Cooperative Pursuit by Multiple Pursuers of a Single Evader

Abstract

This paper considers pursuit-evasion differential games in the Euclidean plane where an evader is engaged by multiple pursuers and point capture is required. The players have simple motion (i.e., holonomic) in the manner of Isaacs, and the pursuers are faster than the evader. The attention of this paper is confined to the case where the pursuers have the same speed, and so the game’s parameter is that the evader/pursuers speed ratio is . State feedback capture strategies and an evader strategy that yields a lower bound on his/her time-to-capture are devised using a geometric method. It is shown that, in group/swarm pursuit, when the players are in general position, capture is effected by one, two, or three critical pursuers, and this is irrespective of the size of the pursuit pack. Group pursuit devolves into pure pursuit by one of the pursuers or into a pincer movement pursuit by two or three pursuers who isochronously capture the evader. The critical pursuers are identified. However, these geometric method-based pursuit and evasion strategies are optimal only in a part of the state space where a strategic saddle point is obtained and the value of the differential game is established. As such, these strategies are suboptimal. To fully explore the differential game’s high-dimensional state space and get a better understanding of group pursuit, numerical experimentation is undertaken. The state space region where the geometric solution of the group pursuit differential game is the optimal solution becomes larger the smaller the speed ratio parameter is.