Distributed Hybrid Control for Multiple-Pursuer Multiple-Evader Games

Multiple-pursuer multiple-evader games raise fundamental and novel problems in control theory and robotics. In this paper, we propose a distributed solution to this problem that simultaneously addresses the discrete assignment of pursuers to evaders as well as the continuous control strategies for capturing individual evaders. The resulting hybrid controller for each pursuer consists of both local coordination protocols guaranteeing that distinct evaders are captured by distinct pursuers, and time-varying potential fields ensuring capturability of single evaders. The overall hybrid system guarantees not only the mutual exclusion property of the assignment for all initial conditions, but also capturing all evaders after exploring at most a polynomial number of discrete assignments. Therefore, our distributed approach dramatically reduces the combinatorial nature of purely discrete assignment problems. Our scalable approach is illustrated with nontrivial computer simulations.