Optimal Strategy for Multiple Evaders Against an Agile Pursuer

This paper focuses on the problem of multiple slow moving and less maneuverable evaders against an agile pursuer, addressing the optimal strategy for multiple evaders. This is the so-called wolf-sheep game. Two scenarios are examined: 1) both pursuer and evaders have perfect knowledge about opponents, and 2) the pursuer has limited detection capability. Since the wolf-sheep game involves the Boolean value state, the game is hard to solve using traditional methods. This paper adopts a hierarchical approach. The two player game is solved first. Then the solution of the multiplayer game is based on the two-player game and the pursuer chasing order. The optimal strategy is calculated based on Nash equilibrium. The game with limited detection capability is solved by maximizing the Close Point of Approach (CPA). The optimal solution will be found theoretically and numerically.