_parameter(robot_name + ".drone.controller.gains.komega", gains[3]); - - vector J_(3); - this->get_parameter(robot_name + ".drone.model.J.jxx", J_[0]); - this->get_parameter(robot_name + ".drone.model.J.jyy", J_[1]); - this->get_parameter(robot_name + ".drone.model.J.jzz", J_[2]); + + declare_parameter("controller_gains", std::vector(4, 0.0)); + vector gains = get_parameter("controller_gains").as_double_array(); - params_.J << J_[0], 0, 0, + declare_parameter("model.m", 0.00); + declare_parameter("model.gravity", 9.81); + declare_parameter("model.d", 0.08); + declare_parameter("model.ctf", 0.0037); + declare_parameter("model.J", std::vector(3, 0.0)); + params_.mass = get_parameter("model.m").as_double(); + params_.gravity = get_parameter("model.gravity").as_double(); + + vector J_ = get_parameter("model.J").as_double_array();; + params_.J << J_[0], 0, 0, 0, J_[1], 0, 0, 0, J_[2]; params_.J_inv = params_.J.inverse(); - - // Load mass params_.F = 0; params_.M = Vector3d(0, 0, 0); - + RCLCPP_INFO(this->get_logger(), "Param: Gravity: %s ",to_string(params_.gravity).c_str()); + RCLCPP_INFO(this->get_logger(), "Param: Mass: %s ",to_string(params_.mass).c_str()); + RCLCPP_INFO(this->get_logger(), "Param: MOI: %6f %6f %6f",J_[0], J_[1], J_[2]); + RCLCPP_INFO(this->get_logger(), "Param: Controller Gains: %4f %4f %4f %4f", gains[0], gains[1], + gains[2], gains[3] + ); RCLCPP_INFO(this->get_logger(), "Loaded control parameters"); return true; } @@ -180,21 +169,21 @@ bool load_params() { // void publish_state(); void move(const desired_state_t &d_state) { - control_out_t control = controller->get_control(dynamics_->get_state(), d_state); - // dynamics->update(control, sim_time); - RCLCPP_INFO(this->get_logger(), "IN MOVE"); - // updating the model on rviz - // set_state_space(); - // send_transform(); - // dynamics->reset_dynamics(); - sim_time += dt; + // control_out_t control = controller->get_control(dynamics_->get_state(), d_state); + // dynamics->update(control, sim_time); + RCLCPP_INFO(this->get_logger(), "IN MOVE"); + // updating the model on rviz + // set_state_space(); + // send_transform(); + // dynamics->reset_dynamics(); + sim_time += dt; } void iteration() { Vector3d xd = simulator_utils::ned_nwu_rotation(Vector3d{0,0,0}); Vector3d b1d(1, 0, 0); desired_state_t dss = {xd, b1d}; - // this->move(dss); + this->move(dss); RCLCPP_INFO(this->get_logger(), "Iteration: "); // this->publish_path(); diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index 44951ea..f8d2d96 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -10,7 +10,8 @@ output="screen"> - + + diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 5185fb0..0495f30 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -229,9 +229,9 @@ int main(int argc, char **argv) { RCLCPP_INFO(logger, "Initialing drone: %s", to_string(robot_id).c_str()); rclcpp::init(argc, argv); stringstream ss; - ss << "robot_0"<(ss.str()); - Quadrotor quad(robot_id, frequency); + // ss << "robot_0"<(ss.str()); + // Quadrotor quad(robot_id, frequency); rclcpp::spin(std::make_shared(0, frequency)); rclcpp::shutdown(); From 7a3fd4824b060cbd8ff52a7294d1165703dd43dc Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Tue, 11 Jun 2024 17:37:37 +0530 Subject: [PATCH 10/24] fix: control not being compouted --- CMakeLists.txt | 10 ++++-- config/initial_conditions_2.yaml | 28 +++------------ include/mavswarm2/quadrotor.hpp | 58 ++++++++++++++++++++++---------- launch/quadrotor.launch | 5 +-- src/quadrotor.cpp | 2 +- 5 files changed, 57 insertions(+), 46 deletions(-) diff --git a/CMakeLists.txt b/CMakeLists.txt index 4115f98..d799e91 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -7,15 +7,15 @@ if(CMAKE_COMPILER_IS_GNUCXX OR CMAKE_CXX_COMPILER_ID MATCHES "Clang") # find dependencies - # find_package(Armadillo REQUIRED) - # find_package(GSL REQUIRED) + find_package(Armadillo REQUIRED) + find_package(GSL REQUIRED) find_package(ament_cmake REQUIRED) find_package(rclcpp REQUIRED) find_package(simulator_interfaces REQUIRED) # # find_package(simulator_utils REQUIRED) # # find_package(controller REQUIRED) find_package(std_msgs REQUIRED) - # find_package(turtlesim REQUIRED) + # find_package(GSL REQUIRED) find_package(geometry_msgs REQUIRED) # find_package(sensor_msgs REQUIRED) @@ -36,6 +36,7 @@ ament_target_dependencies(${PROJECT_NAME} tf2_ros visualization_msgs simulator_interfaces + # turtlesim ) @@ -65,6 +66,9 @@ install( # ) ament_package() +target_link_libraries(mavswarm2 + GSL::gsl + GSL::gslcblas) # install( # DIRECTORY include/ diff --git a/config/initial_conditions_2.yaml b/config/initial_conditions_2.yaml index 785d9e8..4c437e7 100644 --- a/config/initial_conditions_2.yaml +++ b/config/initial_conditions_2.yaml @@ -1,27 +1,9 @@ # define the initial positions of each robot in NWU frame # change the initial rotation matrix to [1, 0, 0, 0, 1, 0, 0, 0, 1] for initialing the # drones right side up. -robot_1: +robot_0: ros__parameters: - position: - x: 2 - y: 2 - z: -2 - velocity: - x: 0 - y: 0 - z: 0 - rotation: - - 1 - - 0 - - 0 - - 0 - - -0.9995 - - -0.0314 - - 0 - - 0.0314 - - -0.9995 - omega: - r: 0 - p: 0 - y: 0 \ No newline at end of file + position: [2.0, 2.0, -2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 420f092..2addedb 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -58,7 +58,7 @@ class Quadrotor : public rclcpp::Node { m_state = State::Idle; this->u << 0,0,0; - timer_ = this->create_wall_timer(500ms, std::bind(&Quadrotor::iteration, this)); + timer_ = this->create_wall_timer(2ms, std::bind(&Quadrotor::iteration, this)); RCLCPP_INFO(this->get_logger(), "Loading parameters"); @@ -74,10 +74,8 @@ class Quadrotor : public rclcpp::Node { // ros::Duration(1).sleep(); // } controller = std::make_shared(params_, gains_, dt); - - - - + dynamics = std::make_shared(params_, init_vals); + this->setState(State::Autonomous); } void setState(State m_state_) { @@ -117,7 +115,7 @@ class Quadrotor : public rclcpp::Node { std::shared_ptr controller; state_space_t state_space; // rclcpp::Logger logger; - std::shared_ptr dynamics_; + std::shared_ptr dynamics; params_t params_; init_vals_t init_vals; rclcpp::TimerBase::SharedPtr timer_; @@ -148,19 +146,32 @@ bool load_params() { params_.mass = get_parameter("model.m").as_double(); params_.gravity = get_parameter("model.gravity").as_double(); - vector J_ = get_parameter("model.J").as_double_array();; + vector J_ = get_parameter("model.J").as_double_array(); params_.J << J_[0], 0, 0, 0, J_[1], 0, 0, 0, J_[2]; params_.J_inv = params_.J.inverse(); params_.F = 0; params_.M = Vector3d(0, 0, 0); + + declare_parameter(to_string(robot_id)+".position", std::vector(3, 0.0)); + declare_parameter(to_string(robot_id)+".velocity", std::vector(3, 0.0)); + declare_parameter(to_string(robot_id)+".rotation", std::vector(3, 0.0)); + declare_parameter(to_string(robot_id)+".omega", std::vector(3, 0.0)); + vector pos_ = get_parameter(to_string(robot_id)+".position").as_double_array(); + vector vel_ = get_parameter(to_string(robot_id)+".velocity").as_double_array(); + vector rot_ = get_parameter(to_string(robot_id)+".rotation").as_double_array(); + vector omega_ = get_parameter(to_string(robot_id)+".omega").as_double_array(); + init_vals.position = Vector3d(pos_.data()); + init_vals.velocity << Vector3d(vel_.data()); + init_vals.R << Matrix3d(rot_.data()); + init_vals.omega << Vector3d(omega_.data()); + RCLCPP_INFO(this->get_logger(), "Param: Gravity: %s ",to_string(params_.gravity).c_str()); RCLCPP_INFO(this->get_logger(), "Param: Mass: %s ",to_string(params_.mass).c_str()); RCLCPP_INFO(this->get_logger(), "Param: MOI: %6f %6f %6f",J_[0], J_[1], J_[2]); - RCLCPP_INFO(this->get_logger(), "Param: Controller Gains: %4f %4f %4f %4f", gains[0], gains[1], - gains[2], gains[3] - ); + RCLCPP_INFO(this->get_logger(), "Param: Controller Gains: %4f %4f %4f %4f", gains[0], gains[1], + gains[2], gains[3]); RCLCPP_INFO(this->get_logger(), "Loaded control parameters"); return true; } @@ -169,22 +180,35 @@ bool load_params() { // void publish_state(); void move(const desired_state_t &d_state) { - // control_out_t control = controller->get_control(dynamics_->get_state(), d_state); - // dynamics->update(control, sim_time); - RCLCPP_INFO(this->get_logger(), "IN MOVE"); + state_space_t s = dynamics->get_state(); + control_out_t control = controller->get_control(dynamics->get_state(), d_state); + dynamics->update(control, sim_time); + RCLCPP_INFO(this->get_logger(), "control %4f %4f %4f", control.F, control.M[0], control.M[1]); // updating the model on rviz - // set_state_space(); + set_state_space(); // send_transform(); - // dynamics->reset_dynamics(); + dynamics->reset_dynamics(); + RCLCPP_INFO(this->get_logger(), "position: %4f %4f %4f", s.position[0], + s.position[1], s.position[2]); + RCLCPP_INFO(this->get_logger(), "rotation: %4f %4f %4f", state_space.R(0, 0), + state_space.R(1,1), state_space.R(2,2)); sim_time += dt; } + void set_state_space() { + state_space_t ss = dynamics->get_state(); + state_space.position = simulator_utils::ned_nwu_rotation(ss.position); + state_space.R = simulator_utils::ned_nwu_rotation(ss.R); + state_space.velocity = simulator_utils::ned_nwu_rotation(ss.velocity); + state_space.omega = simulator_utils::ned_nwu_rotation(ss.omega); + } + void iteration() { - Vector3d xd = simulator_utils::ned_nwu_rotation(Vector3d{0,0,0}); + Vector3d xd = simulator_utils::ned_nwu_rotation(Vector3d{2,2,-2.5}); Vector3d b1d(1, 0, 0); desired_state_t dss = {xd, b1d}; this->move(dss); - RCLCPP_INFO(this->get_logger(), "Iteration: "); + // RCLCPP_INFO(this->get_logger(), "Iteration: "); // this->publish_path(); // this->publish_state(); diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index f8d2d96..e375255 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -1,7 +1,7 @@ - + - + + diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 0495f30..8cbafb3 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -232,7 +232,7 @@ int main(int argc, char **argv) { // ss << "robot_0"<(ss.str()); // Quadrotor quad(robot_id, frequency); - rclcpp::spin(std::make_shared(0, frequency)); + rclcpp::spin(std::make_shared(0, 500)); rclcpp::shutdown(); return 0; From da66a48f25e4a9f66c59c75d0872bae4d0ab6a99 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Wed, 12 Jun 2024 21:13:00 +0530 Subject: [PATCH 11/24] fix: state space not getting initialized --- include/mavswarm2/dynamics_provider.hpp | 3 ++- include/mavswarm2/quadrotor.hpp | 20 +++++++++++++------- include/mavswarm2/utils.hpp | 1 - launch/quadrotor.launch | 2 +- src/quadrotor.cpp | 4 ++-- 5 files changed, 18 insertions(+), 12 deletions(-) diff --git a/include/mavswarm2/dynamics_provider.hpp b/include/mavswarm2/dynamics_provider.hpp index 222f67d..aba4bce 100644 --- a/include/mavswarm2/dynamics_provider.hpp +++ b/include/mavswarm2/dynamics_provider.hpp @@ -28,7 +28,7 @@ limitations under the License. #include #include // #include "rcutils/logging.h" - +#include using namespace Eigen; /** * The equations and state_space use NED inertial frame. Therefore, the initial values are needed to be @@ -47,6 +47,7 @@ DynamicsProvider(params_t params, init_vals_t init_vals) this->init_vals = init_vals; if (!state_set) { + std::cout << "in set state 0 "<u << 0,0,0; - timer_ = this->create_wall_timer(2ms, std::bind(&Quadrotor::iteration, this)); + timer_ = this->create_wall_timer(10ms, std::bind(&Quadrotor::iteration, this)); RCLCPP_INFO(this->get_logger(), "Loading parameters"); @@ -73,8 +73,9 @@ class Quadrotor : public rclcpp::Node { // RCLCPP_INFO(logger, "Waiting for subscriber"); // ros::Duration(1).sleep(); // } - controller = std::make_shared(params_, gains_, dt); + controller = std::make_shared(params_, gains, dt); dynamics = std::make_shared(params_, init_vals); + set_state_space(); this->setState(State::Autonomous); } @@ -102,7 +103,7 @@ class Quadrotor : public rclcpp::Node { double sim_time, tau, dt, frequency; int robot_id; std::string worldframe, localframe, robot_link_name; - gains_t gains_; + gains_t gains; std::vector traj_piece; int xd_it; Vector3d u, target_pos; @@ -136,7 +137,7 @@ class Quadrotor : public rclcpp::Node { bool load_params() { declare_parameter("controller_gains", std::vector(4, 0.0)); - vector gains = get_parameter("controller_gains").as_double_array(); + vector gains_ = get_parameter("controller_gains").as_double_array(); declare_parameter("model.m", 0.00); declare_parameter("model.gravity", 9.81); @@ -166,12 +167,14 @@ bool load_params() { init_vals.velocity << Vector3d(vel_.data()); init_vals.R << Matrix3d(rot_.data()); init_vals.omega << Vector3d(omega_.data()); + gains = {.kx = gains_[0], .kv = gains_[1], .kr = gains_[3], .komega = gains_[3]}; + RCLCPP_INFO(this->get_logger(), "Init Params: : %4f %4f %4f ", init_vals.position[0], init_vals.position[1],init_vals.position[2]); RCLCPP_INFO(this->get_logger(), "Param: Gravity: %s ",to_string(params_.gravity).c_str()); RCLCPP_INFO(this->get_logger(), "Param: Mass: %s ",to_string(params_.mass).c_str()); RCLCPP_INFO(this->get_logger(), "Param: MOI: %6f %6f %6f",J_[0], J_[1], J_[2]); - RCLCPP_INFO(this->get_logger(), "Param: Controller Gains: %4f %4f %4f %4f", gains[0], gains[1], - gains[2], gains[3]); + RCLCPP_INFO(this->get_logger(), "Param: Controller Gains: %4f %4f %4f %4f", gains.kx, gains.kv, + gains.kr, gains.komega); RCLCPP_INFO(this->get_logger(), "Loaded control parameters"); return true; } @@ -181,7 +184,10 @@ bool load_params() { void move(const desired_state_t &d_state) { state_space_t s = dynamics->get_state(); - control_out_t control = controller->get_control(dynamics->get_state(), d_state); + // RCLCPP_INFO(this->get_logger(), "dss %4f %4f %4f", d_state.x[0], d_state.x[1], d_state.x[2]); + RCLCPP_INFO(this->get_logger(), "ss %4f %4f %4f", s.position[0], s.position[1], s.position[2]); + + control_out_t control = controller->get_control(s, d_state); dynamics->update(control, sim_time); RCLCPP_INFO(this->get_logger(), "control %4f %4f %4f", control.F, control.M[0], control.M[1]); // updating the model on rviz diff --git a/include/mavswarm2/utils.hpp b/include/mavswarm2/utils.hpp index 665bbf7..65bad32 100755 --- a/include/mavswarm2/utils.hpp +++ b/include/mavswarm2/utils.hpp @@ -1,4 +1,3 @@ -/* Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index e375255..166fe4a 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -1,7 +1,7 @@ - + (ss.str()); // Quadrotor quad(robot_id, frequency); - rclcpp::spin(std::make_shared(0, 500)); + rclcpp::spin(std::make_shared(robot_id, frequency)); rclcpp::shutdown(); return 0; From 55d8dc33e42b2bbab53c556f6a35fb417dad2c39 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Thu, 13 Jun 2024 17:53:27 +0530 Subject: [PATCH 12/24] fixed: reading initial params --- include/mavswarm2/dynamics_provider.hpp | 2 +- include/mavswarm2/quadrotor.hpp | 34 +++++++++++++------------ 2 files changed, 19 insertions(+), 17 deletions(-) diff --git a/include/mavswarm2/dynamics_provider.hpp b/include/mavswarm2/dynamics_provider.hpp index aba4bce..4fef756 100644 --- a/include/mavswarm2/dynamics_provider.hpp +++ b/include/mavswarm2/dynamics_provider.hpp @@ -47,7 +47,7 @@ DynamicsProvider(params_t params, init_vals_t init_vals) this->init_vals = init_vals; if (!state_set) { - std::cout << "in set state 0 "<dt = 1/frequency; + // this->dt = 1/frequency; + dt = 0.01; // this->initialize(1 / frequency); m_state = State::Idle; @@ -155,14 +156,14 @@ bool load_params() { params_.F = 0; params_.M = Vector3d(0, 0, 0); - declare_parameter(to_string(robot_id)+".position", std::vector(3, 0.0)); - declare_parameter(to_string(robot_id)+".velocity", std::vector(3, 0.0)); - declare_parameter(to_string(robot_id)+".rotation", std::vector(3, 0.0)); - declare_parameter(to_string(robot_id)+".omega", std::vector(3, 0.0)); - vector pos_ = get_parameter(to_string(robot_id)+".position").as_double_array(); - vector vel_ = get_parameter(to_string(robot_id)+".velocity").as_double_array(); - vector rot_ = get_parameter(to_string(robot_id)+".rotation").as_double_array(); - vector omega_ = get_parameter(to_string(robot_id)+".omega").as_double_array(); + declare_parameter("position", std::vector(3, 0.0)); + declare_parameter("velocity", std::vector(3, 0.0)); + declare_parameter("rotation", std::vector(3, 0.0)); + declare_parameter("omega", std::vector(3, 0.0)); + vector pos_ = get_parameter("position").as_double_array(); + vector vel_ = get_parameter("velocity").as_double_array(); + vector rot_ = get_parameter("rotation").as_double_array(); + vector omega_ = get_parameter("omega").as_double_array(); init_vals.position = Vector3d(pos_.data()); init_vals.velocity << Vector3d(vel_.data()); init_vals.R << Matrix3d(rot_.data()); @@ -185,19 +186,20 @@ bool load_params() { void move(const desired_state_t &d_state) { state_space_t s = dynamics->get_state(); // RCLCPP_INFO(this->get_logger(), "dss %4f %4f %4f", d_state.x[0], d_state.x[1], d_state.x[2]); - RCLCPP_INFO(this->get_logger(), "ss %4f %4f %4f", s.position[0], s.position[1], s.position[2]); + RCLCPP_INFO(this->get_logger(), "%2f position %4f %4f %4f", sim_time, s.position[0], s.position[1], s.position[2]); + RCLCPP_INFO(this->get_logger(), "%2f rotation %4f %4f %4f", sim_time, s.R(0,0), s.R(1,1), s.R(2,2)); control_out_t control = controller->get_control(s, d_state); dynamics->update(control, sim_time); - RCLCPP_INFO(this->get_logger(), "control %4f %4f %4f", control.F, control.M[0], control.M[1]); + // RCLCPP_INFO(this->get_logger(), "control %4f %4f %4f", control.F, control.M[0], control.M[1]); // updating the model on rviz set_state_space(); // send_transform(); dynamics->reset_dynamics(); - RCLCPP_INFO(this->get_logger(), "position: %4f %4f %4f", s.position[0], - s.position[1], s.position[2]); - RCLCPP_INFO(this->get_logger(), "rotation: %4f %4f %4f", state_space.R(0, 0), - state_space.R(1,1), state_space.R(2,2)); + // RCLCPP_INFO(this->get_logger(), "position: %4f %4f %4f", s.position[0], + // s.position[1], s.position[2]); + // RCLCPP_INFO(this->get_logger(), "rotation: %4f %4f %4f", state_space.R(0, 0), + // state_space.R(1,1), state_space.R(2,2)); sim_time += dt; } @@ -210,7 +212,7 @@ bool load_params() { } void iteration() { - Vector3d xd = simulator_utils::ned_nwu_rotation(Vector3d{2,2,-2.5}); + Vector3d xd = Vector3d{2, 2, -2}; Vector3d b1d(1, 0, 0); desired_state_t dss = {xd, b1d}; this->move(dss); From dc376f9a74c78adf88a5ce4ee8db9d6cbcf210b8 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Fri, 14 Jun 2024 18:35:12 +0530 Subject: [PATCH 13/24] update readme --- readme.md | 135 +++++++++++------------------------------------------- 1 file changed, 26 insertions(+), 109 deletions(-) diff --git a/readme.md b/readme.md index ac41a3f..bf80d2a 100644 --- a/readme.md +++ b/readme.md @@ -1,138 +1,55 @@ -# Mavswarm2: Under Development... +# Mavswarm2 (Under development) -Mavswarm is a lightweight and fast Multi-Aerial Vehicle simulator based on ROS (Robot Operating System). It supports simulating heterogenous quadrotor swarms of upto 10 robots on a single desktop with physics. Mavswarm also supports quadrotor control, trajectory optimization and receding horizon planning (RHP). Currently, the internal controller uses the Lee's geometric tracking controller [3] and it is tuned for two different quadrotor models out of the box. -In addition you can extend the swarm simulation with more quadrotor models by simply adding the new quadrotor model parameters through a yaml configuration file. +Mavswarm is a lightweight and fast Multi-Aerial Vehicle simulator based on ROS (Robot Operating System). It supports simulating heterogenous quadrotor swarms of upto 10 robots on a single desktop with physics. -Consider citing our work [1][2] if you find this code helpful for your publications. - -| ![Cover Image](https://github.com/malintha/multi_uav_simulator/blob/master/cover.gif?raw=true) | -|:--:| -| *A hetergenous swarm of 5 quadrotors stabilizing from an upside-down initialization* | - -## Mostly Automated Installation - -A Makefile has been compiled to install ros, install dependancies and/or create and build a catkin workspace, and build the entire uav simulator package. - -Note: This package currently runs with ROS1 which is only compatible on older linux distros - for example, it is not supported on anything later than Ubuntu 20.04 - -**To get the makefile, run:** +It has -```bash -wget https://gist.githubusercontent.com/matteovidali/caab443e66425e260b6a1c1bd842d28c/raw/188effd1f7e5c4a49cf636abd96bc325a9ac9bd9/Makefile -``` +- quadrotor control (ROS1/ROS2) +- trajectory optimization and receding horizon planning (only working in ROS1. I welcome any PRs/Contributions). -Then, if you wish to do a full desktop installation of ROS1, this can be done with: -```bash -make ros_desktop_install -``` +The internal controller uses the Lee's geometric tracking controller [3] and it is tuned for two different quadrotor models out of the box. -To get and install the required dependancies, run: -```bash -make deps -``` +**Compared to Mavswarm1, Mavswarm2 has a simpler installation, and the code is more self-contained. Everything is in the header files, so easier to manage and export as a library**. -To create and initialize a NEW catkin_ws with all required packages -First in the makefile, change the value of 'CATKIN_WS_NAME' from '../catkin_ws' to the path where your workspace should exist. -Then, run: -```bash -make wstool-new -``` - -If you have a PRE-EXISTING catkin workspace you would like to build this module into, -First change the 'CATKIN_WS_NAME' variable to the path of your catkin workspace, then run: - -```bash -make wstool-exists -``` - -Finally, if you would like to run a catkin build, you may run: -```bash -make build -``` -This will build the entire catkin space, so be sure to customize this if necessary - -After building, you can launch the simulator with -```bash -make launch -``` - -## Manual Installation -**Install dependencies** - -Install [`Eigen`](http://eigen.tuxfamily.org/index.php?title=Main_Page), [`Armadillo`](https://www.uio.no/studier/emner/matnat/fys/FYS4411/v13/guides/installing-armadillo/) and [`GNU Science Library (GSL)`](https://www.gnu.org/software/gsl/) before you continue. +Consider citing our work [1][2] if you find this code helpful for your publications. -Install eigen-coversions (make sure to change the ROS version name i.e.; melodic, kinetic). +| ![Cover Image](https://github.com/malintha/multi_uav_simulator/blob/master/cover.gif?raw=true) | +|:--:| +| *A hetergenous swarm of 5 quadrotors stabilizing from an upside-down initialization* | - sudo apt install ros-noetic-eigen-conversions +## Installation -**Building the simulator** +**Install the dependencies** -Create a new catkin workspace and use `wstool` to download the `multi_uav_simulator` package. +Install Eigen, Armadillo and GNU Science Library (GSL) before you continue. - mkdir catkin_ws - wstool init src - cd src/ - wstool set --git multi_uav_simulator git@github.com:malintha/multi_uav_simulator.git -y - wstool update - -Mavswarm uses `ethz-asl/mav_trajectory_generation` package to generate trajectories for the robots. Use the`rosinstall/dependencies.rosinstall` file to download the required dependencies. +**Clone the repositories** - wstool merge multi_uav_simulator/rosinstall/dependencies.rosinstall - wstool update - -This will clone the following packages to the workspace automatically : `catkin_simple`, `eigen_catkin`, `eigen_checks`, `glog_catkin`, `mav_comm`, `mav_trajectory_generation`, `nlopt`. + mkdir -p mavswarm2/src + cd mavswarm2/src + git clone -b ros2 git@github.com:malintha/simulator_utils.git + git clone -b ros2 git@github.com:malintha/multi_uav_simulator.git -Now build the simulator. +**Building the simulator** cd ../ - catkin build multi_uav_simulator - - Run the simulator. + colcon build - source devel/setup.bash - roslaunch multi_uav_simulator simu.launch +**Running the simulator** + source install/setup.bash + ros2 launch mavswarm2 quadrotor.launch -This will open an Rviz window and show 5 drones flip from an upside-down initialization. **Publishing Goals** -Mavswarm supports Receding Horizon Planning (RHP) and trajectory optimization out of the box. You can publish a new desired goal position using rostopics for any drone to see it navigating. To do so, open a new command window and publish the following message. - - rostopic pub /robot_1/desired_state geometry_msgs/Point '{x: 4, y: -1, z: 3}' - -Each drone listnes to its `desired_state` topic which uses the ROS standard `geometry_msgs/Point` message type to recieve new goal locations. The command above simply adds the goal `{x: 4, y: -1, z: 3}` into the first drone's goal list. To See RHP in working, publish a different goal before the drone reaches the previous goal. This will recalculate a new trajectory to match the robot's current speed and acceleration to ensure smooth transitions between rapidly changing goal locations. +- Under development, not working in right now **Adding a new drone to the environment** -Mavswarm uses xacro to spawn new models into the simulation environment. Out of the box, it has 5 drones in the environment and two separate quadrotor models to choose from; namely, Bigquad (the quadrotor model from [2]) and Crazyflie. If you want to add a sixth drone to the environment, simply follow the steps below. - -1) In the `launch/simu.launch` file, add a new line with the corresponding drone id. Make sure to change `` and the robot_id accordingly. For example, - - - - This adds a new Crazyflie model to the environment. If you want a larger quadrotor model, you can use `bigquad_description/bigquad.urdf.xacro` instead. - -2) Now add the following block to bind a quadrotor instance to the URDF model. Here we pass the `robot_id` and the internal controller's frequency as arguments to the quadrotor instance. In addition, we use `rosparam` to specify the quadrotor's model parameters and the controller gains. The parameters for the Bigquad and the Crazyflie can be found in `config/bigquad_params.yaml` and `config/crazyflie_params.yaml` files respectively. - - - - - - - -3) In order to specify the initial conditions for the new drone add a new block to the `config/initial_conditions.yaml` file as below. - - robot_6: - position: [2, 4, 0] - velocity: [0, 0, 0] - rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] - omega: [0, 0, 0] - - The rotation and omega stands for the initial rotation matrix (3x3) and the angular velocity (3x1) of the rigid body. Here, we initialize the drone up-side down. To make it right way up, change the rotation matrix to identity: `[1, 0, 0, 0, 1, 0, 0, 0, 1]`. +- under development, not working in right now -4) Finally, to visualize the newly added drone, add a robot_model visualization type to RViz. Change its description to corresponding param name of the newly added element in the launch file. i.e.: "`robot_6`". [1] Our work based on this controller: From 759d015ff990d6e406238598e152a15c805ddc50 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Fri, 14 Jun 2024 23:35:11 +0530 Subject: [PATCH 14/24] fixed: pass init values converted to the NED frame --- include/mavswarm2/dynamics_provider.hpp | 1 - include/mavswarm2/quadrotor.hpp | 24 +- launch/quadrotor.launch | 10 +- readme.md | 5 +- src/quadrotor.cpp | 343 +----------------------- 5 files changed, 21 insertions(+), 362 deletions(-) diff --git a/include/mavswarm2/dynamics_provider.hpp b/include/mavswarm2/dynamics_provider.hpp index 4fef756..b24970f 100644 --- a/include/mavswarm2/dynamics_provider.hpp +++ b/include/mavswarm2/dynamics_provider.hpp @@ -47,7 +47,6 @@ DynamicsProvider(params_t params, init_vals_t init_vals) this->init_vals = init_vals; if (!state_set) { - std::cout << "in set state ### "<dt = 1/frequency; - dt = 0.01; - // this->initialize(1 / frequency); + dt = 1/frequency; + RCLCPP_INFO(this->get_logger(), "dt: %4f ", dt); + // dt = 0.01; m_state = State::Idle; this->u << 0,0,0; - timer_ = this->create_wall_timer(10ms, std::bind(&Quadrotor::iteration, this)); + timer_ = this->create_wall_timer(std::chrono::duration(dt), std::bind(&Quadrotor::iteration, this)); RCLCPP_INFO(this->get_logger(), "Loading parameters"); @@ -164,10 +163,10 @@ bool load_params() { vector vel_ = get_parameter("velocity").as_double_array(); vector rot_ = get_parameter("rotation").as_double_array(); vector omega_ = get_parameter("omega").as_double_array(); - init_vals.position = Vector3d(pos_.data()); - init_vals.velocity << Vector3d(vel_.data()); - init_vals.R << Matrix3d(rot_.data()); - init_vals.omega << Vector3d(omega_.data()); + init_vals.position = simulator_utils::ned_nwu_rotation(Vector3d(pos_.data())); + init_vals.velocity << simulator_utils::ned_nwu_rotation(Vector3d(vel_.data())); + init_vals.R << simulator_utils::ned_nwu_rotation(Matrix3d(rot_.data())); + init_vals.omega << simulator_utils::ned_nwu_rotation(Vector3d(omega_.data())); gains = {.kx = gains_[0], .kv = gains_[1], .kr = gains_[3], .komega = gains_[3]}; RCLCPP_INFO(this->get_logger(), "Init Params: : %4f %4f %4f ", init_vals.position[0], init_vals.position[1],init_vals.position[2]); @@ -186,10 +185,11 @@ bool load_params() { void move(const desired_state_t &d_state) { state_space_t s = dynamics->get_state(); // RCLCPP_INFO(this->get_logger(), "dss %4f %4f %4f", d_state.x[0], d_state.x[1], d_state.x[2]); - RCLCPP_INFO(this->get_logger(), "%2f position %4f %4f %4f", sim_time, s.position[0], s.position[1], s.position[2]); - RCLCPP_INFO(this->get_logger(), "%2f rotation %4f %4f %4f", sim_time, s.R(0,0), s.R(1,1), s.R(2,2)); + RCLCPP_DEBUG(this->get_logger(), "%2f position %4f %4f %4f", sim_time, s.position[0], s.position[1], s.position[2]); + // RCLCPP_INFO(this->get_logger(), "%2f rotation %4f %4f %4f", sim_time, s.R(0,0), s.R(1,1), s.R(2,2)); control_out_t control = controller->get_control(s, d_state); + RCLCPP_DEBUG(this->get_logger(), "%2f control %4f %4f %4f %4f", sim_time, control.F, control.M[0], control.M[1], control.M[2]); dynamics->update(control, sim_time); // RCLCPP_INFO(this->get_logger(), "control %4f %4f %4f", control.F, control.M[0], control.M[1]); // updating the model on rviz @@ -212,7 +212,7 @@ bool load_params() { } void iteration() { - Vector3d xd = Vector3d{2, 2, -2}; + Vector3d xd = simulator_utils::ned_nwu_rotation(init_vals.position); Vector3d b1d(1, 0, 0); desired_state_t dss = {xd, b1d}; this->move(dss); diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index 166fe4a..671ceb3 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -3,14 +3,14 @@ - + + - - - + output="screen" + args="$(var robot_id) $(var controller_frequency) --ros-args --log-level $(var log_level)"> + diff --git a/readme.md b/readme.md index bf80d2a..011aafa 100644 --- a/readme.md +++ b/readme.md @@ -1,9 +1,8 @@ -# Mavswarm2 (Under development) +# Mavswarm2 (under development) -Mavswarm is a lightweight and fast Multi-Aerial Vehicle simulator based on ROS (Robot Operating System). It supports simulating heterogenous quadrotor swarms of upto 10 robots on a single desktop with physics. +Mavswarm is a lightweight and fast Multi-Aerial Vehicle simulator built on Robot Operating System (ROS), entirely written in C++. Mavswarm2 is the ROS2-compatible version of Mavswarm. It supports simulating heterogenous quadrotor swarms of upto 10 robots on a single desktop with physics. It has - - quadrotor control (ROS1/ROS2) - trajectory optimization and receding horizon planning (only working in ROS1. I welcome any PRs/Contributions). diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 92642bb..81ccbcd 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -16,360 +16,21 @@ limitations under the License. #include "quadrotor.hpp" #include "rclcpp/rclcpp.hpp" -// #include -// #include -// #include "simulator_utils/simulator_utils.h" - - - -/** - * converts the dynamics state_space (NED) to NWU and stores for the quadrotor - * This is for broadcasting the transformation -*/ -// void Quadrotor::set_state_space() { -// state_space_t ss = dynamics->get_state(); -// state_space.position = simulator_utils::ned_nwu_rotation(ss.position); -// state_space.R = simulator_utils::ned_nwu_rotation(ss.R); -// state_space.velocity = simulator_utils::ned_nwu_rotation(ss.velocity); -// state_space.omega = simulator_utils::ned_nwu_rotation(ss.omega); -// } - -// void Quadrotor::send_transform() { -// static tf::TransformBroadcaster br; -// tf::Transform transform; -// Vector3d position = state_space.position; -// Matrix3d R = state_space.R; -// Vector3d rpy = simulator_utils::R2RPY(R); -// transform.setOrigin(tf::Vector3(position[0], position[1], -position[2])); -// tf::Quaternion q; -// q.setRPY(rpy[0], rpy[1], rpy[2]); -// transform.setRotation(q); -// if(quad_initialized && !isnan(q.x())) -// br.sendTransform(tf::StampedTransform(transform, ros::Time::now(), worldframe, robot_link_name)); -// } - -// State Quadrotor::getState() { -// return this->m_state; -// } - -// bool Quadrotor::load_params() { -// stringstream ss; -// ss << "/robot_" << to_string(this->robot_id); -// string robot_name = ss.str(); -// double temp; -// if (!nh.getParam(ros::names::append(robot_name, "drone/model/gravity"), params.gravity)) return false; -// // = temp; -// vector J_; -// if (!nh.getParam(ros::names::append(robot_name, "drone/model/J"), J_)) return false; -// // Matrix3d J; -// params.J << J_[0], 0, 0, -// 0, J_[1], 0, -// 0, 0, J_[2]; -// params.J_inv = params.J.inverse(); -// if (!nh.getParam(ros::names::append(robot_name, "drone/model/m"), params.mass)) return false; -// // = temp; -// params.F = 0; -// Vector3d M(0, 0, 0); -// params.M = M; -// vector gains_; -// if (!nh.getParam(ros::names::append(robot_name, "drone/controller/gains"), gains_)) return false; -// this->gains = {gains_[0], gains_[1], gains_[2], gains_[3]}; - -// ROS_DEBUG_STREAM(this->logger, "Loaded control parameters"); -// return true; -// } - -// bool Quadrotor::load_init_vals() { -// vector position, vel, R, omega; -// stringstream ss; -// ss << "/robot_" << to_string(this->robot_id); -// string robot_name = ss.str(); -// if (!nh.getParam(ros::names::append(robot_name, "position"), position)) return false; -// if (!nh.getParam(ros::names::append(robot_name, "velocity"), vel)) return false; -// if (!nh.getParam(ros::names::append(robot_name, "rotation"), R)) return false; -// if (!nh.getParam(ros::names::append(robot_name, "omega"), omega)) return false; -// if (!nh.getParam("/frame/fixed", worldframe)) return false; -// if (!nh.getParam("/frame/prefix", localframe)) return false; -// init_vals.position = Vector3d(position.data()); -// init_vals.velocity = Vector3d(vel.data()); -// init_vals.R = Matrix3d(R.data()); -// init_vals.omega = Vector3d(omega.data()); - -// this->x0.position = simulator_utils::ned_nwu_rotation(init_vals.position); -// this->x0.velocity = simulator_utils::ned_nwu_rotation(init_vals.velocity); -// this->xd0.position = this->x0.position; -// this->target_pos = simulator_utils::ned_nwu_rotation(init_vals.position); -// ROS_DEBUG_STREAM(this->logger, "Loaded the drone initialization values"); -// return true; -// } - -// void Quadrotor::desired_pos_cb(const geometry_msgs::Point &pt) { -// Vector3d xd = {pt.x, pt.y, pt.z}; -// Vector3d b1d(1, 0, 0); -// this->dss = {xd, b1d}; - -// } - - -// xd should be in NED frame and so does dynamics and controller. -// void Quadrotor::iteration(const ros::TimerEvent &e) { -// this->move(this->dss); -// this->publish_path(); -// this->publish_state(); -// } - -// void Quadrotor::publish_path() { -// constexpr int arrowLength = 0.05; -// Vector3d x = this->dynamics->get_state().position; -// x[1] = -x[1]; -// geometry_msgs::Point p; -// if(!isnan(x[0]) && !isnan(x[1])) { -// p.x = x[0]; -// p.y = x[1]; -// p.z = x[2]; -// quad_initialized = true; -// } -// else -// { -// p.x = 0; -// p.y = 0; -// p.z = 0; -// } - -// m.points.push_back(p); -// if (m.points.size() > 1000) -// m.points.erase(m.points.begin()); - -// g.pose.position.x = this->target_pos[0]; -// g.pose.position.y = -this->target_pos[1]; -// g.pose.position.z = this->target_pos[2]; -// g.pose.orientation.x = 0.0; -// g.pose.orientation.y = 0.0; -// g.pose.orientation.z = 0.0; -// g.pose.orientation.w = 1.0; - -// goal_pub.publish(g); -// marker_pub.publish(m); -// } - -// void Quadrotor::run() { -// ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration_rhp, this); -// ros::spin(); -// } - -// void Quadrotor::publish_state() { -// simulator_utils::Waypoint wp; -// geometry_msgs::Point p,v; -// state_space_t ned_state = this->dynamics->get_state(); -// p.x = ned_state.position[0]; -// p.y = ned_state.position[1]; -// p.z = ned_state.position[2]; -// v.x = ned_state.velocity[0]; -// v.y = ned_state.velocity[1]; -// v.z = ned_state.velocity[2]; -// wp.position = p; -// wp.velocity = v; -// wp.acceleration.x = wp.acceleration.y = wp.acceleration.z = 0; -// this->state_pub.publish(wp); -// } - -// bool Quadrotor::initialize(double dt_) { -// m_state = State::Idle; -// // load drone params -// if (!load_params()) { -// RCLCPP_ERROR(this->get_logger(), "Could not load the drone parameters"); -// return false; -// } -// // load init params -// if (!load_init_vals()) { -// RCLCPP_ERROR(this->get_logger(), "Could not load the drone initial values"); -// return false; -// } - -// std::stringstream ss; -// ss << localframe << robot_id; -// robot_link_name = ss.str(); - -// // set initial values -// state_space.position = init_vals.position; -// state_space.velocity = init_vals.velocity; -// state_space.R = init_vals.R; -// state_space.omega = init_vals.omega; - -// dynamics = new DynamicsProvider(params, init_vals); -// controller = new ControllerImpl(params, init_vals, gains, dt_); - -// this->setState(State::Autonomous); -// initPaths(); - -// desired_state_sub = this->create_subscription( -// "desired_state", 10, std::bind(&Quadrotor::desired_pos_cb, this, std::placeholders::_1)); -// state_pub = this->create_publisher("current_state", 10); -// RCLCPP_INFO(this->get_logger(), "Drone initialized %d", robot_id); -// RCLCPP_INFO(this->get_logger(), "Desired state subscriber topic: robot_%d/desired_state", robot_id); -// RCLCPP_INFO(this->get_logger(), "State publisher topic: robot_%d/current_state", robot_id); - -// this->set_init_target = false; -// return true; -// } - -// void Quadrotor::setState(State m_state_) { -// this->m_state = m_state_; -// } /* ros2 run mavswarm2 mavswarm2 0 50 --ros-args --log-level DEBUG */ int main(int argc, char **argv) { + rclcpp::init(argc, argv); int robot_id = std::atoi(argv[1]); double frequency = (double)std::atof(argv[2]); auto logger = rclcpp::get_logger("logger"); RCLCPP_INFO(logger, "Initialing drone: %d %3f", robot_id, frequency); - rclcpp::init(argc, argv); - stringstream ss; - // ss << "robot_0"<(ss.str()); - // Quadrotor quad(robot_id, frequency); + rclcpp::spin(std::make_shared(robot_id, frequency)); rclcpp::shutdown(); return 0; } - -// #include -// #include -// #include -// #include - -// #include "geometry_msgs/msg/transform_stamped.hpp" -// #include "geometry_msgs/msg/twist.hpp" -// #include "rclcpp/rclcpp.hpp" -// #include "tf2/exceptions.h" -// #include "tf2_ros/transform_listener.h" -// #include "tf2_ros/buffer.h" -// #include "turtlesim/srv/spawn.hpp" - -// using namespace std::chrono_literals; - -// class FrameListener : public rclcpp::Node -// { -// public: -// FrameListener() -// : Node("turtle_tf2_frame_listener"), -// turtle_spawning_service_ready_(false), -// turtle_spawned_(false) -// { -// // Declare and acquire `target_frame` parameter -// target_frame_ = this->declare_parameter("target_frame", "turtle1"); - -// tf_buffer_ = -// std::make_unique(this->get_clock()); -// tf_listener_ = -// std::make_shared(*tf_buffer_); - -// // Create a client to spawn a turtle -// spawner_ = -// this->create_client("spawn"); - -// // Create turtle2 velocity publisher -// publisher_ = -// this->create_publisher("turtle2/cmd_vel", 1); - -// // Call on_timer function every second -// timer_ = this->create_wall_timer( -// 1s, std::bind(&FrameListener::on_timer, this)); -// } - -// private: -// void on_timer() -// { -// // Store frame names in variables that will be used to -// // compute transformations -// std::string fromFrameRel = target_frame_.c_str(); -// std::string toFrameRel = "turtle2"; - -// if (turtle_spawning_service_ready_) { -// if (turtle_spawned_) { -// geometry_msgs::msg::TransformStamped t; - -// // Look up for the transformation between target_frame and turtle2 frames -// // and send velocity commands for turtle2 to reach target_frame -// try { -// t = tf_buffer_->lookupTransform( -// toFrameRel, fromFrameRel, -// tf2::TimePointZero); -// } catch (const tf2::TransformException & ex) { -// RCLCPP_INFO( -// this->get_logger(), "Could not transform %s to %s: %s", -// toFrameRel.c_str(), fromFrameRel.c_str(), ex.what()); -// return; -// } - -// geometry_msgs::msg::Twist msg; - -// static const double scaleRotationRate = 1.0; -// msg.angular.z = scaleRotationRate * atan2( -// t.transform.translation.y, -// t.transform.translation.x); - -// static const double scaleForwardSpeed = 0.5; -// msg.linear.x = scaleForwardSpeed * sqrt( -// pow(t.transform.translation.x, 2) + -// pow(t.transform.translation.y, 2)); - -// publisher_->publish(msg); -// } else { -// RCLCPP_INFO(this->get_logger(), "Successfully spawned"); -// turtle_spawned_ = true; -// } -// } else { -// // Check if the service is ready -// if (spawner_->service_is_ready()) { -// // Initialize request with turtle name and coordinates -// // Note that x, y and theta are defined as floats in turtlesim/srv/Spawn -// auto request = std::make_shared(); -// request->x = 4.0; -// request->y = 2.0; -// request->theta = 0.0; -// request->name = "turtle2"; - -// // Call request -// using ServiceResponseFuture = -// rclcpp::Client::SharedFuture; -// auto response_received_callback = [this](ServiceResponseFuture future) { -// auto result = future.get(); -// if (strcmp(result->name.c_str(), "turtle2") == 0) { -// turtle_spawning_service_ready_ = true; -// } else { -// RCLCPP_ERROR(this->get_logger(), "Service callback result mismatch"); -// } -// }; -// auto result = spawner_->async_send_request(request, response_received_callback); -// } else { -// RCLCPP_INFO(this->get_logger(), "Service is not ready"); -// } -// } -// } - -// // Boolean values to store the information -// // if the service for spawning turtle is available -// bool turtle_spawning_service_ready_; -// // if the turtle was successfully spawned -// bool turtle_spawned_; -// rclcpp::Client::SharedPtr spawner_{nullptr}; -// rclcpp::TimerBase::SharedPtr timer_{nullptr}; -// rclcpp::Publisher::SharedPtr publisher_{nullptr}; -// std::shared_ptr tf_listener_{nullptr}; -// std::unique_ptr tf_buffer_; -// std::string target_frame_; -// }; - -// int main(int argc, char * argv[]) -// { -// rclcpp::init(argc, argv); -// rclcpp::spin(std::make_shared()); -// rclcpp::shutdown(); -// return 0; -// } \ No newline at end of file From b9d8226747bd2cd4947b48798747f6744adcce31 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Sat, 15 Jun 2024 14:54:23 +0530 Subject: [PATCH 15/24] single drone simulation --- .../controller/geometric_controller.hpp | 2 +- include/mavswarm2/dynamics_provider.hpp | 4 +- include/mavswarm2/quadrotor.hpp | 62 ++-- include/misc/visualizer.hpp | 327 ------------------ launch/quadrotor.launch | 36 +- src/quadrotor.cpp | 3 +- 6 files changed, 59 insertions(+), 375 deletions(-) delete mode 100644 include/misc/visualizer.hpp diff --git a/include/mavswarm2/controller/geometric_controller.hpp b/include/mavswarm2/controller/geometric_controller.hpp index ccae68f..c7bf7e4 100644 --- a/include/mavswarm2/controller/geometric_controller.hpp +++ b/include/mavswarm2/controller/geometric_controller.hpp @@ -36,7 +36,7 @@ class Geometric_Controller public: Geometric_Controller(params_t params_, gains_t gains_, double dt_) - :params(std::move(params_)), gains(gains_), dt(dt_) + :params(std::move(params_)), dt(dt_), gains(gains_) { // initialize derivative operators diff --git a/include/mavswarm2/dynamics_provider.hpp b/include/mavswarm2/dynamics_provider.hpp index b24970f..580baba 100644 --- a/include/mavswarm2/dynamics_provider.hpp +++ b/include/mavswarm2/dynamics_provider.hpp @@ -41,10 +41,9 @@ class DynamicsProvider { public: -DynamicsProvider(params_t params, init_vals_t init_vals) +DynamicsProvider(params_t params, state_space_t init_vals) { this->params = params; - this->init_vals = init_vals; if (!state_set) { state_space.position = simulator_utils::ned_nwu_rotation(init_vals.position); @@ -149,7 +148,6 @@ void reset_dynamics() { private: const size_t DIMENSIONS = 18; const gsl_odeiv2_step_type *T = gsl_odeiv2_step_rkf45; - // Check if GSL is compatible with ROS 2, otherwise use alternatives bool state_set = false; state_space_t state_space; params_t params; diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index abc9b9c..41adc26 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -30,8 +30,10 @@ limitations under the License. #include "dynamics_provider.hpp" #include "controller/geometric_controller.hpp" #include "simulator_interfaces/msg/waypoint.hpp" +#include "simulator_interfaces/msg/geometric_ctrl.hpp" using namespace std::chrono_literals; + #ifndef STATE_H #define STATE_H enum State { @@ -53,11 +55,10 @@ class Quadrotor : public rclcpp::Node { :Node("robot_"+to_string(robot_id)), frequency(frequency), robot_id(robot_id) { sim_time = 0; dt = 1/frequency; - RCLCPP_INFO(this->get_logger(), "dt: %4f ", dt); - // dt = 0.01; + RCLCPP_INFO(this->get_logger(), "Initialing drone: %d %3f", robot_id, frequency); + m_state = State::Idle; - this->u << 0,0,0; timer_ = this->create_wall_timer(std::chrono::duration(dt), std::bind(&Quadrotor::iteration, this)); RCLCPP_INFO(this->get_logger(), "Loading parameters"); @@ -67,6 +68,8 @@ class Quadrotor : public rclcpp::Node { rclcpp::shutdown(); } + d_state_sub = this->create_subscription( + "robot_"+to_string(this->robot_id)+"/desired_state", 10, std::bind(&Quadrotor::desired_state_cb, this, std::placeholders::_1)); // logger = this->get_logger(); // while (marker_pub.getNumSubscribers() < 1) { @@ -74,7 +77,7 @@ class Quadrotor : public rclcpp::Node { // ros::Duration(1).sleep(); // } controller = std::make_shared(params_, gains, dt); - dynamics = std::make_shared(params_, init_vals); + dynamics = std::make_shared(params_, x0); set_state_space(); this->setState(State::Autonomous); @@ -91,27 +94,18 @@ class Quadrotor : public rclcpp::Node { // xd should be in NED frame and so does dynamics and controller. - // void run() { - // // ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration, this); - // ros::spin(); - // } private: State m_state; - double sim_time, tau, dt, frequency; + double sim_time, dt, frequency; int robot_id; std::string worldframe, localframe, robot_link_name; gains_t gains; - std::vector traj_piece; - int xd_it; - Vector3d u, target_pos; - state_space_t x0, xd0; - desired_state_t dss; - bool set_init_target; - geometry_msgs::msg::Point target_next; - bool set_next_target = false; + state_space_t x0; + // geometry_msgs::msg::Point target_next; + // bool set_next_target = false; std::shared_ptr controller; state_space_t state_space; @@ -120,6 +114,13 @@ class Quadrotor : public rclcpp::Node { params_t params_; init_vals_t init_vals; rclcpp::TimerBase::SharedPtr timer_; + rclcpp::Subscription::SharedPtr d_state_sub; + + +void desired_state_cb(const simulator_interfaces::msg::GeometricCtrl::SharedPtr msg) const { + RCLCPP_INFO(this->get_logger(), "I heard: '%s'", to_string(msg->heading.x).c_str()); + } + // rclcpp::Publisher::SharedPtr marker_pub, goal_pub, state_pub; // visualization_msgs::msg::Marker m, g; @@ -163,12 +164,12 @@ bool load_params() { vector vel_ = get_parameter("velocity").as_double_array(); vector rot_ = get_parameter("rotation").as_double_array(); vector omega_ = get_parameter("omega").as_double_array(); - init_vals.position = simulator_utils::ned_nwu_rotation(Vector3d(pos_.data())); - init_vals.velocity << simulator_utils::ned_nwu_rotation(Vector3d(vel_.data())); - init_vals.R << simulator_utils::ned_nwu_rotation(Matrix3d(rot_.data())); - init_vals.omega << simulator_utils::ned_nwu_rotation(Vector3d(omega_.data())); - gains = {.kx = gains_[0], .kv = gains_[1], .kr = gains_[3], .komega = gains_[3]}; - RCLCPP_INFO(this->get_logger(), "Init Params: : %4f %4f %4f ", init_vals.position[0], init_vals.position[1],init_vals.position[2]); + x0.position = simulator_utils::ned_nwu_rotation(Vector3d(pos_.data())); + x0.velocity << simulator_utils::ned_nwu_rotation(Vector3d(vel_.data())); + x0.R << simulator_utils::ned_nwu_rotation(Matrix3d(rot_.data())); + x0.omega << simulator_utils::ned_nwu_rotation(Vector3d(omega_.data())); + gains = {gains_[0], gains_[1], gains_[3], gains_[3]}; + RCLCPP_INFO(this->get_logger(), "Init Params: : %4f %4f %4f ", x0.position[0], x0.position[1],x0.position[2]); RCLCPP_INFO(this->get_logger(), "Param: Gravity: %s ",to_string(params_.gravity).c_str()); RCLCPP_INFO(this->get_logger(), "Param: Mass: %s ",to_string(params_.mass).c_str()); @@ -184,18 +185,17 @@ bool load_params() { void move(const desired_state_t &d_state) { state_space_t s = dynamics->get_state(); - // RCLCPP_INFO(this->get_logger(), "dss %4f %4f %4f", d_state.x[0], d_state.x[1], d_state.x[2]); - RCLCPP_DEBUG(this->get_logger(), "%2f position %4f %4f %4f", sim_time, s.position[0], s.position[1], s.position[2]); - // RCLCPP_INFO(this->get_logger(), "%2f rotation %4f %4f %4f", sim_time, s.R(0,0), s.R(1,1), s.R(2,2)); - control_out_t control = controller->get_control(s, d_state); - RCLCPP_DEBUG(this->get_logger(), "%2f control %4f %4f %4f %4f", sim_time, control.F, control.M[0], control.M[1], control.M[2]); dynamics->update(control, sim_time); - // RCLCPP_INFO(this->get_logger(), "control %4f %4f %4f", control.F, control.M[0], control.M[1]); + // updating the model on rviz set_state_space(); // send_transform(); + dynamics->reset_dynamics(); + RCLCPP_DEBUG(this->get_logger(), "%2f position %4f %4f %4f", sim_time, s.position[0], s.position[1], s.position[2]); + RCLCPP_DEBUG(this->get_logger(), "%2f control %4f %4f %4f %4f", sim_time, control.F, control.M[0], control.M[1], control.M[2]); + // RCLCPP_INFO(this->get_logger(), "position: %4f %4f %4f", s.position[0], // s.position[1], s.position[2]); // RCLCPP_INFO(this->get_logger(), "rotation: %4f %4f %4f", state_space.R(0, 0), @@ -212,11 +212,11 @@ bool load_params() { } void iteration() { - Vector3d xd = simulator_utils::ned_nwu_rotation(init_vals.position); + Vector3d xd = simulator_utils::ned_nwu_rotation(x0.position); Vector3d b1d(1, 0, 0); desired_state_t dss = {xd, b1d}; + this->move(dss); - // RCLCPP_INFO(this->get_logger(), "Iteration: "); // this->publish_path(); // this->publish_state(); diff --git a/include/misc/visualizer.hpp b/include/misc/visualizer.hpp deleted file mode 100644 index c74c153..0000000 --- a/include/misc/visualizer.hpp +++ /dev/null @@ -1,327 +0,0 @@ -#ifndef VISUALIZER_HPP -#define VISUALIZER_HPP - -#include "gcopter/trajectory.hpp" -#include "gcopter/quickhull.hpp" -#include "gcopter/geo_utils.hpp" - -#include -#include -#include -#include - -#include -#include -#include -#include -#include -#include - -// Visualizer for the planner -class Visualizer -{ -private: - // config contains the scale for some markers - ros::NodeHandle nh; - - // These are publishers for path, waypoints on the trajectory, - // the entire trajectory, the mesh of free-space polytopes, - // the edge of free-space polytopes, and spheres for safety radius - ros::Publisher routePub; - ros::Publisher wayPointsPub; - ros::Publisher trajectoryPub; - ros::Publisher meshPub; - ros::Publisher edgePub; - ros::Publisher spherePub; - -public: - ros::Publisher speedPub; - ros::Publisher thrPub; - ros::Publisher tiltPub; - ros::Publisher bdrPub; - -public: - Visualizer(ros::NodeHandle &nh_) - : nh(nh_) - { - routePub = nh.advertise("/visualizer/route", 10); - wayPointsPub = nh.advertise("/visualizer/waypoints", 10); - trajectoryPub = nh.advertise("/visualizer/trajectory", 10); - meshPub = nh.advertise("/visualizer/mesh", 1000); - edgePub = nh.advertise("/visualizer/edge", 1000); - spherePub = nh.advertise("/visualizer/spheres", 1000); - speedPub = nh.advertise("/visualizer/speed", 1000); - thrPub = nh.advertise("/visualizer/total_thrust", 1000); - tiltPub = nh.advertise("/visualizer/tilt_angle", 1000); - bdrPub = nh.advertise("/visualizer/body_rate", 1000); - } - - // Visualize the trajectory and its front-end path - template - inline void visualize(const Trajectory &traj, - const std::vector &route) - { - visualization_msgs::Marker routeMarker, wayPointsMarker, trajMarker; - - routeMarker.id = 0; - routeMarker.type = visualization_msgs::Marker::LINE_LIST; - routeMarker.header.stamp = ros::Time::now(); - routeMarker.header.frame_id = "odom"; - routeMarker.pose.orientation.w = 1.00; - routeMarker.action = visualization_msgs::Marker::ADD; - routeMarker.ns = "route"; - routeMarker.color.r = 1.00; - routeMarker.color.g = 0.00; - routeMarker.color.b = 0.00; - routeMarker.color.a = 1.00; - routeMarker.scale.x = 0.1; - - wayPointsMarker = routeMarker; - wayPointsMarker.id = -wayPointsMarker.id - 1; - wayPointsMarker.type = visualization_msgs::Marker::SPHERE_LIST; - wayPointsMarker.ns = "waypoints"; - wayPointsMarker.color.r = 1.00; - wayPointsMarker.color.g = 0.00; - wayPointsMarker.color.b = 0.00; - wayPointsMarker.scale.x = 0.35; - wayPointsMarker.scale.y = 0.35; - wayPointsMarker.scale.z = 0.35; - - trajMarker = routeMarker; - trajMarker.header.frame_id = "odom"; - trajMarker.id = 0; - trajMarker.ns = "trajectory"; - trajMarker.color.r = 0.00; - trajMarker.color.g = 0.50; - trajMarker.color.b = 1.00; - trajMarker.scale.x = 0.30; - - if (route.size() > 0) - { - bool first = true; - Eigen::Vector3d last; - for (auto it : route) - { - if (first) - { - first = false; - last = it; - continue; - } - geometry_msgs::Point point; - - point.x = last(0); - point.y = last(1); - point.z = last(2); - routeMarker.points.push_back(point); - point.x = it(0); - point.y = it(1); - point.z = it(2); - routeMarker.points.push_back(point); - last = it; - } - - routePub.publish(routeMarker); - } - - if (traj.getPieceNum() > 0) - { - Eigen::MatrixXd wps = traj.getPositions(); - for (int i = 0; i < wps.cols(); i++) - { - geometry_msgs::Point point; - point.x = wps.col(i)(0); - point.y = wps.col(i)(1); - point.z = wps.col(i)(2); - wayPointsMarker.points.push_back(point); - } - - wayPointsPub.publish(wayPointsMarker); - } - - if (traj.getPieceNum() > 0) - { - double T = 0.01; - Eigen::Vector3d lastX = traj.getPos(0.0); - for (double t = T; t < traj.getTotalDuration(); t += T) - { - geometry_msgs::Point point; - Eigen::Vector3d X = traj.getPos(t); - point.x = lastX(0); - point.y = lastX(1); - point.z = lastX(2); - trajMarker.points.push_back(point); - point.x = X(0); - point.y = X(1); - point.z = X(2); - trajMarker.points.push_back(point); - lastX = X; - } - trajectoryPub.publish(trajMarker); - } - } - - // Visualize some polytopes in H-representation - inline void visualizePolytope(const std::vector &hPolys) - { - - // Due to the fact that H-representation cannot be directly visualized - // We first conduct vertex enumeration of them, then apply quickhull - // to obtain triangle meshs of polyhedra - Eigen::Matrix3Xd mesh(3, 0), curTris(3, 0), oldTris(3, 0); - for (size_t id = 0; id < hPolys.size(); id++) - { - oldTris = mesh; - Eigen::Matrix vPoly; - geo_utils::enumerateVs(hPolys[id], vPoly); - - quickhull::QuickHull tinyQH; - const auto polyHull = tinyQH.getConvexHull(vPoly.data(), vPoly.cols(), false, true); - const auto &idxBuffer = polyHull.getIndexBuffer(); - int hNum = idxBuffer.size() / 3; - - curTris.resize(3, hNum * 3); - for (int i = 0; i < hNum * 3; i++) - { - curTris.col(i) = vPoly.col(idxBuffer[i]); - } - mesh.resize(3, oldTris.cols() + curTris.cols()); - mesh.leftCols(oldTris.cols()) = oldTris; - mesh.rightCols(curTris.cols()) = curTris; - } - - // RVIZ support tris for visualization - visualization_msgs::Marker meshMarker, edgeMarker; - - meshMarker.id = 0; - meshMarker.header.stamp = ros::Time::now(); - meshMarker.header.frame_id = "odom"; - meshMarker.pose.orientation.w = 1.00; - meshMarker.action = visualization_msgs::Marker::ADD; - meshMarker.type = visualization_msgs::Marker::TRIANGLE_LIST; - meshMarker.ns = "mesh"; - meshMarker.color.r = 0.00; - meshMarker.color.g = 0.00; - meshMarker.color.b = 1.00; - meshMarker.color.a = 0.15; - meshMarker.scale.x = 1.0; - meshMarker.scale.y = 1.0; - meshMarker.scale.z = 1.0; - - edgeMarker = meshMarker; - edgeMarker.type = visualization_msgs::Marker::LINE_LIST; - edgeMarker.ns = "edge"; - edgeMarker.color.r = 0.00; - edgeMarker.color.g = 1.00; - edgeMarker.color.b = 1.00; - edgeMarker.color.a = 1.00; - edgeMarker.scale.x = 0.02; - - geometry_msgs::Point point; - - int ptnum = mesh.cols(); - - for (int i = 0; i < ptnum; i++) - { - point.x = mesh(0, i); - point.y = mesh(1, i); - point.z = mesh(2, i); - meshMarker.points.push_back(point); - } - - for (int i = 0; i < ptnum / 3; i++) - { - for (int j = 0; j < 3; j++) - { - point.x = mesh(0, 3 * i + j); - point.y = mesh(1, 3 * i + j); - point.z = mesh(2, 3 * i + j); - edgeMarker.points.push_back(point); - point.x = mesh(0, 3 * i + (j + 1) % 3); - point.y = mesh(1, 3 * i + (j + 1) % 3); - point.z = mesh(2, 3 * i + (j + 1) % 3); - edgeMarker.points.push_back(point); - } - } - - meshPub.publish(meshMarker); - edgePub.publish(edgeMarker); - - return; - } - - // Visualize all spheres with centers sphs and the same radius - inline void visualizeSphere(const Eigen::Vector3d ¢er, - const double &radius) - { - visualization_msgs::Marker sphereMarkers, sphereDeleter; - - sphereMarkers.id = 0; - sphereMarkers.type = visualization_msgs::Marker::SPHERE_LIST; - sphereMarkers.header.stamp = ros::Time::now(); - sphereMarkers.header.frame_id = "odom"; - sphereMarkers.pose.orientation.w = 1.00; - sphereMarkers.action = visualization_msgs::Marker::ADD; - sphereMarkers.ns = "spheres"; - sphereMarkers.color.r = 0.00; - sphereMarkers.color.g = 0.00; - sphereMarkers.color.b = 1.00; - sphereMarkers.color.a = 1.00; - sphereMarkers.scale.x = radius * 2.0; - sphereMarkers.scale.y = radius * 2.0; - sphereMarkers.scale.z = radius * 2.0; - - sphereDeleter = sphereMarkers; - sphereDeleter.action = visualization_msgs::Marker::DELETE; - - geometry_msgs::Point point; - point.x = center(0); - point.y = center(1); - point.z = center(2); - sphereMarkers.points.push_back(point); - - spherePub.publish(sphereDeleter); - spherePub.publish(sphereMarkers); - } - - inline void visualizeStartGoal(const Eigen::Vector3d ¢er, - const double &radius, - const int sg) - { - visualization_msgs::Marker sphereMarkers, sphereDeleter; - - sphereMarkers.id = sg; - sphereMarkers.type = visualization_msgs::Marker::SPHERE_LIST; - sphereMarkers.header.stamp = ros::Time::now(); - sphereMarkers.header.frame_id = "odom"; - sphereMarkers.pose.orientation.w = 1.00; - sphereMarkers.action = visualization_msgs::Marker::ADD; - sphereMarkers.ns = "StartGoal"; - sphereMarkers.color.r = 1.00; - sphereMarkers.color.g = 0.00; - sphereMarkers.color.b = 0.00; - sphereMarkers.color.a = 1.00; - sphereMarkers.scale.x = radius * 2.0; - sphereMarkers.scale.y = radius * 2.0; - sphereMarkers.scale.z = radius * 2.0; - - sphereDeleter = sphereMarkers; - sphereDeleter.action = visualization_msgs::Marker::DELETEALL; - - geometry_msgs::Point point; - point.x = center(0); - point.y = center(1); - point.z = center(2); - sphereMarkers.points.push_back(point); - - if (sg == 0) - { - spherePub.publish(sphereDeleter); - ros::Duration(1.0e-9).sleep(); - sphereMarkers.header.stamp = ros::Time::now(); - } - spherePub.publish(sphereMarkers); - } -}; - -#endif \ No newline at end of file diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index 671ceb3..7184e08 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -1,19 +1,31 @@ - - - - + + + + - - - + pkg="mavswarm2" + exec="mavswarm2" + output="screen" + name="robot_0" + namespace="mavswarm2" + args="$(var robot_id) $(var controller_frequency) --ros-args --log-level $(var log_level)"> + + + + + + + - + \ No newline at end of file diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 81ccbcd..6ff8a35 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -19,6 +19,8 @@ limitations under the License. /* ros2 run mavswarm2 mavswarm2 0 50 --ros-args --log-level DEBUG +ros2 topic pub --rate 1 /desired_state simulator_interfaces/msg/GeometricCtrl "{position:{x: 2.0, y: 2.4, z: -3.0},heading:{x: 1, y: 0, z: 0}}" + */ int main(int argc, char **argv) { @@ -27,7 +29,6 @@ int main(int argc, char **argv) { double frequency = (double)std::atof(argv[2]); auto logger = rclcpp::get_logger("logger"); - RCLCPP_INFO(logger, "Initialing drone: %d %3f", robot_id, frequency); rclcpp::spin(std::make_shared(robot_id, frequency)); rclcpp::shutdown(); From bfec351bc3c5d4961053904a55dd3e73dee02a18 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Wed, 25 Jun 2025 12:30:48 +0530 Subject: [PATCH 16/24] Fix#19:add simulator_interfaces repo, update src, launch --- .../controller/geometric_controller.hpp | 2 +- include/mavswarm2/dynamics_provider.hpp | 4 +- include/mavswarm2/quadrotor.hpp | 62 ++-- include/misc/visualizer.hpp | 327 ++++++++++++++++++ launch/quadrotor.launch | 36 +- readme.md | 2 +- src/quadrotor.cpp | 3 +- 7 files changed, 376 insertions(+), 60 deletions(-) create mode 100644 include/misc/visualizer.hpp diff --git a/include/mavswarm2/controller/geometric_controller.hpp b/include/mavswarm2/controller/geometric_controller.hpp index c7bf7e4..ccae68f 100644 --- a/include/mavswarm2/controller/geometric_controller.hpp +++ b/include/mavswarm2/controller/geometric_controller.hpp @@ -36,7 +36,7 @@ class Geometric_Controller public: Geometric_Controller(params_t params_, gains_t gains_, double dt_) - :params(std::move(params_)), dt(dt_), gains(gains_) + :params(std::move(params_)), gains(gains_), dt(dt_) { // initialize derivative operators diff --git a/include/mavswarm2/dynamics_provider.hpp b/include/mavswarm2/dynamics_provider.hpp index 580baba..b24970f 100644 --- a/include/mavswarm2/dynamics_provider.hpp +++ b/include/mavswarm2/dynamics_provider.hpp @@ -41,9 +41,10 @@ class DynamicsProvider { public: -DynamicsProvider(params_t params, state_space_t init_vals) +DynamicsProvider(params_t params, init_vals_t init_vals) { this->params = params; + this->init_vals = init_vals; if (!state_set) { state_space.position = simulator_utils::ned_nwu_rotation(init_vals.position); @@ -148,6 +149,7 @@ void reset_dynamics() { private: const size_t DIMENSIONS = 18; const gsl_odeiv2_step_type *T = gsl_odeiv2_step_rkf45; + // Check if GSL is compatible with ROS 2, otherwise use alternatives bool state_set = false; state_space_t state_space; params_t params; diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 41adc26..abc9b9c 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -30,10 +30,8 @@ limitations under the License. #include "dynamics_provider.hpp" #include "controller/geometric_controller.hpp" #include "simulator_interfaces/msg/waypoint.hpp" -#include "simulator_interfaces/msg/geometric_ctrl.hpp" using namespace std::chrono_literals; - #ifndef STATE_H #define STATE_H enum State { @@ -55,10 +53,11 @@ class Quadrotor : public rclcpp::Node { :Node("robot_"+to_string(robot_id)), frequency(frequency), robot_id(robot_id) { sim_time = 0; dt = 1/frequency; - RCLCPP_INFO(this->get_logger(), "Initialing drone: %d %3f", robot_id, frequency); - + RCLCPP_INFO(this->get_logger(), "dt: %4f ", dt); + // dt = 0.01; m_state = State::Idle; + this->u << 0,0,0; timer_ = this->create_wall_timer(std::chrono::duration(dt), std::bind(&Quadrotor::iteration, this)); RCLCPP_INFO(this->get_logger(), "Loading parameters"); @@ -68,8 +67,6 @@ class Quadrotor : public rclcpp::Node { rclcpp::shutdown(); } - d_state_sub = this->create_subscription( - "robot_"+to_string(this->robot_id)+"/desired_state", 10, std::bind(&Quadrotor::desired_state_cb, this, std::placeholders::_1)); // logger = this->get_logger(); // while (marker_pub.getNumSubscribers() < 1) { @@ -77,7 +74,7 @@ class Quadrotor : public rclcpp::Node { // ros::Duration(1).sleep(); // } controller = std::make_shared(params_, gains, dt); - dynamics = std::make_shared(params_, x0); + dynamics = std::make_shared(params_, init_vals); set_state_space(); this->setState(State::Autonomous); @@ -94,18 +91,27 @@ class Quadrotor : public rclcpp::Node { // xd should be in NED frame and so does dynamics and controller. + // void run() { + // // ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration, this); + // ros::spin(); + // } private: State m_state; - double sim_time, dt, frequency; + double sim_time, tau, dt, frequency; int robot_id; std::string worldframe, localframe, robot_link_name; gains_t gains; - state_space_t x0; - // geometry_msgs::msg::Point target_next; - // bool set_next_target = false; + std::vector traj_piece; + int xd_it; + Vector3d u, target_pos; + state_space_t x0, xd0; + desired_state_t dss; + bool set_init_target; + geometry_msgs::msg::Point target_next; + bool set_next_target = false; std::shared_ptr controller; state_space_t state_space; @@ -114,13 +120,6 @@ class Quadrotor : public rclcpp::Node { params_t params_; init_vals_t init_vals; rclcpp::TimerBase::SharedPtr timer_; - rclcpp::Subscription::SharedPtr d_state_sub; - - -void desired_state_cb(const simulator_interfaces::msg::GeometricCtrl::SharedPtr msg) const { - RCLCPP_INFO(this->get_logger(), "I heard: '%s'", to_string(msg->heading.x).c_str()); - } - // rclcpp::Publisher::SharedPtr marker_pub, goal_pub, state_pub; // visualization_msgs::msg::Marker m, g; @@ -164,12 +163,12 @@ bool load_params() { vector vel_ = get_parameter("velocity").as_double_array(); vector rot_ = get_parameter("rotation").as_double_array(); vector omega_ = get_parameter("omega").as_double_array(); - x0.position = simulator_utils::ned_nwu_rotation(Vector3d(pos_.data())); - x0.velocity << simulator_utils::ned_nwu_rotation(Vector3d(vel_.data())); - x0.R << simulator_utils::ned_nwu_rotation(Matrix3d(rot_.data())); - x0.omega << simulator_utils::ned_nwu_rotation(Vector3d(omega_.data())); - gains = {gains_[0], gains_[1], gains_[3], gains_[3]}; - RCLCPP_INFO(this->get_logger(), "Init Params: : %4f %4f %4f ", x0.position[0], x0.position[1],x0.position[2]); + init_vals.position = simulator_utils::ned_nwu_rotation(Vector3d(pos_.data())); + init_vals.velocity << simulator_utils::ned_nwu_rotation(Vector3d(vel_.data())); + init_vals.R << simulator_utils::ned_nwu_rotation(Matrix3d(rot_.data())); + init_vals.omega << simulator_utils::ned_nwu_rotation(Vector3d(omega_.data())); + gains = {.kx = gains_[0], .kv = gains_[1], .kr = gains_[3], .komega = gains_[3]}; + RCLCPP_INFO(this->get_logger(), "Init Params: : %4f %4f %4f ", init_vals.position[0], init_vals.position[1],init_vals.position[2]); RCLCPP_INFO(this->get_logger(), "Param: Gravity: %s ",to_string(params_.gravity).c_str()); RCLCPP_INFO(this->get_logger(), "Param: Mass: %s ",to_string(params_.mass).c_str()); @@ -185,17 +184,18 @@ bool load_params() { void move(const desired_state_t &d_state) { state_space_t s = dynamics->get_state(); + // RCLCPP_INFO(this->get_logger(), "dss %4f %4f %4f", d_state.x[0], d_state.x[1], d_state.x[2]); + RCLCPP_DEBUG(this->get_logger(), "%2f position %4f %4f %4f", sim_time, s.position[0], s.position[1], s.position[2]); + // RCLCPP_INFO(this->get_logger(), "%2f rotation %4f %4f %4f", sim_time, s.R(0,0), s.R(1,1), s.R(2,2)); + control_out_t control = controller->get_control(s, d_state); + RCLCPP_DEBUG(this->get_logger(), "%2f control %4f %4f %4f %4f", sim_time, control.F, control.M[0], control.M[1], control.M[2]); dynamics->update(control, sim_time); - + // RCLCPP_INFO(this->get_logger(), "control %4f %4f %4f", control.F, control.M[0], control.M[1]); // updating the model on rviz set_state_space(); // send_transform(); - dynamics->reset_dynamics(); - RCLCPP_DEBUG(this->get_logger(), "%2f position %4f %4f %4f", sim_time, s.position[0], s.position[1], s.position[2]); - RCLCPP_DEBUG(this->get_logger(), "%2f control %4f %4f %4f %4f", sim_time, control.F, control.M[0], control.M[1], control.M[2]); - // RCLCPP_INFO(this->get_logger(), "position: %4f %4f %4f", s.position[0], // s.position[1], s.position[2]); // RCLCPP_INFO(this->get_logger(), "rotation: %4f %4f %4f", state_space.R(0, 0), @@ -212,11 +212,11 @@ bool load_params() { } void iteration() { - Vector3d xd = simulator_utils::ned_nwu_rotation(x0.position); + Vector3d xd = simulator_utils::ned_nwu_rotation(init_vals.position); Vector3d b1d(1, 0, 0); desired_state_t dss = {xd, b1d}; - this->move(dss); + // RCLCPP_INFO(this->get_logger(), "Iteration: "); // this->publish_path(); // this->publish_state(); diff --git a/include/misc/visualizer.hpp b/include/misc/visualizer.hpp new file mode 100644 index 0000000..c74c153 --- /dev/null +++ b/include/misc/visualizer.hpp @@ -0,0 +1,327 @@ +#ifndef VISUALIZER_HPP +#define VISUALIZER_HPP + +#include "gcopter/trajectory.hpp" +#include "gcopter/quickhull.hpp" +#include "gcopter/geo_utils.hpp" + +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include + +// Visualizer for the planner +class Visualizer +{ +private: + // config contains the scale for some markers + ros::NodeHandle nh; + + // These are publishers for path, waypoints on the trajectory, + // the entire trajectory, the mesh of free-space polytopes, + // the edge of free-space polytopes, and spheres for safety radius + ros::Publisher routePub; + ros::Publisher wayPointsPub; + ros::Publisher trajectoryPub; + ros::Publisher meshPub; + ros::Publisher edgePub; + ros::Publisher spherePub; + +public: + ros::Publisher speedPub; + ros::Publisher thrPub; + ros::Publisher tiltPub; + ros::Publisher bdrPub; + +public: + Visualizer(ros::NodeHandle &nh_) + : nh(nh_) + { + routePub = nh.advertise("/visualizer/route", 10); + wayPointsPub = nh.advertise("/visualizer/waypoints", 10); + trajectoryPub = nh.advertise("/visualizer/trajectory", 10); + meshPub = nh.advertise("/visualizer/mesh", 1000); + edgePub = nh.advertise("/visualizer/edge", 1000); + spherePub = nh.advertise("/visualizer/spheres", 1000); + speedPub = nh.advertise("/visualizer/speed", 1000); + thrPub = nh.advertise("/visualizer/total_thrust", 1000); + tiltPub = nh.advertise("/visualizer/tilt_angle", 1000); + bdrPub = nh.advertise("/visualizer/body_rate", 1000); + } + + // Visualize the trajectory and its front-end path + template + inline void visualize(const Trajectory &traj, + const std::vector &route) + { + visualization_msgs::Marker routeMarker, wayPointsMarker, trajMarker; + + routeMarker.id = 0; + routeMarker.type = visualization_msgs::Marker::LINE_LIST; + routeMarker.header.stamp = ros::Time::now(); + routeMarker.header.frame_id = "odom"; + routeMarker.pose.orientation.w = 1.00; + routeMarker.action = visualization_msgs::Marker::ADD; + routeMarker.ns = "route"; + routeMarker.color.r = 1.00; + routeMarker.color.g = 0.00; + routeMarker.color.b = 0.00; + routeMarker.color.a = 1.00; + routeMarker.scale.x = 0.1; + + wayPointsMarker = routeMarker; + wayPointsMarker.id = -wayPointsMarker.id - 1; + wayPointsMarker.type = visualization_msgs::Marker::SPHERE_LIST; + wayPointsMarker.ns = "waypoints"; + wayPointsMarker.color.r = 1.00; + wayPointsMarker.color.g = 0.00; + wayPointsMarker.color.b = 0.00; + wayPointsMarker.scale.x = 0.35; + wayPointsMarker.scale.y = 0.35; + wayPointsMarker.scale.z = 0.35; + + trajMarker = routeMarker; + trajMarker.header.frame_id = "odom"; + trajMarker.id = 0; + trajMarker.ns = "trajectory"; + trajMarker.color.r = 0.00; + trajMarker.color.g = 0.50; + trajMarker.color.b = 1.00; + trajMarker.scale.x = 0.30; + + if (route.size() > 0) + { + bool first = true; + Eigen::Vector3d last; + for (auto it : route) + { + if (first) + { + first = false; + last = it; + continue; + } + geometry_msgs::Point point; + + point.x = last(0); + point.y = last(1); + point.z = last(2); + routeMarker.points.push_back(point); + point.x = it(0); + point.y = it(1); + point.z = it(2); + routeMarker.points.push_back(point); + last = it; + } + + routePub.publish(routeMarker); + } + + if (traj.getPieceNum() > 0) + { + Eigen::MatrixXd wps = traj.getPositions(); + for (int i = 0; i < wps.cols(); i++) + { + geometry_msgs::Point point; + point.x = wps.col(i)(0); + point.y = wps.col(i)(1); + point.z = wps.col(i)(2); + wayPointsMarker.points.push_back(point); + } + + wayPointsPub.publish(wayPointsMarker); + } + + if (traj.getPieceNum() > 0) + { + double T = 0.01; + Eigen::Vector3d lastX = traj.getPos(0.0); + for (double t = T; t < traj.getTotalDuration(); t += T) + { + geometry_msgs::Point point; + Eigen::Vector3d X = traj.getPos(t); + point.x = lastX(0); + point.y = lastX(1); + point.z = lastX(2); + trajMarker.points.push_back(point); + point.x = X(0); + point.y = X(1); + point.z = X(2); + trajMarker.points.push_back(point); + lastX = X; + } + trajectoryPub.publish(trajMarker); + } + } + + // Visualize some polytopes in H-representation + inline void visualizePolytope(const std::vector &hPolys) + { + + // Due to the fact that H-representation cannot be directly visualized + // We first conduct vertex enumeration of them, then apply quickhull + // to obtain triangle meshs of polyhedra + Eigen::Matrix3Xd mesh(3, 0), curTris(3, 0), oldTris(3, 0); + for (size_t id = 0; id < hPolys.size(); id++) + { + oldTris = mesh; + Eigen::Matrix vPoly; + geo_utils::enumerateVs(hPolys[id], vPoly); + + quickhull::QuickHull tinyQH; + const auto polyHull = tinyQH.getConvexHull(vPoly.data(), vPoly.cols(), false, true); + const auto &idxBuffer = polyHull.getIndexBuffer(); + int hNum = idxBuffer.size() / 3; + + curTris.resize(3, hNum * 3); + for (int i = 0; i < hNum * 3; i++) + { + curTris.col(i) = vPoly.col(idxBuffer[i]); + } + mesh.resize(3, oldTris.cols() + curTris.cols()); + mesh.leftCols(oldTris.cols()) = oldTris; + mesh.rightCols(curTris.cols()) = curTris; + } + + // RVIZ support tris for visualization + visualization_msgs::Marker meshMarker, edgeMarker; + + meshMarker.id = 0; + meshMarker.header.stamp = ros::Time::now(); + meshMarker.header.frame_id = "odom"; + meshMarker.pose.orientation.w = 1.00; + meshMarker.action = visualization_msgs::Marker::ADD; + meshMarker.type = visualization_msgs::Marker::TRIANGLE_LIST; + meshMarker.ns = "mesh"; + meshMarker.color.r = 0.00; + meshMarker.color.g = 0.00; + meshMarker.color.b = 1.00; + meshMarker.color.a = 0.15; + meshMarker.scale.x = 1.0; + meshMarker.scale.y = 1.0; + meshMarker.scale.z = 1.0; + + edgeMarker = meshMarker; + edgeMarker.type = visualization_msgs::Marker::LINE_LIST; + edgeMarker.ns = "edge"; + edgeMarker.color.r = 0.00; + edgeMarker.color.g = 1.00; + edgeMarker.color.b = 1.00; + edgeMarker.color.a = 1.00; + edgeMarker.scale.x = 0.02; + + geometry_msgs::Point point; + + int ptnum = mesh.cols(); + + for (int i = 0; i < ptnum; i++) + { + point.x = mesh(0, i); + point.y = mesh(1, i); + point.z = mesh(2, i); + meshMarker.points.push_back(point); + } + + for (int i = 0; i < ptnum / 3; i++) + { + for (int j = 0; j < 3; j++) + { + point.x = mesh(0, 3 * i + j); + point.y = mesh(1, 3 * i + j); + point.z = mesh(2, 3 * i + j); + edgeMarker.points.push_back(point); + point.x = mesh(0, 3 * i + (j + 1) % 3); + point.y = mesh(1, 3 * i + (j + 1) % 3); + point.z = mesh(2, 3 * i + (j + 1) % 3); + edgeMarker.points.push_back(point); + } + } + + meshPub.publish(meshMarker); + edgePub.publish(edgeMarker); + + return; + } + + // Visualize all spheres with centers sphs and the same radius + inline void visualizeSphere(const Eigen::Vector3d ¢er, + const double &radius) + { + visualization_msgs::Marker sphereMarkers, sphereDeleter; + + sphereMarkers.id = 0; + sphereMarkers.type = visualization_msgs::Marker::SPHERE_LIST; + sphereMarkers.header.stamp = ros::Time::now(); + sphereMarkers.header.frame_id = "odom"; + sphereMarkers.pose.orientation.w = 1.00; + sphereMarkers.action = visualization_msgs::Marker::ADD; + sphereMarkers.ns = "spheres"; + sphereMarkers.color.r = 0.00; + sphereMarkers.color.g = 0.00; + sphereMarkers.color.b = 1.00; + sphereMarkers.color.a = 1.00; + sphereMarkers.scale.x = radius * 2.0; + sphereMarkers.scale.y = radius * 2.0; + sphereMarkers.scale.z = radius * 2.0; + + sphereDeleter = sphereMarkers; + sphereDeleter.action = visualization_msgs::Marker::DELETE; + + geometry_msgs::Point point; + point.x = center(0); + point.y = center(1); + point.z = center(2); + sphereMarkers.points.push_back(point); + + spherePub.publish(sphereDeleter); + spherePub.publish(sphereMarkers); + } + + inline void visualizeStartGoal(const Eigen::Vector3d ¢er, + const double &radius, + const int sg) + { + visualization_msgs::Marker sphereMarkers, sphereDeleter; + + sphereMarkers.id = sg; + sphereMarkers.type = visualization_msgs::Marker::SPHERE_LIST; + sphereMarkers.header.stamp = ros::Time::now(); + sphereMarkers.header.frame_id = "odom"; + sphereMarkers.pose.orientation.w = 1.00; + sphereMarkers.action = visualization_msgs::Marker::ADD; + sphereMarkers.ns = "StartGoal"; + sphereMarkers.color.r = 1.00; + sphereMarkers.color.g = 0.00; + sphereMarkers.color.b = 0.00; + sphereMarkers.color.a = 1.00; + sphereMarkers.scale.x = radius * 2.0; + sphereMarkers.scale.y = radius * 2.0; + sphereMarkers.scale.z = radius * 2.0; + + sphereDeleter = sphereMarkers; + sphereDeleter.action = visualization_msgs::Marker::DELETEALL; + + geometry_msgs::Point point; + point.x = center(0); + point.y = center(1); + point.z = center(2); + sphereMarkers.points.push_back(point); + + if (sg == 0) + { + spherePub.publish(sphereDeleter); + ros::Duration(1.0e-9).sleep(); + sphereMarkers.header.stamp = ros::Time::now(); + } + spherePub.publish(sphereMarkers); + } +}; + +#endif \ No newline at end of file diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index 7184e08..671ceb3 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -1,31 +1,19 @@ - - - - + + + + - - - - - - - + pkg="mavswarm2" + exec="mavswarm2" + output="screen" + args="$(var robot_id) $(var controller_frequency) --ros-args --log-level $(var log_level)"> + + + - + \ No newline at end of file diff --git a/readme.md b/readme.md index 011aafa..0a20c2f 100644 --- a/readme.md +++ b/readme.md @@ -26,7 +26,7 @@ Install Eigen, Armadillo and GNU Science Library (GSL) before you continue. mkdir -p mavswarm2/src cd mavswarm2/src - git clone -b ros2 git@github.com:malintha/simulator_utils.git + git clone -b ros2 git@github.com:malintha/simulator_interfaces.git git clone -b ros2 git@github.com:malintha/multi_uav_simulator.git **Building the simulator** diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 6ff8a35..81ccbcd 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -19,8 +19,6 @@ limitations under the License. /* ros2 run mavswarm2 mavswarm2 0 50 --ros-args --log-level DEBUG -ros2 topic pub --rate 1 /desired_state simulator_interfaces/msg/GeometricCtrl "{position:{x: 2.0, y: 2.4, z: -3.0},heading:{x: 1, y: 0, z: 0}}" - */ int main(int argc, char **argv) { @@ -29,6 +27,7 @@ int main(int argc, char **argv) { double frequency = (double)std::atof(argv[2]); auto logger = rclcpp::get_logger("logger"); + RCLCPP_INFO(logger, "Initialing drone: %d %3f", robot_id, frequency); rclcpp::spin(std::make_shared(robot_id, frequency)); rclcpp::shutdown(); From 9d57120819442fcc648b227411cd8b56a871499a Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Wed, 25 Jun 2025 12:36:49 +0530 Subject: [PATCH 17/24] revert launch file changes --- launch/quadrotor.launch | 38 +++++++++++++++++++++++++------------- 1 file changed, 25 insertions(+), 13 deletions(-) diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index 671ceb3..9f5b9c2 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -1,19 +1,31 @@ - - - - + + + + - - - + pkg="mavswarm2" + exec="mavswarm2" + output="screen" + name="robot_0" + namespace="mavswarm2" + args="$(var robot_id) $(var controller_frequency) --ros-args --log-level $(var log_level)"> + + + + + + + - + - \ No newline at end of file + From fda64c2bc2c8618524d1fa7c9b13406ea99892b6 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Fri, 5 Jun 2026 16:26:50 +0200 Subject: [PATCH 18/24] Adding ROS2 with trajectory optimization --- CMakeLists.txt | 88 +- cf_description/crazyflie.urdf.xacro | 14 + cf_description/crazyflie2.dae | 2882 +++++++++++++++++++++++ config/crazyflie_params.yaml | 2 +- config/initial_conditions.yaml | 44 +- config/initial_conditions_2.yaml | 7 +- include/mavswarm2/dynamics_provider.hpp | 1 - include/mavswarm2/quadrotor.hpp | 399 ++-- launch/quadrotor.launch | 10 + package.xml | 2 + src/quadrotor.cpp | 2 +- 11 files changed, 3220 insertions(+), 231 deletions(-) create mode 100644 cf_description/crazyflie.urdf.xacro create mode 100644 cf_description/crazyflie2.dae diff --git a/CMakeLists.txt b/CMakeLists.txt index d799e91..f8ef780 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -3,80 +3,54 @@ project(mavswarm2) if(CMAKE_COMPILER_IS_GNUCXX OR CMAKE_CXX_COMPILER_ID MATCHES "Clang") add_compile_options(-Wall -Wextra -Wpedantic) - endif() - - - # find dependencies - find_package(Armadillo REQUIRED) - find_package(GSL REQUIRED) - find_package(ament_cmake REQUIRED) - find_package(rclcpp REQUIRED) - find_package(simulator_interfaces REQUIRED) - # # find_package(simulator_utils REQUIRED) - # # find_package(controller REQUIRED) - find_package(std_msgs REQUIRED) - # find_package(GSL REQUIRED) - - find_package(geometry_msgs REQUIRED) - # find_package(sensor_msgs REQUIRED) - find_package(visualization_msgs REQUIRED) - find_package(tf2_ros REQUIRED) - - -# add_library(${PROJECT_NAME} SHARED -# src/quadrotor.cpp -# ) +endif() + +find_package(ament_cmake REQUIRED) +find_package(rclcpp REQUIRED) +find_package(Armadillo REQUIRED) +find_package(GSL REQUIRED) +find_package(Eigen3 REQUIRED) +find_package(simulator_interfaces REQUIRED) +find_package(std_msgs REQUIRED) +find_package(geometry_msgs REQUIRED) +find_package(visualization_msgs REQUIRED) +find_package(tf2 REQUIRED) +find_package(tf2_ros REQUIRED) +find_package(mav_trajectory_generation_ros2 REQUIRED) +find_package(glog REQUIRED) add_executable(mavswarm2 src/quadrotor.cpp) -ament_target_dependencies(${PROJECT_NAME} - geometry_msgs +ament_target_dependencies(mavswarm2 rclcpp + geometry_msgs tf2 tf2_ros visualization_msgs simulator_interfaces - - # turtlesim + mav_trajectory_generation_ros2 ) -# ament_target_dependencies(mavswarm2 -# rclcpp -# geometry_msgs -# visualization_msgs -# std_msgs -# tf2 -# tf2_ros -# simulator_interfaces -# ) +target_link_libraries(mavswarm2 + GSL::gsl + GSL::gslcblas + ${mav_trajectory_generation_ros2_LIBRARIES} + glog::glog +) install( - TARGETS ${PROJECT_NAME} + TARGETS mavswarm2 DESTINATION lib/${PROJECT_NAME} ) install( - DIRECTORY launch config + DIRECTORY launch config cf_description DESTINATION share/${PROJECT_NAME}/ ) -# # EXPORT ${PROJECT_NAME} -# # LIBRARY DESTINATION lib -# # ARCHIVE DESTINATION lib -# # RUNTIME DESTINATION bin -# # INCLUDES DESTINATION include -# ) -ament_package() - -target_link_libraries(mavswarm2 - GSL::gsl - GSL::gslcblas) - -# install( -# DIRECTORY include/ -# DESTINATION include -# ) include_directories( - include/${PROJECT_NAME} - # include/gcopter - # include/misc + include/${PROJECT_NAME} + ${mav_trajectory_generation_ros2_INCLUDE_DIRS} + ${EIGEN3_INCLUDE_DIRS} ) + +ament_package() diff --git a/cf_description/crazyflie.urdf.xacro b/cf_description/crazyflie.urdf.xacro new file mode 100644 index 0000000..9b751c0 --- /dev/null +++ b/cf_description/crazyflie.urdf.xacro @@ -0,0 +1,14 @@ + + + + + + + + + + + + + + diff --git a/cf_description/crazyflie2.dae b/cf_description/crazyflie2.dae new 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1014 1014 1015 1015 1016 1016 1017 1017 1018 1018 1019 1019 1020 1020 1021 1021 1022 1022 1023 1023 1024 1024 1025 1025 1026 1026 1027 1027 1028 1028 1029 1029 1030 1030 1031 1031 1032 1032 1033 1033 1034 1034 1035 1035 1036 1036 1037 1037 1038 1038 1039 1039 1040 1040 1041 1041 1042 1042 1043 1043 1044 1044 1045 1045 1046 1046 1047 1047 1048 1048 1049 1049 1050 1050 1051 1051 1052 1052 1053 1053 1054 1054 1055 1055 1056 1056 1057 1057 1058 1058 1059 1059 1060 1060 1061 1061 1062 1062 1063 1063 1064 1064 1065 1065 1066 1066 1067 1067 1068 1068 1069 1069 1070 1070 1071 1071 1069 1069 1072 1072 1068 1068 1073 1073 1074 1074 1073 1073 1068 1068 1070 1070 1075 1075 1076 1076 1074 1074 1074 1074 1073 1073 1075 1075 1077 1077 1076 1076 1078 1078 1075 1075 1078 1078 1076 1076 1077 1077 1079 1079 1080 1080 1079 1079 1077 1077 1078 1078 1081 1081 1082 1082 1080 1080 1080 1080 1079 1079 1081 1081 1083 1083 1082 1082 1084 1084 1081 1081 1084 1084 1082 1082 1083 1083 1085 1085 1086 1086 1085 1085 1083 1083 1084 1084 1087 1087 1019 1019 1086 1086 1086 1086 1085 1085 1087 1087 1071 1071 1072 1072 1064 1064 1087 1087 1017 1017 1019 1019 1069 1069 1071 1071 1070 1070 1065 1065 1063 1063 1062 1062 1062 1062 1064 1064 1072 1072 1057 1057 1067 1067 1066 1066 1067 1067 1063 1063 1065 1065 1056 1056 1058 1058 1061 1061 1057 1057 1066 1066 1058 1058 1060 1060 1059 1059 1050 1050 1056 1056 1061 1061 1060 1060 1051 1051 1054 1054 1052 1052 1059 1059 1051 1051 1050 1050 1055 1055 1046 1046 1053 1053 1054 1054 1053 1053 1052 1052 1047 1047 1045 1045 1044 1044 1044 1044 1046 1046 1055 1055 1039 1039 1049 1049 1048 1048 1049 1049 1045 1045 1047 1047 1038 1038 1040 1040 1043 1043 1039 1039 1048 1048 1040 1040 1042 1042 1041 1041 1032 1032 1038 1038 1043 1043 1042 1042 1033 1033 1036 1036 1034 1034 1041 1041 1033 1033 1032 1032 1037 1037 1028 1028 1035 1035 1036 1036 1035 1035 1034 1034 1029 1029 1027 1027 1026 1026 1026 1026 1028 1028 1037 1037 1021 1021 1031 1031 1030 1030 1031 1031 1027 1027 1029 1029 1020 1020 1022 1022 1023 1023 1021 1021 1030 1030 1022 1022 1025 1025 1024 1024 1016 1016 1020 1020 1023 1023 1025 1025 1014 1014 1018 1018 1015 1015 1024 1024 1014 1014 1016 1016 1017 1017 1015 1015 1018 1018

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1088 1088 1089 1089 1090 1090 1091 1091 1092 1092 1093 1093 1094 1094 1095 1095 1096 1096 1097 1097 1098 1098 1099 1099 1100 1100 1101 1101 1102 1102 1103 1103 1104 1104 1105 1105 1102 1102 1106 1106 1107 1107 1107 1107 1100 1100 1102 1102 1108 1108 1109 1109 1106 1106 1107 1107 1106 1106 1109 1109 1105 1105 1101 1101 1103 1103 1103 1103 1101 1101 1100 1100 1095 1095 1104 1104 1096 1096 1095 1095 1105 1105 1104 1104 1094 1094 1097 1097 1099 1099 1094 1094 1096 1096 1097 1097 1098 1098 1088 1088 1090 1090 1099 1099 1098 1098 1090 1090 1092 1092 1091 1091 1089 1089 1088 1088 1092 1092 1089 1089

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1110 1110 1111 1111 1112 1112 1113 1113 1114 1114 1115 1115 1116 1116 1117 1117 1118 1118 1119 1119 1120 1120 1121 1121 1122 1122 1123 1123 1124 1124 1125 1125 1126 1126 1127 1127 1124 1124 1128 1128 1129 1129 1129 1129 1122 1122 1124 1124 1130 1130 1131 1131 1128 1128 1129 1129 1128 1128 1131 1131 1127 1127 1123 1123 1125 1125 1125 1125 1123 1123 1122 1122 1117 1117 1126 1126 1118 1118 1117 1117 1127 1127 1126 1126 1116 1116 1119 1119 1121 1121 1116 1116 1118 1118 1119 1119 1120 1120 1110 1110 1112 1112 1121 1121 1120 1120 1112 1112 1114 1114 1113 1113 1111 1111 1110 1110 1114 1114 1111 1111

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1132 1132 1133 1133 1134 1134 1135 1135 1136 1136 1137 1137 1138 1138 1139 1139 1140 1140 1141 1141 1142 1142 1143 1143 1144 1144 1145 1145 1146 1146 1147 1147 1148 1148 1149 1149 1146 1146 1150 1150 1151 1151 1151 1151 1144 1144 1146 1146 1152 1152 1153 1153 1150 1150 1151 1151 1150 1150 1153 1153 1149 1149 1145 1145 1147 1147 1147 1147 1145 1145 1144 1144 1139 1139 1148 1148 1140 1140 1139 1139 1149 1149 1148 1148 1138 1138 1141 1141 1143 1143 1138 1138 1140 1140 1141 1141 1142 1142 1132 1132 1134 1134 1143 1143 1142 1142 1134 1134 1136 1136 1135 1135 1133 1133 1132 1132 1136 1136 1133 1133

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1154 1154 1155 1155 1156 1156 1157 1157 1158 1158 1159 1159 1160 1160 1161 1161 1162 1162 1163 1163 1164 1164 1165 1165 1166 1166 1167 1167 1168 1168 1169 1169 1170 1170 1171 1171 1168 1168 1172 1172 1173 1173 1173 1173 1166 1166 1168 1168 1174 1174 1175 1175 1172 1172 1173 1173 1172 1172 1175 1175 1171 1171 1167 1167 1169 1169 1169 1169 1167 1167 1166 1166 1161 1161 1170 1170 1162 1162 1161 1161 1171 1171 1170 1170 1160 1160 1163 1163 1165 1165 1160 1160 1162 1162 1163 1163 1164 1164 1154 1154 1156 1156 1165 1165 1164 1164 1156 1156 1158 1158 1157 1157 1155 1155 1154 1154 1158 1158 1155 1155

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1176 1176 1177 1177 1178 1178 1179 1179 1180 1180 1181 1181 1182 1182 1183 1183 1184 1184 1185 1185 1186 1186 1187 1187 1188 1188 1189 1189 1190 1190 1191 1191 1192 1192 1193 1193 1194 1194 1195 1195 1196 1196 1195 1195 1194 1194 1190 1190 1197 1197 1198 1198 1196 1196 1196 1196 1195 1195 1197 1197 1191 1191 1189 1189 1188 1188 1197 1197 1199 1199 1198 1198 1188 1188 1190 1190 1194 1194 1183 1183 1193 1193 1192 1192 1193 1193 1189 1189 1191 1191 1182 1182 1184 1184 1185 1185 1183 1183 1192 1192 1184 1184 1187 1187 1186 1186 1178 1178 1182 1182 1185 1185 1187 1187 1176 1176 1180 1180 1177 1177 1186 1186 1176 1176 1178 1178 1179 1179 1177 1177 1180 1180

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1200 1200 1201 1201 1202 1202 1203 1203 1204 1204 1205 1205 1206 1206 1207 1207 1208 1208 1209 1209 1210 1210 1211 1211 1212 1212 1213 1213 1214 1214 1215 1215 1216 1216 1217 1217 1218 1218 1219 1219 1220 1220 1219 1219 1218 1218 1214 1214 1221 1221 1222 1222 1220 1220 1220 1220 1219 1219 1221 1221 1215 1215 1213 1213 1212 1212 1221 1221 1223 1223 1222 1222 1212 1212 1214 1214 1218 1218 1207 1207 1217 1217 1216 1216 1217 1217 1213 1213 1215 1215 1206 1206 1208 1208 1209 1209 1207 1207 1216 1216 1208 1208 1211 1211 1210 1210 1202 1202 1206 1206 1209 1209 1211 1211 1200 1200 1204 1204 1201 1201 1210 1210 1200 1200 1202 1202 1203 1203 1201 1201 1204 1204

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1224 1224 1225 1225 1226 1226 1227 1227 1228 1228 1229 1229 1230 1230 1231 1231 1232 1232 1233 1233 1234 1234 1235 1235 1236 1236 1237 1237 1238 1238 1239 1239 1240 1240 1241 1241 1238 1238 1242 1242 1243 1243 1243 1243 1236 1236 1238 1238 1244 1244 1245 1245 1242 1242 1243 1243 1242 1242 1245 1245 1241 1241 1237 1237 1239 1239 1239 1239 1237 1237 1236 1236 1231 1231 1240 1240 1232 1232 1231 1231 1241 1241 1240 1240 1230 1230 1233 1233 1235 1235 1230 1230 1232 1232 1233 1233 1234 1234 1224 1224 1226 1226 1235 1235 1234 1234 1226 1226 1228 1228 1227 1227 1225 1225 1224 1224 1228 1228 1225 1225

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+ + + + + + + + + + + 1 1 1 1 + + + 1 + + + + + + + + + + + 0.101961 0.101961 0.101961 1 + + + 1 + + + + + + + + + + + 0.898039 0.898039 0.898039 1 + + + 1 + + + + + + + + + + + 0.631373 0.658824 0.678431 1 + + + 1 + + + + + + + + + + + 0.968627 0.878431 0.6 1 + + + 1 + + + + + + + + + + + 0.109804 0.184314 0 1 + + + 1 + + + + + + + + + + + 0.792157 0.819608 0.933333 1 + + + 1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -8.88178e-015 -9.81308e-018 -1 -0.703947 -9.81308e-018 -1 9.81308e-018 4.82341 -1 9.81308e-018 8.88178e-015 -0.640698 0 0 0 1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 1 -9.81308e-018 -9.81308e-018 -0.703947 -9.81308e-018 9.81308e-018 -1 4.22341 9.81308e-018 1 9.81308e-018 -0.640698 0 0 0 1 + + + + + + + + + + + + -7.46625e-015 -1 9.81308e-018 -0.703947 -9.81308e-018 9.81308e-018 1 -5.39659 -1 7.46625e-015 -9.81308e-018 -0.640698 0 0 0 1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + -0.959406 0 0.282028 -11.2194 0 1 0 1.70341 -0.282028 0 -0.959406 -45.9898 0 0 0 1 + + + + + + + + + + + + 0.144807 0 -0.98946 38.4702 0 1 0 1.70341 0.98946 0 0.144807 76.5429 0 0 0 1 + + + + + + + + + + + + 1 0 0 11.6382 0 1 0 1.70341 0 0 1 32.0172 0 0 0 1 + + + + + + + + + + + + -0.00822618 0 0.999966 -33.732 0 1 0 1.70341 -0.999966 0 -0.00822618 -78.297 0 0 0 1 + + + + + + + + + + + + + + + + + diff --git a/config/crazyflie_params.yaml b/config/crazyflie_params.yaml index 4d3a829..74c5a7e 100644 --- a/config/crazyflie_params.yaml +++ b/config/crazyflie_params.yaml @@ -1,6 +1,6 @@ /**: ros__parameters: - controller_gains: [1.0, 0.5, 0.015, 0.00075] + controller_gains: [1.0, 0.5, 0.0015, 0.00075] # kx: 1 # kv: 0.5 # kr: 0.0015 diff --git a/config/initial_conditions.yaml b/config/initial_conditions.yaml index 6d593b6..5e56764 100644 --- a/config/initial_conditions.yaml +++ b/config/initial_conditions.yaml @@ -2,31 +2,31 @@ # change the initial rotation matrix to [1, 0, 0, 0, 1, 0, 0, 0, 1] for initialing the # drones right side up. robot_1: - position: [2, 2, -2] + position: [0, 0, -10] velocity: [0, 0, 0] - rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] + rotation: [1, 0, 0, 0, 1, 0, 0, 0, 1] omega: [0, 0, 0] -robot_2: - position: [-2, -2, -2] - velocity: [0, 0, 0] - rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] - omega: [0, 0, 0] +# robot_2: +# position: [-2, -2, -2] +# velocity: [0, 0, 0] +# rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] +# omega: [0, 0, 0] -robot_3: - position: [-1, 1, -2] - velocity: [0, 0, 0] - rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] - omega: [0, 0, 0] +# robot_3: +# position: [-1, 1, -2] +# velocity: [0, 0, 0] +# rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] +# omega: [0, 0, 0] -robot_4: - position: [1, -1, -2] - velocity: [0, 0, 0] - rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] - omega: [0, 0, 0] +# robot_4: +# position: [1, -1, -2] +# velocity: [0, 0, 0] +# rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] +# omega: [0, 0, 0] -robot_5: - position: [0, 0, -2] - velocity: [0, 0, 0] - rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] - omega: [0, 0, 0] \ No newline at end of file +# robot_5: +# position: [0, 0, -2] +# velocity: [0, 0, 0] +# rotation: [1, 0, 0, 0, -0.9995, -0.0314, 0, 0.0314, -0.9995] +# omega: [0, 0, 0] \ No newline at end of file diff --git a/config/initial_conditions_2.yaml b/config/initial_conditions_2.yaml index 4c437e7..4e873cd 100644 --- a/config/initial_conditions_2.yaml +++ b/config/initial_conditions_2.yaml @@ -1,9 +1,12 @@ # define the initial positions of each robot in NWU frame # change the initial rotation matrix to [1, 0, 0, 0, 1, 0, 0, 0, 1] for initialing the # drones right side up. -robot_0: +# "/**/robot_0" matches the node whether it is namespaced (e.g. /mavswarm2/robot_0 +# when started from the launch file) or run bare as /robot_0. A plain "robot_0:" key +# does NOT match a namespaced node, which silently drops these params. +/**/robot_0: ros__parameters: - position: [2.0, 2.0, -2.0] + position: [2.0, 2.0, 2.0] velocity: [0.0, 0.0, 0.0] rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] omega: [0.0, 0.0, 0.0] diff --git a/include/mavswarm2/dynamics_provider.hpp b/include/mavswarm2/dynamics_provider.hpp index b24970f..dfe9aa0 100644 --- a/include/mavswarm2/dynamics_provider.hpp +++ b/include/mavswarm2/dynamics_provider.hpp @@ -132,7 +132,6 @@ void update(control_out_t control, double sim_time_) { state_space.omega[i] = y[k]; } - // ROS_DEBUG_STREAM(t_stop<<" R: \n" << state_space.R << " \n v: \n" << state_space.velocity); sim_time = t_stop; } diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index abc9b9c..3f198d8 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -19,19 +19,30 @@ limitations under the License. #define PROJECT_QUADROTOR_H #include +#include +#include #include +#include "rclcpp/rclcpp.hpp" #include "rclcpp/logging.hpp" +#include "geometry_msgs/msg/point.hpp" +#include "geometry_msgs/msg/transform_stamped.hpp" +#include "visualization_msgs/msg/marker.hpp" +#include "tf2_ros/transform_broadcaster.h" +#include "tf2/LinearMath/Quaternion.h" + +#include "mav_trajectory_generation_ros2/polynomial_optimization_linear.h" +#include "mav_trajectory_generation_ros2/trajectory.h" +#include "mav_trajectory_generation_ros2/motion_defines.h" +#include "mav_trajectory_generation_ros2/vertex.h" #include "trajectory_t.hpp" -#include "std_msgs/msg/float32_multi_array.hpp" -#include "tf2_ros/transform_listener.h" -#include "visualization_msgs/msg/marker.hpp" #include "dynamics_provider.hpp" #include "controller/geometric_controller.hpp" #include "simulator_interfaces/msg/waypoint.hpp" using namespace std::chrono_literals; + #ifndef STATE_H #define STATE_H enum State { @@ -45,183 +56,277 @@ enum State { using namespace Eigen; using namespace std; -using namespace std::chrono_literals; class Quadrotor : public rclcpp::Node { public: Quadrotor(int robot_id, double frequency) - :Node("robot_"+to_string(robot_id)), frequency(frequency), robot_id(robot_id) { - sim_time = 0; - dt = 1/frequency; - RCLCPP_INFO(this->get_logger(), "dt: %4f ", dt); - // dt = 0.01; - m_state = State::Idle; - - this->u << 0,0,0; - timer_ = this->create_wall_timer(std::chrono::duration(dt), std::bind(&Quadrotor::iteration, this)); - - RCLCPP_INFO(this->get_logger(), "Loading parameters"); - - if (!load_params()) { - RCLCPP_ERROR(this->get_logger(), "Could not load the drone parameters"); - rclcpp::shutdown(); + : Node("robot_" + to_string(robot_id)), frequency(frequency), robot_id(robot_id) + { + sim_time = 0; + tau = 0; + dt = 1.0 / frequency; + m_state = State::Idle; + set_init_target = false; + set_next_target = false; + + RCLCPP_INFO(this->get_logger(), "dt: %4f ", dt); + + timer_ = this->create_wall_timer( + std::chrono::duration(dt), + std::bind(&Quadrotor::iteration, this)); + + RCLCPP_INFO(this->get_logger(), "Loading parameters"); + if (!load_params()) { + RCLCPP_ERROR(this->get_logger(), "Could not load the drone parameters"); + rclcpp::shutdown(); + return; + } + + controller = std::make_shared(params_, gains, dt); + dynamics = std::make_shared(params_, init_vals); + set_state_space(); + + tf_broadcaster_ = std::make_unique(*this); + worldframe = "map"; + robot_link_name = "base_link"; + + // initialise hover target to the drone's starting position (NWU) + target_pos = simulator_utils::ned_nwu_rotation(init_vals.position); + + desired_state_sub_ = this->create_subscription( + "desired_state", 10, + std::bind(&Quadrotor::desired_pos_cb, this, std::placeholders::_1)); + + this->setState(State::Autonomous); } - - // logger = this->get_logger(); - // while (marker_pub.getNumSubscribers() < 1) { - // RCLCPP_INFO(logger, "Waiting for subscriber"); - // ros::Duration(1).sleep(); - // } - controller = std::make_shared(params_, gains, dt); - dynamics = std::make_shared(params_, init_vals); - set_state_space(); - this->setState(State::Autonomous); + void setState(State m_state_) { this->m_state = m_state_; } -} - void setState(State m_state_) { - this->m_state = m_state_; -} +private: + // ----------------------------------------------------------------------- + // State + // ----------------------------------------------------------------------- + State m_state; + double sim_time, tau, dt, frequency; + int robot_id; + std::string worldframe, robot_link_name; - // State getState(); + gains_t gains; + Vector3d u, target_pos; + state_space_t state_space; + bool set_init_target; + bool set_next_target; + geometry_msgs::msg::Point target_next; - // bool initialize(double dt); + mav_trajectory_generation::Trajectory traj_; - // void desired_pos_cb(const geometry_msgs::msg::Point &pt); + std::shared_ptr controller; + std::shared_ptr dynamics; + std::unique_ptr tf_broadcaster_; + rclcpp::Subscription::SharedPtr desired_state_sub_; + rclcpp::TimerBase::SharedPtr timer_; - // xd should be in NED frame and so does dynamics and controller. + params_t params_; + init_vals_t init_vals; - // void run() { - // // ros::Timer timer = nh.createTimer(ros::Duration(1 / frequency), &Quadrotor::iteration, this); - // ros::spin(); - // } + // ----------------------------------------------------------------------- + // Parameter loading + // ----------------------------------------------------------------------- + bool load_params() { + declare_parameter("controller_gains", std::vector(4, 0.0)); + vector gains_ = get_parameter("controller_gains").as_double_array(); + + declare_parameter("model.m", 0.00); + declare_parameter("model.gravity", 9.81); + declare_parameter("model.d", 0.08); + declare_parameter("model.ctf", 0.0037); + declare_parameter("model.J", std::vector(3, 0.0)); + + params_.mass = get_parameter("model.m").as_double(); + params_.gravity = get_parameter("model.gravity").as_double(); + vector J_ = get_parameter("model.J").as_double_array(); + params_.J << J_[0], 0, 0, + 0, J_[1], 0, + 0, 0, J_[2]; + params_.J_inv = params_.J.inverse(); + params_.F = 0; + params_.M = Vector3d(0, 0, 0); + + declare_parameter("position", std::vector(3, 0.0)); + declare_parameter("velocity", std::vector(3, 0.0)); + declare_parameter("rotation", std::vector(9, 0.0)); + declare_parameter("omega", std::vector(3, 0.0)); + + vector pos_ = get_parameter("position").as_double_array(); + vector vel_ = get_parameter("velocity").as_double_array(); + vector rot_ = get_parameter("rotation").as_double_array(); + vector omega_ = get_parameter("omega").as_double_array(); + + // store raw values (NWU position/velocity, the NED-matched "upside-down" R). + // ned_nwu_rotation is applied downstream (dynamics start state, iteration xd, + // and broadcast) — converting here would double-convert and break frames. + init_vals.position = Vector3d(pos_.data()); + init_vals.velocity = Vector3d(vel_.data()); + init_vals.R = Matrix3d(rot_.data()); + init_vals.omega = Vector3d(omega_.data()); + + gains = {.kx = gains_[0], .kv = gains_[1], .kr = gains_[2], .komega = gains_[3]}; + + RCLCPP_INFO(this->get_logger(), "Init Params: : %4f %4f %4f ", + init_vals.position[0], init_vals.position[1], init_vals.position[2]); + RCLCPP_INFO(this->get_logger(), "Param: Gravity: %s ", to_string(params_.gravity).c_str()); + RCLCPP_INFO(this->get_logger(), "Param: Mass: %s ", to_string(params_.mass).c_str()); + RCLCPP_INFO(this->get_logger(), "Param: MOI: %6f %6f %6f", J_[0], J_[1], J_[2]); + RCLCPP_INFO(this->get_logger(), "Param: Controller Gains: %4f %4f %4f %4f", + gains.kx, gains.kv, gains.kr, gains.komega); + RCLCPP_INFO(this->get_logger(), "Loaded control parameters"); + return true; + } + // ----------------------------------------------------------------------- + // Trajectory optimisation + // ----------------------------------------------------------------------- + mav_trajectory_generation::Trajectory get_opt_traj(const opt_t &ps, const Vector3d &pe) + { + namespace mtg = mav_trajectory_generation; + mtg::Vertex::Vector vertices; + mtg::Vertex v_s(3), v_e(3); + const int deriv = mtg::derivative_order::JERK; + + v_s.addConstraint(mtg::derivative_order::POSITION, ps.position); + v_s.addConstraint(mtg::derivative_order::VELOCITY, ps.velocity); + v_s.addConstraint(mtg::derivative_order::ACCELERATION, ps.acceleration); + v_e.makeStartOrEnd(pe, deriv); + + vertices.push_back(v_s); + vertices.push_back(v_e); + + const double v_max = 1.0, a_max = 4.0; + std::vector segment_times = mtg::estimateSegmentTimes(vertices, v_max, a_max); + + mtg::PolynomialOptimization<8> opt(3); + opt.setupFromVertices(vertices, segment_times, deriv); + opt.solveLinear(); + + mtg::Trajectory trajectory; + opt.getTrajectory(&trajectory); + return trajectory; + } -private: + // Receding horizon replanning: replan from current dynamic state to pending target. + void do_rhp() + { + Vector3d pt(target_next.x, target_next.y, target_next.z); + state_space_t ss = dynamics->get_state(); + opt_t wp = {ss.position, ss.velocity, ss.acceleration, Vector3d(0, 0, 0)}; + traj_ = get_opt_traj(wp, pt); + set_next_target = false; + tau = 0; + RCLCPP_INFO(this->get_logger(), "Replanned trajectory, duration: %.2f s", traj_.getMaxTime()); + } - State m_state; - double sim_time, tau, dt, frequency; - int robot_id; - std::string worldframe, localframe, robot_link_name; - gains_t gains; - std::vector traj_piece; - int xd_it; - Vector3d u, target_pos; - state_space_t x0, xd0; - desired_state_t dss; - bool set_init_target; - geometry_msgs::msg::Point target_next; - bool set_next_target = false; + // ----------------------------------------------------------------------- + // Goal subscription + // ----------------------------------------------------------------------- + void desired_pos_cb(const geometry_msgs::msg::Point::SharedPtr pt) + { + Vector3d p1(pt->x, pt->y, pt->z); + if ((target_pos - p1).norm() < 0.2) return; + + if (!set_init_target) { + set_init_target = true; + Vector3d zero(0, 0, 0); + opt_t ps = {target_pos, zero, zero, zero}; + traj_ = get_opt_traj(ps, p1); + target_pos = p1; + RCLCPP_INFO(this->get_logger(), "Set initial trajectory to [%.2f %.2f %.2f]", + p1[0], p1[1], p1[2]); + } else { + target_next = *pt; + target_pos = p1; + set_next_target = true; + RCLCPP_INFO(this->get_logger(), "Queued new target [%.2f %.2f %.2f]", + p1[0], p1[1], p1[2]); + } + } - std::shared_ptr controller; - state_space_t state_space; - // rclcpp::Logger logger; - std::shared_ptr dynamics; - params_t params_; - init_vals_t init_vals; - rclcpp::TimerBase::SharedPtr timer_; - - // rclcpp::Publisher::SharedPtr marker_pub, goal_pub, state_pub; - // visualization_msgs::msg::Marker m, g; - // std::vector points; - // rclcpp::Subscription::SharedPtr desired_state_sub; - // vector positions; - - // bool quad_initialized = false; - - // rclcpp::TimerBase::SharedPtr timer; - - // void initPaths(); - // void set_state_space(); - -bool load_params() { - - declare_parameter("controller_gains", std::vector(4, 0.0)); - vector gains_ = get_parameter("controller_gains").as_double_array(); - - declare_parameter("model.m", 0.00); - declare_parameter("model.gravity", 9.81); - declare_parameter("model.d", 0.08); - declare_parameter("model.ctf", 0.0037); - declare_parameter("model.J", std::vector(3, 0.0)); - params_.mass = get_parameter("model.m").as_double(); - params_.gravity = get_parameter("model.gravity").as_double(); - - vector J_ = get_parameter("model.J").as_double_array(); - params_.J << J_[0], 0, 0, - 0, J_[1], 0, - 0, 0, J_[2]; - params_.J_inv = params_.J.inverse(); - params_.F = 0; - params_.M = Vector3d(0, 0, 0); - - declare_parameter("position", std::vector(3, 0.0)); - declare_parameter("velocity", std::vector(3, 0.0)); - declare_parameter("rotation", std::vector(3, 0.0)); - declare_parameter("omega", std::vector(3, 0.0)); - vector pos_ = get_parameter("position").as_double_array(); - vector vel_ = get_parameter("velocity").as_double_array(); - vector rot_ = get_parameter("rotation").as_double_array(); - vector omega_ = get_parameter("omega").as_double_array(); - init_vals.position = simulator_utils::ned_nwu_rotation(Vector3d(pos_.data())); - init_vals.velocity << simulator_utils::ned_nwu_rotation(Vector3d(vel_.data())); - init_vals.R << simulator_utils::ned_nwu_rotation(Matrix3d(rot_.data())); - init_vals.omega << simulator_utils::ned_nwu_rotation(Vector3d(omega_.data())); - gains = {.kx = gains_[0], .kv = gains_[1], .kr = gains_[3], .komega = gains_[3]}; - RCLCPP_INFO(this->get_logger(), "Init Params: : %4f %4f %4f ", init_vals.position[0], init_vals.position[1],init_vals.position[2]); - - RCLCPP_INFO(this->get_logger(), "Param: Gravity: %s ",to_string(params_.gravity).c_str()); - RCLCPP_INFO(this->get_logger(), "Param: Mass: %s ",to_string(params_.mass).c_str()); - RCLCPP_INFO(this->get_logger(), "Param: MOI: %6f %6f %6f",J_[0], J_[1], J_[2]); - RCLCPP_INFO(this->get_logger(), "Param: Controller Gains: %4f %4f %4f %4f", gains.kx, gains.kv, - gains.kr, gains.komega); - RCLCPP_INFO(this->get_logger(), "Loaded control parameters"); - return true; -} - // void send_transform(); - // void publish_path(); - // void publish_state(); - - void move(const desired_state_t &d_state) { + // ----------------------------------------------------------------------- + // TF broadcasting + // ----------------------------------------------------------------------- + void send_transform() + { + Vector3d position = state_space.position; + Vector3d rpy = simulator_utils::R2RPY(state_space.R); + + tf2::Quaternion q; + q.setRPY(rpy[0], rpy[1], rpy[2]); + if (std::isnan(q.x())) return; + + geometry_msgs::msg::TransformStamped t; + t.header.stamp = this->get_clock()->now(); + t.header.frame_id = worldframe; + t.child_frame_id = robot_link_name; + t.transform.translation.x = position[0]; + t.transform.translation.y = position[1]; + t.transform.translation.z = position[2]; + t.transform.rotation.x = q.x(); + t.transform.rotation.y = q.y(); + t.transform.rotation.z = q.z(); + t.transform.rotation.w = q.w(); + // RCLCPP_INFO(this->get_logger(), " %4f %4f %4f %4f %4f %4f %4f", position[0], position[1],position[2], q.x(), q.y(), q.z(), q.w()); + + tf_broadcaster_->sendTransform(t); + } + + // ----------------------------------------------------------------------- + // Control loop + // ----------------------------------------------------------------------- + void move(const desired_state_t &d_state) + { state_space_t s = dynamics->get_state(); - // RCLCPP_INFO(this->get_logger(), "dss %4f %4f %4f", d_state.x[0], d_state.x[1], d_state.x[2]); - RCLCPP_DEBUG(this->get_logger(), "%2f position %4f %4f %4f", sim_time, s.position[0], s.position[1], s.position[2]); - // RCLCPP_INFO(this->get_logger(), "%2f rotation %4f %4f %4f", sim_time, s.R(0,0), s.R(1,1), s.R(2,2)); + RCLCPP_DEBUG(this->get_logger(), "%2f position %4f %4f %4f", + sim_time, s.position[0], s.position[1], s.position[2]); control_out_t control = controller->get_control(s, d_state); - RCLCPP_DEBUG(this->get_logger(), "%2f control %4f %4f %4f %4f", sim_time, control.F, control.M[0], control.M[1], control.M[2]); + Vector3d rpy = simulator_utils::R2RPY(state_space.R); + + RCLCPP_INFO(this->get_logger(), "%2f current vs desired %4f %4f %4f | %4f %4f %4f", + sim_time, rpy[0], rpy[1], rpy[2], d_state.b1[0],d_state.b1[1], d_state.b1[2]); dynamics->update(control, sim_time); - // RCLCPP_INFO(this->get_logger(), "control %4f %4f %4f", control.F, control.M[0], control.M[1]); - // updating the model on rviz set_state_space(); - // send_transform(); + send_transform(); dynamics->reset_dynamics(); - // RCLCPP_INFO(this->get_logger(), "position: %4f %4f %4f", s.position[0], - // s.position[1], s.position[2]); - // RCLCPP_INFO(this->get_logger(), "rotation: %4f %4f %4f", state_space.R(0, 0), - // state_space.R(1,1), state_space.R(2,2)); sim_time += dt; -} + } - void set_state_space() { + void set_state_space() + { + // convert the internal NED state back to map frame (NWU) for broadcasting state_space_t ss = dynamics->get_state(); state_space.position = simulator_utils::ned_nwu_rotation(ss.position); - state_space.R = simulator_utils::ned_nwu_rotation(ss.R); + state_space.R = simulator_utils::ned_nwu_rotation(ss.R); state_space.velocity = simulator_utils::ned_nwu_rotation(ss.velocity); - state_space.omega = simulator_utils::ned_nwu_rotation(ss.omega); + state_space.omega = simulator_utils::ned_nwu_rotation(ss.omega); } - void iteration() { - Vector3d xd = simulator_utils::ned_nwu_rotation(init_vals.position); + void iteration() + { Vector3d b1d(1, 0, 0); + Vector3d xd = simulator_utils::ned_nwu_rotation(init_vals.position); + + if (set_init_target) { + if (set_next_target) { + do_rhp(); + } + xd = traj_.evaluate(tau, mav_trajectory_generation::derivative_order::POSITION); + // advance, clamping to the trajectory end so we hold exactly at the + // zero-velocity endpoint instead of freezing a fraction of dt short. + tau = std::min(tau + dt, traj_.getMaxTime()); + } + desired_state_t dss = {xd, b1d}; this->move(dss); - // RCLCPP_INFO(this->get_logger(), "Iteration: "); - - // this->publish_path(); - // this->publish_state(); } - }; #endif diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index 9f5b9c2..81d3982 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -18,6 +18,16 @@ + + + + sensor_msgs visualization_msgs tf2 + tf2_ros + mav_trajectory_generation_ros2 ament_lint_auto ament_lint_common diff --git a/src/quadrotor.cpp b/src/quadrotor.cpp index 81ccbcd..37541e6 100644 --- a/src/quadrotor.cpp +++ b/src/quadrotor.cpp @@ -1,5 +1,5 @@ /* -Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) +Copyright (c) 2024 Malintha Fernando (malinthafer@gmail.com) Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. From 558b5242b23701b873e0d244ec66aa484754f904 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Fri, 5 Jun 2026 17:06:44 +0200 Subject: [PATCH 19/24] simulating 10 uavs --- cf_description/crazyflie2.dae | 2 +- config/initial_conditions_2.yaml | 69 ++++++++++++- include/mavswarm2/quadrotor.hpp | 12 ++- launch/quadrotor.launch | 163 ++++++++++++++++++++++++------- 4 files changed, 202 insertions(+), 44 deletions(-) diff --git a/cf_description/crazyflie2.dae b/cf_description/crazyflie2.dae index c9ad350..81ae2d8 100644 --- a/cf_description/crazyflie2.dae +++ b/cf_description/crazyflie2.dae @@ -7,7 +7,7 @@ 2016-04-29T11:06:01Z 2016-04-29T11:06:01Z - + Z_UP diff --git a/config/initial_conditions_2.yaml b/config/initial_conditions_2.yaml index 4e873cd..125e283 100644 --- a/config/initial_conditions_2.yaml +++ b/config/initial_conditions_2.yaml @@ -1,12 +1,77 @@ # define the initial positions of each robot in NWU frame -# change the initial rotation matrix to [1, 0, 0, 0, 1, 0, 0, 0, 1] for initialing the +# change the initial rotation matrix to [1, 0, 0, 0, 1, 0, 0, 0, 1] for initialing the # drones right side up. # "/**/robot_0" matches the node whether it is namespaced (e.g. /mavswarm2/robot_0 # when started from the launch file) or run bare as /robot_0. A plain "robot_0:" key # does NOT match a namespaced node, which silently drops these params. +# +# Line formation along +y, spaced 1.0 m, centred symmetrically about y = 0. /**/robot_0: ros__parameters: - position: [2.0, 2.0, 2.0] + position: [2.0, -4.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_1: + ros__parameters: + position: [2.0, -3.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_2: + ros__parameters: + position: [2.0, -2.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_3: + ros__parameters: + position: [2.0, -1.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_4: + ros__parameters: + position: [2.0, -0.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_5: + ros__parameters: + position: [2.0, 0.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_6: + ros__parameters: + position: [2.0, 1.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_7: + ros__parameters: + position: [2.0, 2.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_8: + ros__parameters: + position: [2.0, 3.5, 2.0] + velocity: [0.0, 0.0, 0.0] + rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] + omega: [0.0, 0.0, 0.0] + +/**/robot_9: + ros__parameters: + position: [2.0, 4.5, 2.0] velocity: [0.0, 0.0, 0.0] rotation: [1.0, 0.0, 0.0, 0.0, -0.9995, -0.0314, 0.0, 0.0314, -0.9995] omega: [0.0, 0.0, 0.0] diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 3f198d8..8e421da 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -88,14 +88,18 @@ class Quadrotor : public rclcpp::Node { tf_broadcaster_ = std::make_unique(*this); worldframe = "map"; - robot_link_name = "base_link"; + // per-robot TF child frame so multiple drones don't all broadcast map->base_link + robot_link_name = "robot_" + std::to_string(robot_id) + "/base_link"; // initialise hover target to the drone's starting position (NWU) target_pos = simulator_utils::ned_nwu_rotation(init_vals.position); + // per-robot desired_state topic, e.g. /mavswarm2/robot_3/desired_state + std::string desired_topic = "robot_" + std::to_string(robot_id) + "/desired_state"; desired_state_sub_ = this->create_subscription( - "desired_state", 10, + desired_topic, 10, std::bind(&Quadrotor::desired_pos_cb, this, std::placeholders::_1)); + RCLCPP_INFO(this->get_logger(), "Subscribing to goal topic: %s", desired_topic.c_str()); this->setState(State::Autonomous); } @@ -290,8 +294,8 @@ class Quadrotor : public rclcpp::Node { control_out_t control = controller->get_control(s, d_state); Vector3d rpy = simulator_utils::R2RPY(state_space.R); - RCLCPP_INFO(this->get_logger(), "%2f current vs desired %4f %4f %4f | %4f %4f %4f", - sim_time, rpy[0], rpy[1], rpy[2], d_state.b1[0],d_state.b1[1], d_state.b1[2]); + // RCLCPP_INFO(this->get_logger(), "%2f current vs desired %4f %4f %4f | %4f %4f %4f", + // sim_time, rpy[0], rpy[1], rpy[2], d_state.b1[0],d_state.b1[1], d_state.b1[2]); dynamics->update(control, sim_time); set_state_space(); send_transform(); diff --git a/launch/quadrotor.launch b/launch/quadrotor.launch index 81d3982..5921071 100644 --- a/launch/quadrotor.launch +++ b/launch/quadrotor.launch @@ -1,41 +1,130 @@ - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From ccd964f0e4faf6262369fbf9a79f3b82fc3d443c Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Fri, 5 Jun 2026 22:17:12 +0200 Subject: [PATCH 20/24] add SCP collision avoidance and letter visualization --- include/mavswarm2/quadrotor.hpp | 162 ++++++------ include/mavswarm2/scp/scp_planner.hpp | 343 ++++++++++++++++++++++++++ 2 files changed, 431 insertions(+), 74 deletions(-) create mode 100644 include/mavswarm2/scp/scp_planner.hpp diff --git a/include/mavswarm2/quadrotor.hpp b/include/mavswarm2/quadrotor.hpp index 8e421da..f942aa5 100644 --- a/include/mavswarm2/quadrotor.hpp +++ b/include/mavswarm2/quadrotor.hpp @@ -31,10 +31,7 @@ limitations under the License. #include "tf2_ros/transform_broadcaster.h" #include "tf2/LinearMath/Quaternion.h" -#include "mav_trajectory_generation_ros2/polynomial_optimization_linear.h" -#include "mav_trajectory_generation_ros2/trajectory.h" -#include "mav_trajectory_generation_ros2/motion_defines.h" -#include "mav_trajectory_generation_ros2/vertex.h" +#include "scp/scp_planner.hpp" #include "trajectory_t.hpp" #include "dynamics_provider.hpp" @@ -67,7 +64,6 @@ class Quadrotor : public rclcpp::Node { dt = 1.0 / frequency; m_state = State::Idle; set_init_target = false; - set_next_target = false; RCLCPP_INFO(this->get_logger(), "dt: %4f ", dt); @@ -101,6 +97,30 @@ class Quadrotor : public rclcpp::Node { std::bind(&Quadrotor::desired_pos_cb, this, std::placeholders::_1)); RCLCPP_INFO(this->get_logger(), "Subscribing to goal topic: %s", desired_topic.c_str()); + // SCP planner owns neighbour-trajectory communication; quad just feeds + // it goals and reads back the reference each tick. + scp_planner_ = std::make_shared(this, robot_id, dt); + + // trajectory trail: a LINE_STRIP marker (last N points) on this robot's + // own topic, e.g. /mavswarm2/robot_3/trajectory. + path_marker_pub_ = this->create_publisher( + "robot_" + std::to_string(robot_id) + "/trajectory", 10); + // distinct colour per robot from the id, via the golden-ratio hue trick: + // well-spread, unique colours for ANY number of robots (no fixed palette). + hsv_to_rgb(std::fmod(robot_id * 0.6180339887f, 1.0f), 0.85f, 1.0f, + base_r_, base_g_, base_b_); + path_marker_.header.frame_id = worldframe; // "map" + path_marker_.ns = "trajectory"; + path_marker_.id = robot_id; + path_marker_.type = visualization_msgs::msg::Marker::LINE_STRIP; + path_marker_.action = visualization_msgs::msg::Marker::ADD; + path_marker_.scale.x = 0.03; // line width + path_marker_.pose.orientation.w = 1.0; + path_marker_.color.r = base_r_; + path_marker_.color.g = base_g_; + path_marker_.color.b = base_b_; + path_marker_.color.a = 1.0; + this->setState(State::Autonomous); } @@ -119,15 +139,17 @@ class Quadrotor : public rclcpp::Node { Vector3d u, target_pos; state_space_t state_space; bool set_init_target; - bool set_next_target; - geometry_msgs::msg::Point target_next; - mav_trajectory_generation::Trajectory traj_; + std::shared_ptr scp_planner_; std::shared_ptr controller; std::shared_ptr dynamics; std::unique_ptr tf_broadcaster_; rclcpp::Subscription::SharedPtr desired_state_sub_; + rclcpp::Publisher::SharedPtr path_marker_pub_; + visualization_msgs::msg::Marker path_marker_; + int path_tick_ = 0; + float base_r_ = 1.0f, base_g_ = 1.0f, base_b_ = 1.0f; rclcpp::TimerBase::SharedPtr timer_; params_t params_; @@ -188,70 +210,17 @@ class Quadrotor : public rclcpp::Node { } // ----------------------------------------------------------------------- - // Trajectory optimisation - // ----------------------------------------------------------------------- - mav_trajectory_generation::Trajectory get_opt_traj(const opt_t &ps, const Vector3d &pe) - { - namespace mtg = mav_trajectory_generation; - mtg::Vertex::Vector vertices; - mtg::Vertex v_s(3), v_e(3); - const int deriv = mtg::derivative_order::JERK; - - v_s.addConstraint(mtg::derivative_order::POSITION, ps.position); - v_s.addConstraint(mtg::derivative_order::VELOCITY, ps.velocity); - v_s.addConstraint(mtg::derivative_order::ACCELERATION, ps.acceleration); - v_e.makeStartOrEnd(pe, deriv); - - vertices.push_back(v_s); - vertices.push_back(v_e); - - const double v_max = 1.0, a_max = 4.0; - std::vector segment_times = mtg::estimateSegmentTimes(vertices, v_max, a_max); - - mtg::PolynomialOptimization<8> opt(3); - opt.setupFromVertices(vertices, segment_times, deriv); - opt.solveLinear(); - - mtg::Trajectory trajectory; - opt.getTrajectory(&trajectory); - return trajectory; - } - - // Receding horizon replanning: replan from current dynamic state to pending target. - void do_rhp() - { - Vector3d pt(target_next.x, target_next.y, target_next.z); - state_space_t ss = dynamics->get_state(); - opt_t wp = {ss.position, ss.velocity, ss.acceleration, Vector3d(0, 0, 0)}; - traj_ = get_opt_traj(wp, pt); - set_next_target = false; - tau = 0; - RCLCPP_INFO(this->get_logger(), "Replanned trajectory, duration: %.2f s", traj_.getMaxTime()); - } - - // ----------------------------------------------------------------------- - // Goal subscription + // Goal subscription -> hand the goal to the SCP planner (NED frame) // ----------------------------------------------------------------------- void desired_pos_cb(const geometry_msgs::msg::Point::SharedPtr pt) { Vector3d p1(pt->x, pt->y, pt->z); if ((target_pos - p1).norm() < 0.2) return; - - if (!set_init_target) { - set_init_target = true; - Vector3d zero(0, 0, 0); - opt_t ps = {target_pos, zero, zero, zero}; - traj_ = get_opt_traj(ps, p1); - target_pos = p1; - RCLCPP_INFO(this->get_logger(), "Set initial trajectory to [%.2f %.2f %.2f]", - p1[0], p1[1], p1[2]); - } else { - target_next = *pt; - target_pos = p1; - set_next_target = true; - RCLCPP_INFO(this->get_logger(), "Queued new target [%.2f %.2f %.2f]", - p1[0], p1[1], p1[2]); - } + target_pos = p1; + set_init_target = true; + state_space_t ss = dynamics->get_state(); + scp_planner_->set_goal(p1, ss.position, ss.velocity); + RCLCPP_INFO(this->get_logger(), "New goal [%.2f %.2f %.2f]", p1[0], p1[1], p1[2]); } // ----------------------------------------------------------------------- @@ -299,10 +268,60 @@ class Quadrotor : public rclcpp::Node { dynamics->update(control, sim_time); set_state_space(); send_transform(); + publish_path(); dynamics->reset_dynamics(); sim_time += dt; } + // Trajectory trail: append the current (map-frame) position to a LINE_STRIP + // marker, keep only the last N points, and publish. Mirrors the ROS 1 + // Quadrotor::publish_path(). + void publish_path() + { + constexpr size_t kMaxPoints = 20; + if (++path_tick_ % 5 != 0) return; // sample ~20 Hz -> ~50 s of trail + + const Vector3d pos = state_space.position; // NWU / map frame + if (std::isnan(pos[0]) || std::isnan(pos[1]) || std::isnan(pos[2])) return; + + geometry_msgs::msg::Point p; + p.x = pos[0]; p.y = pos[1]; p.z = pos[2]; + path_marker_.points.push_back(p); + if (path_marker_.points.size() > kMaxPoints) + path_marker_.points.erase(path_marker_.points.begin()); + + // per-point alpha ramp: oldest point faint, newest solid. The tail then + // fades out smoothly so dropping the front point is barely visible. + const size_t n = path_marker_.points.size(); + path_marker_.colors.resize(n); + for (size_t i = 0; i < n; ++i) { + auto &c = path_marker_.colors[i]; + c.r = base_r_; c.g = base_g_; c.b = base_b_; + c.a = 0.05f + 0.95f * (static_cast(i + 1) / static_cast(n)); + } + + path_marker_.header.stamp = this->get_clock()->now(); + path_marker_pub_->publish(path_marker_); + } + + // HSV (h,s,v in [0,1]) -> RGB, for procedural per-robot trail colours. + static void hsv_to_rgb(float h, float s, float v, float &r, float &g, float &b) + { + const float i = std::floor(h * 6.0f); + const float f = h * 6.0f - i; + const float p = v * (1.0f - s); + const float q = v * (1.0f - f * s); + const float t = v * (1.0f - (1.0f - f) * s); + switch (static_cast(i) % 6) { + case 0: r = v; g = t; b = p; break; + case 1: r = q; g = v; b = p; break; + case 2: r = p; g = v; b = t; break; + case 3: r = p; g = q; b = v; break; + case 4: r = t; g = p; b = v; break; + default: r = v; g = p; b = q; break; + } + } + void set_state_space() { // convert the internal NED state back to map frame (NWU) for broadcasting @@ -319,13 +338,8 @@ class Quadrotor : public rclcpp::Node { Vector3d xd = simulator_utils::ned_nwu_rotation(init_vals.position); if (set_init_target) { - if (set_next_target) { - do_rhp(); - } - xd = traj_.evaluate(tau, mav_trajectory_generation::derivative_order::POSITION); - // advance, clamping to the trajectory end so we hold exactly at the - // zero-velocity endpoint instead of freezing a fraction of dt short. - tau = std::min(tau + dt, traj_.getMaxTime()); + // SCP planner advances playback and replans (with collision avoidance) internally + xd = scp_planner_->reference(); } desired_state_t dss = {xd, b1d}; diff --git a/include/mavswarm2/scp/scp_planner.hpp b/include/mavswarm2/scp/scp_planner.hpp new file mode 100644 index 0000000..1395d98 --- /dev/null +++ b/include/mavswarm2/scp/scp_planner.hpp @@ -0,0 +1,343 @@ +/* +Copyright (c) 2024 Malintha Fernando (malintha@onmail.com) + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. +*/ + +// --------------------------------------------------------------------------- +// +// The trajectory is a discretised double integrator (states = position + +// velocity, input = acceleration). We minimise the control effort while +// honouring the boundary conditions (start state, goal at rest) and the +// per-axis velocity / acceleration limits. +// +// The pairwise keep-out ||p_i[k] - p_j[k]|| >= R is non-convex. Following the +// paper it is convexified about the previous iterate into the affine +// separating-hyperplane constraint +// xi/||xi|| . (p_i[k] - p_j[k]) >= R, xi = p_i^prev[k] - p_j[k], +// and the resulting convex problem is solved; re-linearising and re-solving a +// few times is the SCP loop. (Solved here as a weighted least-squares / penalty +// problem with Eigen, so no external QP solver is required.) +// +// This module is SELF-CONTAINED: it owns the ROS publisher/subscribers used to +// exchange predicted trajectories between robots, so the quadrotor code does not +// need to know about neighbour state at all. Drop-in for the old trajectory +// optimiser: set_goal(...) once, then call reference() every control tick. +// --------------------------------------------------------------------------- + +#ifndef MAVSWARM2_SCP_PLANNER_HPP +#define MAVSWARM2_SCP_PLANNER_HPP + +#include +#include +#include +#include +#include +#include +#include + +#include "rclcpp/rclcpp.hpp" +#include "std_msgs/msg/float32_multi_array.hpp" + +namespace scp { + +using Eigen::Vector3d; +using Eigen::VectorXd; +using Eigen::MatrixXd; + +struct SCPParams { + double v_max = 1.0; // m/s velocity limit + double a_max = 2.0; // m/s^2 acceleration limit + double R = 0.5; // m collision keep-out radius + double downwash = 0.5; // ellipsoid z-scaling (1 = isotropic sphere) + double activation = 0.1; // m outward overshoot past the shell + double dt_grid = 0.15; // s trajectory discretisation step + int K_min = 10; // min / max number of segments + int K_max = 60; + int max_iters = 8; // SCP re-linearisations + int replan_every= 30; // control ticks between receding-horizon replans + // penalty weights + double w_smooth = 10.0; // control effort (acceleration) + double w_init = 1.0e6; // start state (hard) + double w_vel = 1.0e2; // start velocity + double w_goal = 1.0e3; // terminal position = goal + double w_term_vel = 1.0e2; // terminal velocity = 0 + double w_vlim = 1.0e3; // velocity limit (one-sided) + double w_alim = 5.0e2; // acceleration limit (one-sided) + double w_col = 1.0e3; // collision keep-out +}; + +// --------------------------------------------------------------------------- +// Discrete trajectory with a smooth (Catmull-Rom) interpolant. +// --------------------------------------------------------------------------- +class Trajectory { +public: + Trajectory() : h_(0.1), T_(0.0) {} + Trajectory(std::vector pts, double h) + : pts_(std::move(pts)), h_(h), + T_(h * static_cast(pts_.empty() ? 0 : pts_.size() - 1)) {} + + double getMaxTime() const { return T_; } + bool empty() const { return pts_.empty(); } + + // derivative_order: 0 = position, 1 = velocity, 2 = acceleration + Vector3d evaluate(double t, int derivative_order = 0) const + { + const int n = static_cast(pts_.size()); + if (n == 0) return Vector3d::Zero(); + if (n == 1) return (derivative_order == 0) ? pts_[0] : Vector3d::Zero(); + + if (t < 0.0) t = 0.0; + if (t > T_) t = T_; + int i = static_cast(std::floor(t / h_)); + if (i > n - 2) i = n - 2; + const double u = (t - i * h_) / h_; + + const Vector3d &P1 = pts_[i]; + const Vector3d &P2 = pts_[i + 1]; + const Vector3d P0 = (i - 1 >= 0) ? pts_[i - 1] : (2.0 * P1 - P2); + const Vector3d P3 = (i + 2 <= n - 1) ? pts_[i + 2] : (2.0 * P2 - P1); + + const Vector3d a = 2.0 * P1; + const Vector3d b = -P0 + P2; + const Vector3d c = 2.0 * P0 - 5.0 * P1 + 4.0 * P2 - P3; + const Vector3d d = -P0 + 3.0 * P1 - 3.0 * P2 + P3; + + if (derivative_order == 0) return 0.5 * (a + b * u + c * (u * u) + d * (u * u * u)); + if (derivative_order == 1) return 0.5 * (b + 2.0 * c * u + 3.0 * d * (u * u)) / h_; + return 0.5 * (2.0 * c + 6.0 * d * u) / (h_ * h_); + } + +private: + std::vector pts_; + double h_; + double T_; +}; + +// --------------------------------------------------------------------------- +// Per-robot SCP planner. Owns the neighbour-trajectory communication. +// --------------------------------------------------------------------------- +class ScpPlanner { +public: + ScpPlanner(rclcpp::Node *node, int robot_id, double control_dt, + const SCPParams &prm = SCPParams()) + : node_(node), robot_id_(robot_id), dt_(control_dt), prm_(prm) + { + if (!node_->has_parameter("num_robots")) + node_->declare_parameter("num_robots", 10); + if (!node_->has_parameter("safety_radius")) + node_->declare_parameter("safety_radius", prm_.R); + num_robots_ = node_->get_parameter("num_robots").as_int(); + prm_.R = node_->get_parameter("safety_radius").as_double(); + + path_pub_ = node_->create_publisher( + "robot_" + std::to_string(robot_id_) + "/scp_path", 10); + for (int j = 0; j < num_robots_; ++j) { + if (j == robot_id_) continue; + auto sub = node_->create_subscription( + "robot_" + std::to_string(j) + "/scp_path", 10, + [this, j](const std_msgs::msg::Float32MultiArray::SharedPtr m) { on_path(j, m); }); + path_subs_.push_back(sub); + } + } + + // Set / update the goal (NED). Plans immediately from the supplied state. + void set_goal(const Vector3d &goal, const Vector3d &p0, const Vector3d &v0) + { + goal_ = goal; + has_goal_ = true; + traj_ = solve(p0, v0, goal_); + t_play_ = 0.0; + ticks_ = 0; + publish_path(); + } + + // Desired position for this control tick (advances playback, replans as needed). + Vector3d reference() + { + if (!has_goal_) return goal_; + + if (++ticks_ >= prm_.replan_every && !traj_.empty()) { + // receding horizon: re-solve from the current reference (keeps xd smooth) + const Vector3d p0 = traj_.evaluate(t_play_, 0); + const Vector3d v0 = traj_.evaluate(t_play_, 1); + traj_ = solve(p0, v0, goal_); + t_play_ = 0.0; + ticks_ = 0; + } + const Vector3d xd = traj_.evaluate(t_play_, 0); + t_play_ = std::min(t_play_ + dt_, traj_.getMaxTime()); + publish_path(); + return xd; + } + +private: + // ----- neighbour communication ----------------------------------------- + void on_path(int j, const std_msgs::msg::Float32MultiArray::SharedPtr msg) + { + if (msg->data.size() < 4) return; + const double dtj = msg->data[0]; + std::vector s; + for (size_t i = 1; i + 2 < msg->data.size(); i += 3) + s.emplace_back(msg->data[i], msg->data[i + 1], msg->data[i + 2]); + neighbor_paths_[j] = {dtj, std::move(s)}; + } + + void publish_path() + { + std_msgs::msg::Float32MultiArray msg; + const double dtp = prm_.dt_grid; + const int M = 20; + msg.data.push_back(static_cast(dtp)); + for (int m = 0; m <= M; ++m) { + Vector3d q = traj_.empty() ? goal_ + : traj_.evaluate(std::min(t_play_ + m * dtp, traj_.getMaxTime()), 0); + msg.data.push_back(static_cast(q[0])); + msg.data.push_back(static_cast(q[1])); + msg.data.push_back(static_cast(q[2])); + } + path_pub_->publish(msg); + } + + // neighbour j's predicted position at relative time t (clamped) + Vector3d neighbor_at(int j, double t) const + { + const auto it = neighbor_paths_.find(j); + if (it == neighbor_paths_.end() || it->second.second.empty()) + return Vector3d::Constant(1e9); // unknown -> effectively absent + const double dtj = it->second.first; + const auto &s = it->second.second; + const double fm = t / std::max(dtj, 1e-6); + const int m = static_cast(std::floor(fm)); + if (m >= static_cast(s.size()) - 1) return s.back(); + const double a = fm - m; + return (1.0 - a) * s[m] + a * s[m + 1]; + } + + // ----- the SCP solve --------------------------------------------------- + Trajectory solve(const Vector3d &p0, const Vector3d &v0, const Vector3d &goal) + { + const double dist = (goal - p0).norm(); + // horizon sized to actually reach the goal at <= v_max (no overspeed) + const double T = std::max(2.0, 1.2 * dist / std::max(prm_.v_max, 1e-3)); + const int K = std::clamp(static_cast(std::round(T / prm_.dt_grid)), + prm_.K_min, prm_.K_max); + const double h = T / K; + const int nv = 3 * (K + 1); + + std::vector p(K + 1); + for (int k = 0; k <= K; ++k) + p[k] = p0 + (static_cast(k) / K) * (goal - p0); + + auto idx = [](int k, int d) { return 3 * k + d; }; + const double cz = prm_.downwash; + + for (int iter = 0; iter < prm_.max_iters; ++iter) { + MatrixXd H = MatrixXd::Zero(nv, nv); + VectorXd c = VectorXd::Zero(nv); + auto addRes = [&](double w, const std::vector> &t, double tgt) { + for (const auto &ta : t) { + c(ta.first) += w * ta.second * tgt; + for (const auto &tb : t) H(ta.first, tb.first) += w * ta.second * tb.second; + } + }; + + // boundary conditions + for (int d = 0; d < 3; ++d) addRes(prm_.w_init, {{idx(0, d), 1.0}}, p0[d]); + for (int d = 0; d < 3; ++d) addRes(prm_.w_vel, {{idx(1, d), 1.0}, {idx(0, d), -1.0}}, h * v0[d]); + for (int d = 0; d < 3; ++d) addRes(prm_.w_goal, {{idx(K, d), 1.0}}, goal[d]); + for (int d = 0; d < 3; ++d) addRes(prm_.w_term_vel, {{idx(K, d), 1.0}, {idx(K - 1, d), -1.0}}, 0.0); + + // control effort: minimise acceleration (double-integrator input) + for (int k = 1; k <= K - 1; ++k) + for (int d = 0; d < 3; ++d) + addRes(prm_.w_smooth, {{idx(k + 1, d), 1.0}, {idx(k, d), -2.0}, {idx(k - 1, d), 1.0}}, 0.0); + + // velocity limit (one-sided) + for (int k = 0; k <= K - 1; ++k) { + const Vector3d seg = p[k + 1] - p[k]; + if (seg.norm() / h > prm_.v_max && seg.norm() > 1e-9) { + const Vector3d s = seg / seg.norm(); + addRes(prm_.w_vlim, + {{idx(k + 1, 0), s[0]}, {idx(k, 0), -s[0]}, + {idx(k + 1, 1), s[1]}, {idx(k, 1), -s[1]}, + {idx(k + 1, 2), s[2]}, {idx(k, 2), -s[2]}}, h * prm_.v_max); + } + } + + // acceleration limit (one-sided) + for (int k = 1; k <= K - 1; ++k) { + const Vector3d acc = p[k + 1] - 2.0 * p[k] + p[k - 1]; + if (acc.norm() / (h * h) > prm_.a_max && acc.norm() > 1e-9) { + const Vector3d s = acc / acc.norm(); + addRes(prm_.w_alim, + {{idx(k + 1, 0), s[0]}, {idx(k, 0), -2.0 * s[0]}, {idx(k - 1, 0), s[0]}, + {idx(k + 1, 1), s[1]}, {idx(k, 1), -2.0 * s[1]}, {idx(k - 1, 1), s[1]}, + {idx(k + 1, 2), s[2]}, {idx(k, 2), -2.0 * s[2]}, {idx(k - 1, 2), s[2]}}, + h * h * prm_.a_max); + } + } + + // collision: separating hyperplane vs higher-priority neighbours (lower id). + // Prioritised planning: a robot only avoids smaller-id robots, which + // breaks the symmetry that causes reciprocal dodging / deadlock. + const double shell = prm_.R; + for (int j = 0; j < robot_id_; ++j) { + if (neighbor_paths_.find(j) == neighbor_paths_.end()) continue; + for (int k = 1; k <= K; ++k) { + const Vector3d o = neighbor_at(j, k * h); + const Vector3d e = p[k] - o; + const double ne = std::sqrt(e[0]*e[0] + e[1]*e[1] + cz*cz*e[2]*e[2]); + if (ne < shell && ne > 1e-6) { + const Vector3d a(e[0] / ne, e[1] / ne, cz * cz * e[2] / ne); + addRes(prm_.w_col, + {{idx(k, 0), a[0]}, {idx(k, 1), a[1]}, {idx(k, 2), a[2]}}, + shell + prm_.activation + a.dot(o)); + } + } + } + + for (int i = 0; i < nv; ++i) H(i, i) += 1e-9; + const VectorXd x = H.ldlt().solve(c); + + double step = 0.0; + for (int k = 0; k <= K; ++k) { + const Vector3d pk(x(idx(k, 0)), x(idx(k, 1)), x(idx(k, 2))); + step = std::max(step, (pk - p[k]).norm()); + p[k] = pk; + } + if (step < 1e-3) break; + } + return Trajectory(std::move(p), h); + } + + rclcpp::Node *node_; + int robot_id_; + double dt_; + SCPParams prm_; + int num_robots_ = 10; + + bool has_goal_ = false; + Vector3d goal_ = Vector3d::Zero(); + Trajectory traj_; + double t_play_ = 0.0; + int ticks_ = 0; + + rclcpp::Publisher::SharedPtr path_pub_; + std::vector::SharedPtr> path_subs_; + std::map>> neighbor_paths_; +}; + +} // namespace scp + +#endif // MAVSWARM2_SCP_PLANNER_HPP From ee2e0fa856606a3a8796ae6874e0b1a9b405a773 Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Sat, 6 Jun 2026 00:51:24 +0200 Subject: [PATCH 21/24] updating readme --- .gitignore | 4 +- CMakeLists.txt | 4 - cover.gif | Bin 1564641 -> 0 bytes cover.png | Bin 0 -> 50272 bytes cover2.png | Bin 0 -> 14441 bytes include/mavswarm2/quadrotor.hpp | 2 +- package.xml | 1 - publish_words.py | 287 ++++++++++++++++++++++++++++++++ readme.md | 34 ++-- 9 files changed, 310 insertions(+), 22 deletions(-) delete mode 100644 cover.gif create mode 100644 cover.png create mode 100644 cover2.png create mode 100755 publish_words.py diff --git a/.gitignore b/.gitignore index c29ef59..0d3fc42 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,6 @@ config/simulation.rviz .gitignore .vscode -build \ No newline at end of file +build +install +log \ No newline at end of file diff --git a/CMakeLists.txt b/CMakeLists.txt index f8ef780..c91629c 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -16,7 +16,6 @@ find_package(geometry_msgs REQUIRED) find_package(visualization_msgs REQUIRED) find_package(tf2 REQUIRED) find_package(tf2_ros REQUIRED) -find_package(mav_trajectory_generation_ros2 REQUIRED) find_package(glog REQUIRED) add_executable(mavswarm2 src/quadrotor.cpp) @@ -28,13 +27,11 @@ ament_target_dependencies(mavswarm2 tf2_ros visualization_msgs simulator_interfaces - mav_trajectory_generation_ros2 ) target_link_libraries(mavswarm2 GSL::gsl GSL::gslcblas - ${mav_trajectory_generation_ros2_LIBRARIES} glog::glog ) @@ -49,7 +46,6 @@ install( 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Build the letter as exactly 10 goal slots from a vector stroke-font +# (resampled by arc length), with >= CLEARANCE between any two slots, and +# the whole glyph tilted by TILT degrees so it is not edge-on. +# 2. Read the drones' current positions from TF. +# 3. Solve the optimal drone -> slot assignment with the Hungarian algorithm +# (minimum total transit distance). +# 4. Publish the goals; wait TRANSIT_S for the drones to fly over. +# +# Goals are in the controller's NED frame (x = North, y = East, z = Down; +# negative z = up). A glyph point (h, v) maps to +# x = GX + h*sin(TILT), y = h*cos(TILT), z = -(V_BASE + v) +# +# NOTE: ROS Jazzy's rclpy is built for Python 3.12 -- run with python3.12. +# --------------------------------------------------------------------------- + +import sys +import time +import math +import rclpy +from rclpy.node import Node +from rclpy.time import Time +from geometry_msgs.msg import Point +from tf2_ros import Buffer, TransformListener + +# ---- layout / behaviour knobs --------------------------------------------- +N = 10 # drones (= slots per letter) +GX = 2.0 # North/depth offset of the letter plane +V_BASE = 1.5 # altitude of the bottom of a glyph (m) +TILT = math.radians(30) # yaw tilt of the letter plane (so it has depth) +SCALE = 2.5 # overall glyph size multiplier (bigger = more spacing) +CLEARANCE = 0.75 # min spacing between slots BEFORE scaling (> safety R) +TRANSIT_S = 10.0 # seconds to wait between letters (bigger -> longer transit) +STAGGER_S = 0.2 # small interval between successive drone commands + +# --------------------------------------------------------------------------- +# Vector stroke-font. Each glyph is a list of strokes; each stroke is a polyline +# of (h, v) vertices with h in [-1.5, 1.5] (width) and v in [0, 4.5] (height). +# These ARE the saved letter locations -- the 10 slots are sampled from them. +# --------------------------------------------------------------------------- +ALPHABET = { + "A": [[(-1.5,0),(0,4.5),(1.5,0)], [(-0.85,1.9),(0.85,1.9)]], + "B": [[(-1.5,0),(-1.5,4.5),(0.6,4.5),(1.3,3.6),(0.6,2.25),(-1.5,2.25)], + [(0.6,2.25),(1.4,1.1),(0.5,0),(-1.5,0)]], + "C": [[(1.3,3.7),(0.4,4.5),(-0.9,4.5),(-1.5,3.6),(-1.5,0.9),(-0.9,0),(0.4,0),(1.3,0.8)]], + "D": [[(-1.5,0),(-1.5,4.5),(0.3,4.5),(1.3,3.4),(1.3,1.1),(0.3,0),(-1.5,0)]], + "E": [[(1.3,4.5),(-1.5,4.5),(-1.5,0),(1.3,0)], [(-1.5,2.25),(0.8,2.25)]], + "F": [[(1.3,4.5),(-1.5,4.5),(-1.5,0)], [(-1.5,2.25),(0.8,2.25)]], + "G": [[(1.3,3.7),(0.4,4.5),(-0.9,4.5),(-1.5,3.6),(-1.5,0.9),(-0.9,0), + (0.6,0),(1.3,0.8),(1.3,2.0),(0.4,2.0)]], + "H": [[(-1.5,0),(-1.5,4.5)], [(1.5,0),(1.5,4.5)], [(-1.5,2.25),(1.5,2.25)]], + "I": [[(-1.0,4.5),(1.0,4.5)], [(0,4.5),(0,0)], [(-1.0,0),(1.0,0)]], + "J": [[(1.1,4.5),(1.1,1.0),(0.4,0),(-0.6,0),(-1.3,1.0)]], + "K": [[(-1.5,0),(-1.5,4.5)], [(-1.5,2.1),(1.3,4.5)], [(-1.5,2.1),(1.3,0)]], + "L": [[(-1.5,4.5),(-1.5,0),(1.3,0)]], + "M": [[(-1.5,0),(-1.5,4.5),(0,2.1),(1.5,4.5),(1.5,0)]], + "N": [[(-1.5,0),(-1.5,4.5),(1.5,0),(1.5,4.5)]], + "O": [[(-1.5,1.0),(-1.5,3.5),(-0.7,4.5),(0.7,4.5),(1.5,3.5),(1.5,1.0), + (0.7,0),(-0.7,0),(-1.5,1.0)]], + "P": [[(-1.5,0),(-1.5,4.5),(0.6,4.5),(1.3,3.6),(0.6,2.5),(-1.5,2.5)]], + "Q": [[(-1.5,1.0),(-1.5,3.5),(-0.7,4.5),(0.7,4.5),(1.5,3.5),(1.5,1.0), + (0.7,0),(-0.7,0),(-1.5,1.0)], [(0.3,1.3),(1.5,0)]], + "R": [[(-1.5,0),(-1.5,4.5),(0.6,4.5),(1.3,3.6),(0.6,2.5),(-1.5,2.5)], + [(-0.1,2.5),(1.3,0)]], + "S": [[(1.3,3.7),(0.4,4.5),(-0.9,4.5),(-1.5,3.7),(-0.9,2.4),(0.8,2.0), + (1.3,1.0),(0.6,0),(-0.7,0),(-1.4,0.8)]], + "T": [[(-1.5,4.5),(1.5,4.5)], [(0,4.5),(0,0)]], + "U": [[(-1.5,4.5),(-1.5,1.0),(-0.8,0),(0.8,0),(1.5,1.0),(1.5,4.5)]], + "V": [[(-1.5,4.5),(0,0),(1.5,4.5)]], + "W": [[(-1.5,4.5),(-0.8,0),(0,2.4),(0.8,0),(1.5,4.5)]], + "X": [[(-1.5,0),(1.5,4.5)], [(-1.5,4.5),(1.5,0)]], + "Y": [[(-1.5,4.5),(0,2.3),(1.5,4.5)], [(0,2.3),(0,0)]], + "Z": [[(-1.5,4.5),(1.5,4.5),(-1.5,0),(1.5,0)]], +} + + +# ---- glyph -> 10 slots ---------------------------------------------------- +def _poly_len(poly): + return sum(math.dist(poly[i], poly[i + 1]) for i in range(len(poly) - 1)) + + +def _sample_polyline(poly, count): + """`count` points evenly spaced by arc length along the polyline.""" + if count <= 1: + return [poly[len(poly) // 2]] + seg = [math.dist(poly[i], poly[i + 1]) for i in range(len(poly) - 1)] + total = sum(seg) + if total < 1e-9: + return [poly[0]] * count + out = [] + for s in range(count): + target = total * s / (count - 1) + acc = 0.0 + for i, sl in enumerate(seg): + if acc + sl >= target or i == len(seg) - 1: + r = (target - acc) / sl if sl > 1e-9 else 0.0 + r = max(0.0, min(1.0, r)) + out.append((poly[i][0] + r * (poly[i + 1][0] - poly[i][0]), + poly[i][1] + r * (poly[i + 1][1] - poly[i][1]))) + break + acc += sl + return out + + +def _resample_glyph(strokes, n=N): + """Distribute exactly n points across the strokes, by length (>=2 each).""" + lens = [_poly_len(s) for s in strokes] + total = sum(lens) or 1.0 + counts = [max(2, round(n * l / total)) for l in lens] + while sum(counts) > n: + cand = [k for k in range(len(counts)) if counts[k] > 2] or list(range(len(counts))) + i = min(cand, key=lambda k: lens[k] / counts[k]) + counts[i] -= 1 + while sum(counts) < n: + i = max(range(len(counts)), key=lambda k: lens[k] / counts[k]) + counts[i] += 1 + pts = [] + for s, c in zip(strokes, counts): + pts += _sample_polyline(s, c) + return pts + + +def _enforce_clearance(pts, clear=CLEARANCE, iters=60): + """Push apart any pair closer than `clear` (in the glyph plane = 3D).""" + p = [list(q) for q in pts] + for _ in range(iters): + moved = False + for i in range(len(p)): + for j in range(i + 1, len(p)): + dx, dy = p[j][0] - p[i][0], p[j][1] - p[i][1] + d = math.hypot(dx, dy) + if d < clear: + if d < 1e-6: + dx, dy, d = 0.0, 1.0, 1.0 + push = (clear - d) / 2.0 + 1e-3 + ux, uy = dx / d, dy / d + p[i][0] -= ux * push; p[i][1] -= uy * push + p[j][0] += ux * push; p[j][1] += uy * push + moved = True + if not moved: + break + return [(q[0], q[1]) for q in p] + + +def build_letter(ch): + """Return 10 NED goals for character `ch`, or None if unknown.""" + strokes = ALPHABET.get(ch.upper()) + if strokes is None: + return None + glyph = _enforce_clearance(_resample_glyph(strokes, N), CLEARANCE) + goals = [] + for (h, v) in glyph: + hs, vs = h * SCALE, v * SCALE # enlarge the glyph + x = GX + hs * math.sin(TILT) + y = hs * math.cos(TILT) + z = -(V_BASE + vs) + goals.append((x, y, z)) + return goals + + +# ---- Hungarian assignment (scipy if available, else built-in O(n^3)) ------ +def hungarian(cost): + try: + from scipy.optimize import linear_sum_assignment + r, c = linear_sum_assignment(cost) + ans = [0] * len(cost) + for ri, ci in zip(r, c): + ans[ri] = ci + return ans + except Exception: + pass + n = len(cost) + INF = float('inf') + u = [0.0] * (n + 1); v = [0.0] * (n + 1) + p = [0] * (n + 1); way = [0] * (n + 1) + for i in range(1, n + 1): + p[0] = i; j0 = 0 + minv = [INF] * (n + 1); used = [False] * (n + 1) + while True: + used[j0] = True; i0 = p[j0]; delta = INF; j1 = -1 + for j in range(1, n + 1): + if not used[j]: + cur = cost[i0 - 1][j - 1] - u[i0] - v[j] + if cur < minv[j]: + minv[j] = cur; way[j] = j0 + if minv[j] < delta: + delta = minv[j]; j1 = j + for j in range(n + 1): + if used[j]: + u[p[j]] += delta; v[j] -= delta + else: + minv[j] -= delta + j0 = j1 + if p[j0] == 0: + break + while True: + j1 = way[j0]; p[j0] = p[j1]; j0 = j1 + if j0 == 0: + break + ans = [0] * n + for j in range(1, n + 1): + ans[p[j] - 1] = j - 1 + return ans + + +def _ned_to_map(p): + return (p[0], -p[1], -p[2]) # NWU(map) <-> NED is the involution (x,-y,-z) + + +class WordSpeller(Node): + def __init__(self): + super().__init__('word_speller') + self.pubs = [self.create_publisher(Point, f'/mavswarm2/robot_{i}/desired_state', 10) + for i in range(N)] + self.tf_buffer = Buffer() + self.tf_listener = TransformListener(self.tf_buffer, self) + + def current_positions_map(self): + pos = [None] * N + for i in range(N): + try: + t = self.tf_buffer.lookup_transform('map', f'robot_{i}/base_link', Time()) + tr = t.transform.translation + pos[i] = (tr.x, tr.y, tr.z) + except Exception: + pos[i] = None + return pos + + def assign_and_publish(self, ch, goals_ned): + goals_map = [_ned_to_map(g) for g in goals_ned] + cur = self.current_positions_map() + n_known = sum(1 for c in cur if c is not None) + cost = [[0.0] * N for _ in range(N)] + for i in range(N): + ci = cur[i] if cur[i] is not None else goals_map[i] + for k in range(N): + cost[i][k] = math.dist(ci, goals_map[k]) + assign = hungarian(cost) + total = sum(cost[i][assign[i]] for i in range(N)) + self.get_logger().info( + f"'{ch}': tf {n_known}/{N}, total dist {total:.2f} m, drone->slot {assign}") + # issue commands one drone at a time with a small interval (not all at once) + for i in range(N): + g = goals_ned[assign[i]] + m = Point(); m.x, m.y, m.z = g + self.pubs[i].publish(m) + self.spin_for(STAGGER_S) + + def spin_for(self, seconds): + end = time.time() + seconds + while time.time() < end and rclpy.ok(): + rclpy.spin_once(self, timeout_sec=0.05) + + +def main(): + word = (sys.argv[1] if len(sys.argv) > 1 else "KTH") + rclpy.init() + node = WordSpeller() + node.get_logger().info(f"Spelling: {word}") + node.spin_for(3.0) # let TF fill / publishers match + + for ch in word: + if ch == ' ': + node.get_logger().info("(space)") + node.spin_for(TRANSIT_S) + continue + goals = build_letter(ch) + if goals is None: + node.get_logger().warn(f"no glyph for '{ch}', skipping") + continue + node.assign_and_publish(ch, goals) + node.spin_for(TRANSIT_S) + + node.get_logger().info(f"Done spelling '{word}'.") + node.destroy_node() + rclpy.shutdown() + + +if __name__ == '__main__': + main() diff --git a/readme.md b/readme.md index 0a20c2f..19596d4 100644 --- a/readme.md +++ b/readme.md @@ -1,20 +1,28 @@ -# Mavswarm2 (under development) +# Mavswarm2 -Mavswarm is a lightweight and fast Multi-Aerial Vehicle simulator built on Robot Operating System (ROS), entirely written in C++. Mavswarm2 is the ROS2-compatible version of Mavswarm. It supports simulating heterogenous quadrotor swarms of upto 10 robots on a single desktop with physics. +Mavswarm2 is the ROS2-compatible version of Mavswarm. It supports simulating heterogenous quadrotor swarms of more than 10 robots on a single desktop with physics. -It has -- quadrotor control (ROS1/ROS2) -- trajectory optimization and receding horizon planning (only working in ROS1. I welcome any PRs/Contributions). +New in Mavswarm2 is trajectory optimization with collision avoidance using sequential convex programming. All the functionality is self-contained, and does not depend on any other ros packages except for ``simulator_interfaces``. + +**Functionalities:** +- quadrotor control (same geometric controller as mavswarm) +- trajectory optimization +- receding horizon planning +- collision avoidance The internal controller uses the Lee's geometric tracking controller [3] and it is tuned for two different quadrotor models out of the box. -**Compared to Mavswarm1, Mavswarm2 has a simpler installation, and the code is more self-contained. Everything is in the header files, so easier to manage and export as a library**. +**Compared to Mavswarm1, Mavswarm2 has a simpler installation, and the code is more self-contained. Everything is in the header files, so easier to manage and export as a library.**. Consider citing our work [1][2] if you find this code helpful for your publications. -| ![Cover Image](https://github.com/malintha/multi_uav_simulator/blob/master/cover.gif?raw=true) | +| ![Cover Image](https://github.com/malintha/multi_uav_simulator/blob/ros2/cover.png?raw=true) | +|:--:| +| *A swarm of 10 drones stabilizing from an upside-down initialization* | + +| ![Cover Image](https://github.com/malintha/multi_uav_simulator/blob/ros2/cover2.png?raw=true) | |:--:| -| *A hetergenous swarm of 5 quadrotors stabilizing from an upside-down initialization* | +| *10 drones forming letter "U"* | ## Installation @@ -40,14 +48,10 @@ Install Eigen, Armadillo and GNU Science Library (GSL) before you continue. ros2 launch mavswarm2 quadrotor.launch -**Publishing Goals** - -- Under development, not working in right now - -**Adding a new drone to the environment** - -- under development, not working in right now +**Formation Control Goal Publishing** +The example script ``publish_words.py`` publishes locations to the drones such that it can visualize a word, one letter-at-a-time using a formation of 10 drones. + python publish_words.py HELLO [1] Our work based on this controller: From 06164e4563b5cb93d0dc028d7b1a41ecf959394d Mon Sep 17 00:00:00 2001 From: Malintha Fernando Date: Sat, 6 Jun 2026 00:58:46 +0200 Subject: [PATCH 22/24] updating readme --- readme.md | 18 ++++++++++-------- 1 file changed, 10 insertions(+), 8 deletions(-) diff --git a/readme.md b/readme.md index 19596d4..cf08fb9 100644 --- a/readme.md +++ b/readme.md @@ -2,7 +2,9 @@ Mavswarm2 is the ROS2-compatible version of Mavswarm. It supports simulating heterogenous quadrotor swarms of more than 10 robots on a single desktop with physics. -New in Mavswarm2 is trajectory optimization with collision avoidance using sequential convex programming. All the functionality is self-contained, and does not depend on any other ros packages except for ``simulator_interfaces``. +**New in Mavswarm2 is fully-distributed trajectory optimization with collision avoidance using sequential convex programming!** + +All the functionality is self-contained, and does not depend on any other ros packages except for ``simulator_interfaces``. **Functionalities:** - quadrotor control (same geometric controller as mavswarm) @@ -16,13 +18,12 @@ The internal controller uses the Lee's geometric tracking controller [3] and it Consider citing our work [1][2] if you find this code helpful for your publications. -| ![Cover Image](https://github.com/malintha/multi_uav_simulator/blob/ros2/cover.png?raw=true) | -|:--:| -| *A swarm of 10 drones stabilizing from an upside-down initialization* | +Consider citing our work [1][2] if you find this code helpful for your publications. -| ![Cover Image](https://github.com/malintha/multi_uav_simulator/blob/ros2/cover2.png?raw=true) | -|:--:| -| *10 drones forming letter "U"* | +| Drone stabilization | Letter formation | +|:-------------------:|:----------------:| +| | | +| *A swarm of 10 drones stabilizing from an upside-down initialization* | *10 drones forming letter "U"* | ## Installation @@ -49,7 +50,8 @@ Install Eigen, Armadillo and GNU Science Library (GSL) before you continue. **Formation Control Goal Publishing** -The example script ``publish_words.py`` publishes locations to the drones such that it can visualize a word, one letter-at-a-time using a formation of 10 drones. + +The example script ``publish_words.py`` publishes locations to the drones such that it can visualize a word, one letter-at-a-time using a formation of 10 drones. It computes a bipartite matching to find the least distance matching drones, then issue collision-free trajectory waypoints to be tracked using the internal geometric controller in a decentralized manner. python publish_words.py HELLO From 48be5b945970c485ed623852880c3ccc3f19c6e6 Mon Sep 17 00:00:00 2001 From: Malintha Fernando <3253761+malintha@users.noreply.github.com> Date: Sat, 6 Jun 2026 01:00:52 +0200 Subject: [PATCH 23/24] Update readme.md --- readme.md | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/readme.md b/readme.md index cf08fb9..ff3f705 100644 --- a/readme.md +++ b/readme.md @@ -12,14 +12,12 @@ All the functionality is self-contained, and does not depend on any other ros pa - receding horizon planning - collision avoidance +Consider citing our work [1][2] if you find this code helpful for your publications. + The internal controller uses the Lee's geometric tracking controller [3] and it is tuned for two different quadrotor models out of the box. **Compared to Mavswarm1, Mavswarm2 has a simpler installation, and the code is more self-contained. Everything is in the header files, so easier to manage and export as a library.**. -Consider citing our work [1][2] if you find this code helpful for your publications. - -Consider citing our work [1][2] if you find this code helpful for your publications. - | Drone stabilization | Letter formation | |:-------------------:|:----------------:| | | | From f2cc09b22e4752c057cb8cc29c47e6fecfe04dde Mon Sep 17 00:00:00 2001 From: Malintha Fernando <3253761+malintha@users.noreply.github.com> Date: Sat, 6 Jun 2026 01:16:06 +0200 Subject: [PATCH 24/24] Update readme.md --- readme.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/readme.md b/readme.md index ff3f705..47f1105 100644 --- a/readme.md +++ b/readme.md @@ -1,6 +1,6 @@ -# Mavswarm2 +# Mavswarm2 (ROS2 Support for Mavswarm) -Mavswarm2 is the ROS2-compatible version of Mavswarm. It supports simulating heterogenous quadrotor swarms of more than 10 robots on a single desktop with physics. +Mavswarm2 is the ROS2-compatible version of Mavswarm. It supports simulating heterogenous quadrotor swarms of more than 10 robots on a single desktop with physics. Tested for ROS2 Jazzy. **New in Mavswarm2 is fully-distributed trajectory optimization with collision avoidance using sequential convex programming!**

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