Controlling Rectangular Formations

We consider formation shape control of four point agents 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 standard control law, there may exist equilibrium formations with incorrect interagent distances. This paper studies such equilibria and derives two main results. That each such incorrect equilibrium is attached to at most one desired formation. That all such equilibria are unstable if the desired formation is a rectangle