Research And Implementation Of Multi-Agent Formation Control Algorithm Based On PDE Model

In recent years,multi-agent formation control has been widely used in UAV formation collaboration,sensor networks,data fusion,traffic vehicle control and other fields,it can be used for military patrols,energy exploration,mapping,coordinated rescue and other tasks.Multi-agent formation control refers to using distributed collaborative control methods to make the multi-agent system form the desired formation and maintain stability in the desired formation.In response to the above problems,this paper uses partial differential equations(PDE)to establish a cluster dynamics model of the multi-agent system,and describes the overall dynamics of the system including the interaction between agents.Using the infinite-dimensional backstepping method to design the boundary controller,so that the cluster can move to the desired formation.Adopt the leader-follower control model,set the leader on the boundary as the driver of the entire group,drive the entire system to form a formation formation,and realize the transformation between different expected formations through the leader's re-drive.Through the Lyapunov function method,the stability of the closed-loop system under the L~2 norm is proved.Furthermore,an experimental platform for a ground mobile robot was built,and a set of wheeled mobile robots were used to implement the proposed theoretical algorithm and verify the effectiveness of the algorithm.In the experiment,the Link Track ultra-wideband(UWB)module is used to realize the positioning function,the Kalman filter algorithm is used to improve the positioning accuracy,and the model predictive control(MPC)is used to realize the motion control of the position and angle of the unmanned car.The research content of this paper mainly includes the following two aspects:(1)Modeling,control algorithm design and simulation of multi-agent formation control system.Firstly,it defines the location feature expression of the agent on the 2-D plane,and designs the chain communication topology based on the leader-follower idea.There are two leaders in this structure.One of the leaders has a driving role.It needs to obtain information of all agents and deploy a controller to drive the follower to move.The other leader has the role of formation positioning.The rest of the agents are followers,and the followers only need to obtain local information and relative position information with neighboring agents.Then,PDE is used to model the leader-follower model of the multi-agent system.Based on the PDE model,the controller is designed by using the infinite-dimensional backstepping boundary control method.Through the Lyapunov function method,the exponential stability of the closed-loop system under the L~2 norm is verified.The control laws of the leader and follower agents are obtained after discretization.Finally,the expected formation control and formation conversion control of multi-agents are realized through Matlab numerical simulation.(2)Experimental verification based on ground mobile robots.An experimental platform for a cluster system composed of six unmanned wheeled vehicles was built,and the leader-follower distributed control algorithm was realized.The Raspberry Pi is used as the onboard computer to complete the motion control and bottom-level drive of the car.The PC is used as the host computer to complete the publication of the target position of the car and display the position of the car in real time.Use Link Track UWB technology to realize the positioning of the car and use the Kalman filter algorithm to improve the positioning accuracy.After the PC terminal receives the positioning data of the car,it calculates the target position of the car under the action of the distributed control law and publishes it to the car terminal.The car uses the forward speed,lateral speed and angular velocity of the car as control inputs,and uses the MPC control method to drive the motor at the bottom of the car.Through the four-wheel speed adjustment,the angle and position movement control and position update of the car are realized.The data transfer of the whole experiment is completed in the way of topic publish and subscribe in the robot operating system(ROS).Finally,through the unmanned car experiments under single cluster and dual clusters,the expected formation convergence and formation conversion process of the unmanned car cluster were realized,and the effectiveness of the distributed formation control algorithm was verified.