Three Dimensional Circular Formations Of Multi-agent Systems With Time-delay

In recent years,encirclement control is a basic problem of the cooperative control of multi-agent system which is more and more popular in the field of complex systems.The aim of the encirclement control is enable the multiple follower agents to track the leader agent and move around it in a circular formation.The research of this problem can not only reveal the similar group behavior in the nature,but also help to construct artificial system in capturing and protecting target.Therefore,encirclement control has important significance in the theoretical research and practical application.This paper focuses on the encirclement control in three-dimensional space of multi-agent systems with switching topology.The main contents are as follows:1.Encirclement control of second-order multi-agent systems in plane is investigated.Considering the multi-agent system consisting of one static leader and multiple followers,the purpose is that all followers can eventually converge to the circle centered by the static leader and surround in the circle in a uniform way.To this end,firstly,a distributed control protocol is proposed for the follower to estimate the static leader position,and the sufficient condition that all the followers converging to the specified circle is obtained.Secondly,a distributed control protocol is designed for the followers to move around the circle.All the followers can surround in the circle in an uniform way if the sufficient conditions are met.Simulation results verify the effectiveness of the proposed method.2.Circular formation of multi-agent systems with second-order dynamics and switching topology in three-dimensional space is investigated.This part considers a second-order multi-agent system consisting of one static leader and multiple followers.The classical Euler angles are introduced to describe the pose of each agent in three-dimensional space.Meanwhile,a distributed protocol is proposed based on each agent.It is proved that all the agents ultimately converge to a circle centered at the target and rotate around it in the encirclement plane with a jointly spanning tree,in which the relative positions of all the agents in formation can be arbitrarily adjusted.When the Euler angles equal to zero,the results degenerate into encirclement control problems in the two-dimensional plane.The simulation results verify the validity of the results.3.Three-dimensional circular formation of second-order multi-agent systems with time delay and switching topology is studied.This part considers a second-order multi-agent system consisting of one static leader and multiple followers.Under the condition of weakly communication topology,a distributed protocol with communication delay is designed for each agent to estimate the position of the target.Under the proposed protocol,all the agents can reach consensus based on the static target in a limited time.Meanwhile,communication delay can't affect the convergence to prolongs the convergence time.All the agents ultimately converge to a circle centered at the target and rotate around it with time delay.Simulation results verify the effectiveness of the proposed method.