A novel multi-agent formation control law with collision avoidance

In this paper a stable formation control law that simultaneously ensures collision avoidance has been proposed. It is assumed that the communication graph is undirected and connected. The proposed formation control law is a combination of the consensus term and the collision avoidance term U+0028 CAT U+0029. The first order consensus term is derived for the proposed model, while ensuring the Lyapunov stability. The consensus term creates and maintains the desired formation shape, while the CAT avoids the collision. During the collision avoidance, the potential function based CAT makes the agents repel from each other. This unrestricted repelling magnitude cannot ensure the graph connectivity at the time of collision avoidance. Hence we have proposed a formation control law, which ensures this connectivity even during the collision avoidance. This is achieved by the proposed novel adaptive potential function. The potential function adapts itself, with the online tuning of the critical variable associated with it. The tuning has been done based on the lower bound of the critical variable, which is derived from the proposed connectivity property. The efficacy of the proposed scheme has been validated using simulations done based on formations of six and thirty-two agents respectively.