Control Of Formations: Stepping Beyond Passivity

We consider the problem of forcing a group of agents to achieve a rigid formation specified by a subset of interagent distances, through decentralized control action: Specifically by sensing only their relative position with respect to their neighbors and their own velocity. Prior papers have all assumed that the control input to velocity relationship is a passive system. In this paper we show that passivity is not necessary. We provide a class of linear time invariant (LTI) input to velocity models for which a stable control law can be formulated, provide such a law and prove its local stability.