A differential game approach to formation control for a team of agents with one leader

A team of agents consisting of one leader and N followers is considered. The problem in which the leader is steered towards a target position while the followers create and maintain a formation about the leader, while avoiding collisions, is posed as a nonlinear differential game. Dynamic strategies which approximate the solution to the differential game are constructed. It is shown that for the case in which collisions are not considered the problem simplifies to a linear-quadratic differential game, for which approximate solutions are identified. These approximate solutions are well-suited for situations in which the agents do not have full information regarding the positions of all members of the team. Simulations illustrate the results for both the linear-quadratic and the nonlinear problems.