This article considers a multiplayer reach–avoid game between two adversarial teams in a general convex domain which consists of a target region and a play region. The evasion team, initially lying in the play region, aims to send as many team members into the target region as possible, while the pursuit team with its team members initially distributed in both play region and target region, strives to prevent that by capturing the evaders. We aim at investigating a task assignment about the pursuer–evader matching, which can maximize the number of the evaders who can be captured before reaching the target region safely when both teams play optimally. To address this, two winning regions for a group of pursuers to intercept an evader are determined by constructing an analytical barrier which divides these two parts. Then, a task assignment to guarantee the most evaders intercepted is provided by solving a simplified 0-1 integer programming instead of a nondeterministic polynomial problem, easing the computation burden dramatically. It is worth noting that except the task assignment, the whole analysis is analytical. Finally, simulation results are also presented.

中文翻译：

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多人到达的任务分配——通过分析障碍避免凸域中的游戏

本文考虑由目标区域和游戏区域组成的一般凸域中两个对抗团队之间的多人到达-避免游戏。最初位于游戏区域的逃避团队旨在将尽可能多的团队成员发送到目标区域，而其团队成员最初分布在游戏区域和目标区域的追求团队通过捕获来努力防止这种情况发生逃避者。我们的目标是研究一个关于追捕者-逃避者匹配的任务分配，当两个团队都发挥最佳时，它可以在安全到达目标区域之前最大限度地增加可以被捕获的逃避者的数量。为了解决这个问题，通过构建一个将这两个部分分开的分析屏障来确定一组追击者拦截逃避者的两个获胜区域。然后，通过解决简化的 0-1 整数规划而不是非确定性多项式问题，提供了保证拦截最多逃避者的任务分配，从而显着减轻了计算负担。值得注意的是，除了任务分配，整个分析都是分析性的。最后，还给出了仿真结果。