Reach-Avoid Games with a Noncooperative Target Along a Line Segment

This paper studies a multiplayer reach-avoid differential game where a noncooperative target moves along a line segment. The pursuers cooperate to escort the target moving from the start point to the goal point of the line segment against the evaders, whose objective is to attack the target before the target reaches the goal point and avoid being captured by the pursuers. Due to the complexity of direct analysis, the entire game is decomposed into multiple subgames, each involving one pursuer and one evader. First, the properties of the players' trajectories and control inputs are analyzed under optimal play for various payoff functions. Then, an evasion region is introduced for the pursuer-evader pair, from which a safe distance is defined to evaluate the safety of the target. Three pursuit winning conditions and strategies are presented to guarantee the safety arrival of the target, regardless of the evasion strategy. Finally, a maximum matching is obtained by combining all subgame outcomes, which guarantees a lower bound on the number of defeated evaders. Numerical simulations are presented to illustrate the theoretical results.