The Cooperative Blocking Differential Game

This paper considers a pursuit-evasion problem with two cooperative pursuers and one evader. The problem is posed as a zero-sum differential game where the evader aims at reaching a goal line which is protected by the pursuers. When reaching this goal is not possible, the evader strives to position itself as close as possible with respect to the goal line at the time of capture. The pursuers try to capture the evader as far as possible from the goal line. Leveraging differential game theory, state feedback strategies are both synthesized and verified in this paper. In addition, the Barrier surface that partitions the state space into two winning sets, one for the pursuer team and one for the evader, is obtained in analytical form. Under optimal play, the winning team is determined by evaluating the associated Barrier function.