A differential game approach to intrinsic formation control

This paper addresses the formation control problem of a multi-agent system in a non-cooperative differential game framework. Both finite horizon and infinite horizon games are considered and their Nash equilibria are studied. The desired formation patterns are achieved by Nash equilibrium strategies in an intrinsic way in the sense that they are only attributed to the inter-agent interaction and geometric properties of the network, where the desired formations are not designated directly in the controller. The whole formation manifold of the desired relative pattern is studied by allowing all orientations of the formation and all permutations of the agents. For finite horizon games the terminal formation of Nash equilibrium trajectories is shown to converge to desired pattern as the length of the time interval tends to infinity. Furthermore the asymptotic stability of the desired formation manifold is also guaranteed in infinite horizon games. Relative patterns of regular polyhedra and antipodal formations are achieved by designing the interaction graph while inter-agent collisions are avoided. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed methods.