Distributed Multi-robot Circumnavigation Formation Control

Due to its advantages such as higher robustness,lower requirements on communication bandwidth,computational and storage resources,ability to control a group on a massive scale,distributed multi-robot coordinated control has been used in areas such as military,aerospace,education,scientific competition more and more frequently.Distributed circumnavigation formation control proposed in this thesis belongs to the scope of distributed multi-robot coordinated control.It requires robots to form a circular formation and rotate around a target autonomously through local information interaction among them.Most of the existing literature focuses on the scenario where robots are distributed evenly in the formation.However,in a heterogeneous multi-robot system,due to the differences among robots such as different locomotion capabilities,it will be more valuable in practice if robots are distributed in a formation with arbitrary expected spacing.This thesis revolves around the problem of circumnavigation formation control with arbitrary spacing,and designs control algorithms under different conditions in terms of formation spacing,circumnavigation radius,communication time-delay,etc.The detailed research content and innovations are stated as follows.Firstly,we analyze and design the control algorithm for the fundamental circumnavigation formation control problem.In this problem,fixed values of circumnavigation radius,circumnavigation height,circumnavigation rotation speed and desired formation spacing are given.Therefore,based on the graph theory,consensus algorithms and classic control theory,the corresponding control algorithm for this problem is designed and its stability is proved.As for the control algorithm for formation spacing,which involves distributed multi-robot control,we use the Lyapunov stability theory to analyze its convergence,and find out the relation between its convergence speed and the eigenvalues of the corresponding Laplacian matrix.Secondly,based on the fundamental circumnavigation formation control problem,we analyze and design control algorithms for the problem of dynamic circumnavigation formation reconfiguration.There are some limitations when the desired spacing is given and fixed.For example,in this case,a central robot is required to distribute the formation spacing to each robot,and it also has to be aware of the number of robots in advance etc.Therefore,we introduce the concept of utility.Based on utility,we design the corresponding circumnavigation formation control algorithms,and under different formation principles,this algorithm enables the multi-robot system to dynamically adjust the formation spacing according to the variation of the utilities of robots,which adapts to the potential complex circumstance in practice.This algorithm does not require the knowledge of the number of robots which participate in the circumnavigation process beforehand.It does not require a central robot to allocate the formation spacing.Then we adopt the consensus tracking algorithm based on the leader-follower method,and enable the multirobot system to track a time-varying circumnavigation radius.This realizes the dynamic adjustment of the circumnavigation radius during the circumnavigation process.Lastly,we analyze and derive the maximum allowed time-delay which still stabilizes the circumnavigation formation with time-delay.It is of great significance to consider the stability of the circumnavigation formation with time-delay since time-delay is inevitable in practice.First the notion of stability margin in classic control theory is applied to acquire the maximum allowed time-delay.Then the Lambert W function is utilized to analyze the distribution of poles of the system,which leads to the same maximum allowed time-delay.Among the two methods,the former one is based on the mature theory while the latter one is capable of providing more information about the system's poles.Therefore,deeper insight into the circumnavigation formation control problem with time-delay can be obtained by using these two approaches jointly.The above theoretical results have been verified by experiments.We use both Simulink and Gazebo simulation software for the simulation experiments.The former one treats robots as mass points,which can test the stability of control algorithms in a simple and fast manner.The latter one adopts the more realistic ODE physics engine and simulation models which share the same physical attributes as their physical counterparts.In addition,it is capable of simulating the information noise existing in the real world.Therefore,it is more accurate to verify the theoretical results in terms of their application in practice.Moreover,soccer robots are employed to carry out experiments,which further justify the effectiveness of the theoretical results.