Multi-Robot System Path Planning Based On Cone Programming

In a multi-robot system,reliable collision avoidance and obstacle avoidance have become a basic requirement for any mobile robot.Therefore,path planning is a key issue for multirobot systems,and its basic goal is to generate a collision-free trajectory from the initial position to the target position for each robot.As mobile robots are widely used in various industries,such as service industry,national defense,medical care,etc,humans have put forward higher requirements for the path planning speed of multi-robot systems.For example,when the robot is at the current position,if the path planning algorithm cannot give the predicted position of the next sampling point in time,it will increase the system path planning time,resulting in a decrease in the robot's moving speed,thereby affecting the realtime performance of the multi-robot system.In addition,when the robot encounters a dynamic obstacle in motion,quickly predicting the location of the next sampling point will avoid the collision of the robot with the dynamic obstacle.Therefore,using a fast path planning algorithm in a complex environment can not only enable the robot to avoid obstacles in time,but also improve the robustness and applicability of the system.In order to solve the problem of insufficient calculation speed in existing path planning,this thesis proposes a path planning algorithm for distributed multi-robot systems based on cone planning,and studies the motion trajectory planning of multi-robot systems in unstructured and changing environments.First of all,this thesis adopts the model predictive control(MPC)strategy and the incremental sequential convex programming(i SCP)algorithm to plan the path of the multi-robot system.The basic idea is to discretize the path of multi-robots into multiple sampling points,monitor the local operating environment in real time through the MPC framework,and mathematically model obstacles within the range,thereby establishing a mathematical model of multi-robot path planning.Second,the i SCP algorithm is used to highlight the non-convex constraints in the mathematical model,and the mathematical model after the projection is solved to obtain the prediction information of the next sampling point of each robot,so as to control the movement of each robot to the predicted position.Compared with nonlinear mathematical programming,using convex programming to solve path planning problems is faster.However,there is still a need for faster path planning and solving algorithms to meet human requirements for multi-robot systems.Through the analysis of the above-mentioned mathematical model of multi-robot motion planning,it can be seen that the mathematical model after convexizing the non-convex constraints using the i SCP algorithm belongs to the category of strictly convex quadratic programming.The second-order cone programming is a special convex programming,which not only has a fast solution speed,but also has a wide range of applications.Therefore,this thesis uses the second-order cone programming to plan the path of the multi-robot system.Through the exploration of the strict convex quadratic programming problem and the second-order cone programming problem,the steps and formulas of the conversion process are obtained.On this basis,this thesis proposes a multi-robot path planning algorithm based on the second-order cone planning,and then uses MATLAB software to simulate and analyze the algorithm proposed in this thesis.First of all,by using strict convex quadratic programming and cone programming to solve the planning functions of different scales,and analyzing the results of the two solutions,it can be seen that as the number of unknown variables in the planning function increases,the calculation time of the cone programming decreases,whereas the optimization ratio increases.Second,the strict convex quadratic programming and cone programming algorithm proposed in this thesis are simulated and realized.In order to fully reflect the performance of the two solution algorithms,this thesis sets up four different motion scenarios to plan the robot path separately.Finally,by comparing the solution time,the analysis shows that the second-order cone programming method can increase the calculation speed of the robot path planning by an average of 10%to 20%,which effectively improves the path planning speed of the robot system.Finally,an obstacle avoidance strategy for the robot in a dynamic environment is proposed by predicting the position of the next sampling point of the dynamic obstacle so as to treat it as a static obstacle.After so,we add obstacle avoidance constraints to the robot path planning problem,and then obtain an integrated robot path planning problem.Then,the method of predicting the future position of dynamic obstacles is clarified through MATLAB software.In two typical dynamic environments,the simulation analysis is conducted for the single robot and multi-robot using the path planning algorithm under cone planning and strict convex quadratic planning respectively.The performance of the path planning algorithm under the cone programming proves the effectiveness and superiority of the path planning algorithm under such programming.