This paper presents a multiplayer Homicidal Chauffeur reach-avoid differential game, which involves Dubins-car pursuers and simple-motion evaders. The goal of the pursuers is to cooperatively protect a planar convex region from the evaders, who strive to reach the region. We propose a cooperative strategy for the pursuers based on subgames for multiple pursuers against one evader and optimal task allocation. We introduce pursuit enclosure functions (PEFs) and propose a new enclosure region pursuit (ERP) winning approach that supports forward analysis for the strategy synthesis in the subgames. We show that if a pursuit coalition is able to defend the region against an evader under the ERP winning, then no more than two pursuers in the coalition are necessarily needed. We also propose a steer-to-ERP approach to certify the ERP winning and synthesize the ERP winning strategy. To implement the strategy, we introduce a positional PEF and provide the necessary parameters, states, and strategies that ensure the ERP winning for both one pursuer and two pursuers against one evader. Additionally, we formulate a binary integer program using the subgame outcomes to maximize the captured evaders in the ERP winning for the pursuit task allocation. Finally, we propose a multiplayer receding-horizon strategy where the ERP winnings are checked in each horizon, the task is allocated, and the strategies of the pursuers are determined. Numerical examples are provided to illustrate the results.

翻译：本文提出了一种多人“杀人司机”追击-规避微分博弈，其中涉及杜宾斯车式追击者和简单运动逃跑者。追击者的目标是协同保护一个平面凸区域免受试图进入该区域的逃跑者的侵害。我们基于针对多个追击者对抗一个逃跑者的子博弈与最优任务分配，提出了一种追击者协同策略。我们引入了追逐包围函数（PEF），并提出了一种新的包围区域追逐（ERP）获胜方法，该方法支持子博弈中策略合成的正向分析。我们证明，如果某个追击联盟能够在ERP获胜条件下抵御一个逃跑者对区域的侵犯，则该联盟中最多只需两名追击者即可实现此目标。我们还提出了一种“导向ERP”方法来验证ERP获胜并综合ERP获胜策略。为实施该策略，我们引入了一种位置型PEF，并提供了必要的参数、状态和策略，以确保单名追击者和两名追击者对抗一个逃跑者时的ERP获胜。此外，我们利用子博弈结果构建了一个二值整数规划，以在ERP获胜条件下最大化捕获逃跑者的数量，用于追击任务分配。最后，我们提出了一种多人滚动时域策略：在每个时域内检查ERP获胜状态、分配任务并确定追击者策略。数值算例验证了结果。