Formation Control and Collision Avoidance for Multi-Agent Systems and a Connection between Formation Infeasibility and Flocking Behavior

A feedback control strategy that achieves convergence of a multi-agent system to a desired formation configuration avoiding at the same time collisions is proposed. The collision avoidance objective is handled by a decentralized navigation function that vanishes when the desired formation tends to be realized. When inter-agent objectives that specify the desired formation cannot occur simultaneously in the state space the desired formation is infeasible. It is shown that under certain assumptions, formation infeasibility forces the agents velocity vectors to a common value at steady state. This provides a connection between formation infeasibility and flocking behavior for the multi-agent system.