Optimal Strategies of a Two-Lifeline Differential Game

This article investigates a two-lifeline differential game with two pursuers and one evader in a planar environment that is divided into a game area and two target areas by the two lifelines. The evader aims to enter the target area by passing through either of the two lifelines, eluding capture in the process. Conversely, the pursuers endeavor to capture the evader before it reaches one of the target areas. To construct the barrier, we first divide the two-lifeline differential game into two subgames: one pursuer and one evader with two lifelines; the other pursuer and evader with two lifelines. We construct the reachable region of the evader using the Cartesian oval. Then, we employ a geometric method to obtain the barrier of each subgame and analyze the optimal strategies of the pursuers and the evader in each area. Furthermore, this article proposes a resultant force method to develop strategies for both the evader and the pursuers in the two-lifeline game. Finally, simulation examples are provided to validate the proposed theoretical results.