Control of many agents by moving their targets: Maintaining separation

Consider a large group of agents chasing a small group of moving targets. Assume each agent moves at constant speed toward the closest target. This paper studies the problem of controlling the agents indirectly by specifying the motion of the targets. In particular, it considers the problem of maintaining a minimum separation distance between each pair of agents, something that is impossible to do with only one target. This paper shows that only two targets are necessary to maintain separation between four agents. It also shows results in simulation to support the conjecture that only two targets are necessary to maintain separation between any number of agents, given suitable initial conditions.