Rigid formation control with nonlinear passive actuation

Abstract

This paper presents a distributed control law that locally forces a group of agents to self-organize into a rigid formation specified by a subset of interagent distances. The control law presented here is distributed as its execution requires each agent to only sense its relative positions with its neighbors, i.e. agents with whom they share a specified desired distance, and its own velocity. The paper extends [13], [17], and [18]. In [13] each agent is modeled as a single integrator. On the other hand, [17] assumes double integrator dynamics but requires that agents can also sense the velocities of their neighbors, doubling the communication/sensing overhead. In [18] the agent velocities are generated by the actuation signals through a Linear Time Invariant Positive Real dynamics. Double integrator dynamics are a special case of this. Unlike [17] no agent needs its neighbor's velocities. This paper on its parts relaxes the assumption of linear time invariance and instead assumes that the actuation to velocity dynamics of each agent is nonlinear but passive. We prove that the control law of [18] still guarantees local stability despite the presence of nonlinear actuation dynamics. We argue that, like [13], [17] and [18], no law for this problem can be globally stable.