The formation control of multi-agent systems on a circle

This paper investigates the formation control of a class of multi-agent systems moving on a circle, whose topology is a cyclic graph, and presents several new results for the following two cases: Case I, the agents with single-integrator kinematics, and Case II, the agents with double-integrator kinematics. Firstly, for Case I, two control protocols are proposed under which the multiagent systems keep a uniformly-spaced formation. Secondly, we study Case II, and a control protocol is designed for this case, then the stability of the formation is proved. Finally, three simulations are studied by using our presented results. The study of illustrative examples with simulations shows that our results as well as designed control protocols work very well in studying the formation control of this class of multi-agent systems.