Winning Region Determination and Optimal Cooperative Guidance Design in a Pursuer–Evader–Defender Game

In this paper, we study the pursuer–evader–defender game under the isotropic rocket model. The game involves three agents: the evader, the pursuer, and the defender. The purpose of the pursuer is to capture the evader, and the purpose of the defender is to intercept the former before the pursuer can capture the evader. The concept of the Apollonius circle in the simple motion model is extended to the concept of a ‘circle’ in the isotropic rocket model, and the geometric relationship between the ‘circle’ of the pursuer and the evader and the ‘circle’ of the defender and the pursuer is used to determine in which winning region the current state belongs to. By determining the winning region in which the state is located, a reasonable differential game can be built to obtain the specific strategies of the agent involved in the game. A numerical solution method incorporating the ‘circle’ concept is used for strategy calculations to meet real-time requirements. The performance of the proposed guidance law is demonstrated by numerical simulation.