Control of inter-agent distances in cyclic polygon formations

This paper considers n-agent cyclic polygon formations of mobile autonomous agents in the plane. The aim of each agent is to maintain a desired distance from its neighbor. Since the formation graph is directed, only one agent is responsible for maintaining each distance. The control law for each agent is designed in distributive manner. Hence, it utilizes only local information. We use gradient-like control and Lyapunov-based stability analysis. Since there exist invariant subsets which include undesirable equilibrium state, the inter-agent distances are not globally stable under the given control law. However, once the initial locations of the agents are not inside the subsets, the agents do not approach them.