Control of Formations with Nonlinear Non-Passive Actuation

This paper considers the problem of cooperatively inducing a group of agents to achieve a rigid formation specified by a subset of interagent distances, by decentralized control: The agents have access to their relative positions with respect to their neighbors and their own velocity. Barring our work in [17], all previous papers have assumed that the actuation dynamics represented by the system relating the agent velocity to the control input is passive. On its part [17] relaxed this assumption to include systems that are linear time invariant (LTI) but not passive. In this paper we extend to nonlinear dynamics, and require that it and its inverse be L-2-stable and have an asymptotically stable zero dynamics. We formulate a control algorithm and prove its local asymptotic stability.