Control of multi-agent formation with optimally persistent graph

In this paper, a distributed control law for optimally persistent formation of leader-follower multi-agent systems is presented. According to the characteristic of optimally persistent formation, each follower, except the one which follows the leader, can only communicate with its two precedent neighbors. Based on the state information received from neighbors, a scalable gradient-like control law is designed to control the motion of the formation. Through using this control law, any three agents that are not in a line can achieve a stable triangular persistent formation. Extend this implementation to the whole formation, thus each agent will keep desired distance constraints to its two precedent neighbors. Finally, simulation examples are illustrated to show the efficiency of the proposed control law.