Formation Control For Multi-robot

Because of its distributed characteristics in space domian and time domain,information and resources,control and function and so on,multi-robot system has received more and more attention from researchers.Nowadays,cooperation control of multi-robot,especially cooperation formation control of multi-robot,has been gradually applied in the field of military reconnaissance,large-scale cargo handling and port automatic unloading.and it shows a strong research significance and application prospect.In this paper,we use the heat equation and wave equation in the PDE system to build the dynamical model for the multi-robot system.By combining the leader-follower method in the multi-robot control method,only the border control of the leader robot on the boundary is needed,which can be carried out to complete the control of the whole multi-robot system,so that the multi-robot system can realize the formation tracing.Furthermore,the simulation results by the stability analysis of Lyapunov show that the multi-robot system can keep tracking errors small while keeping formation tracking,which indicates that the tracking error of the error system of two kind of systems is bounded,that is,two kind of PDE models are effective and reliable while keep formation control.Finally,we use three Khepera IV desktop mobile robots to carry out some multi-robot collaborative formation control experiments.The innovation of this paper is that all followers do not need to know their absolute position in the control process and only need to know the relative position of the neighbour robots,which reduces the complexity of the multi-robot formation control process.This method is suitable for large-scale multi-robot systems.Firstly,the multi-robot system is regarded as a whole continuous system.The dynamics equations of the multi-robot system are modeled by the heat equation model and the wave equation model respectively.By the way,the state of the partial differential equation is the position of the robot at that moment.In this paper,the leader-follower method is used to control the multi-robot system,in which the leader robot in the multi-robot system corresponds to the boundary conditions of the two PDE models respectively,and the remaining followers correspond to the PDE master equation.Specifically,the non-homogeneous boundary conditions in the heat equation model and the damping boundary in the wave equation model correspond to the Leader robot,and the remainder is selected as Follower robot.Secondly,according to the heat equation model and the wave equation model established in this paper,this paper uses the finite difference method to discretize them separately,so as to achieve tracking control for each robot.For the heat equation model,two leader robots are directly controlled in this paper.The leader robot knows its position in the desired formation and the reference orbit of the overall system.For the wave equation model,the first leader robot knows the expected formation and the overall system's reference orbit,the second leader knows the desired formation and the speed of the desired orbit of the overall system.All other followers need only know the relative position between themselves and their neighbors,and do not need to know their absolute position.In this way,the formation control of the whole multi-robot system can be accomplished only by controlling the leader robots on the boundary,so that the multi-robot system can keep the desired formation and move according to a certain reference orbit.In this paper,the Lyapunov stability analysis method is used to prove the error system between the actual position and the expected position of the robot is bounded,which under the premise of boundedness of velocity(modeled by thermal equation)and boundedness of acceleration(modeled by wave equation).The simulation results show the proposed method which modeled by partial differential equation can effectively achieve target tracking under the premise of keeping small errors.Finally,three Khepera IV desktop mobile robots developed by K-team of Switzerland were used to control the formation of multi-robots.This paper realize the formation control of robot queue and normal triangle formation experiments,so that the problem of formation control of multi-robot is further researched in the process.