Controlling Four Agent Formations

Abstract

This paper considers formation shape control of a team of four point agents, for the most part in the plane. Control laws based on specified interagent distances are used. For a complete graph, specification of all interagent distances determines the formation shape uniquely. Krick, Broucke and Francis showed that for a now almost standard control law, there may exist equilibrium formation shapes with incorrect interagent distances. This paper studies such equilibria, shows that in some cases they are necessarily unstable.