The relation between redundancy and convergence rate in distributed multi-agent formation control

In an earlier paper we had proposed a one step ahead optimization based distributed control law for autonomous agents, modeled as double integrators, that achieves a formation specified by relative position between agents. The law requires minimal information exchange between the agents and minimal knowledge on the part of each agent of the overall formation objective, and is fault tolerant and scalable, being easily reconfigurable in the face of the loss or arrival of an agent, and the loss of a communication link. In this earlier paper we had provided a framework to incorporate redundancy that allows a network to survive faults caused by the loss of agents and communications links. In this paper we consider a different aspect of redundancy: Specifically the impact it has on control performance of the law as quantified by the speed with which a desired formation is achieved.