This paper studies a multiplayer reach-avoid differential game in the presence of general polygonal obstacles that block the players' motions. The pursuers cooperate to protect a convex region from the evaders who try to reach the region. We propose a multiplayer onsite and close-to-goal (MOCG) pursuit strategy that can tell and achieve an increasing lower bound on the number of guaranteed defeated evaders. This pursuit strategy fuses the subgame outcomes for multiple pursuers against one evader with hierarchical optimal task allocation in the receding-horizon manner. To determine the qualitative subgame outcomes that who is the game winner, we construct three pursuit winning regions and strategies under which the pursuers guarantee to win against the evader, regardless of the unknown evader strategy. First, we utilize the expanded Apollonius circles and propose the onsite pursuit winning that achieves the capture in finite time. Second, we introduce convex goal-covering polygons (GCPs) and propose the close-to-goal pursuit winning for the pursuers whose visibility region contains the whole protected region, and the goal-visible property will be preserved afterwards. Third, we employ Euclidean shortest paths (ESPs) and construct a pursuit winning region and strategy for the non-goal-visible pursuers, where the pursuers are firstly steered to positions with goal visibility along ESPs. In each horizon, the hierarchical optimal task allocation maximizes the number of defeated evaders and consists of four sequential matchings: capture, enhanced, non-dominated and closest matchings. Numerical examples are presented to illustrate the results.

翻译：本文研究了在存在一般多边形障碍物阻碍参与者运动的多智能体追逃微分博弈。追击方协作保护一个凸形区域，阻止试图进入该区域的逃逸方。我们提出了一种多智能体现场与近目标（MOCG）追击策略，该策略能够计算并实现对已确保击败逃逸者数量的递增下界。该追击策略将多个追击者对单个逃逸者的子博弈结果与分层最优任务分配相结合，并以滚动时域方式执行。为了判定定性子博弈结果（即谁是博弈胜者），我们构建了三种追击制胜区域及其对应策略，使追击者能在未知逃逸者策略的情况下保证获胜。首先，利用扩展阿波罗尼斯圆，提出在有限时间内实现捕获的现场追击制胜策略。其次，引入凸覆盖多边形（GCP），针对可视区域包含完整保护区域的追击者提出近目标追击制胜策略，并确保后续保持对目标的可见性。第三，利用欧几里得最短路径（ESP），为非目标可见的追击者构建制胜区域与策略，沿ESP路径引导追击者首先到达目标可见位置。在每个时间窗口内，分层最优任务分配通过四个顺序匹配（捕获匹配、增强匹配、非支配匹配和最近匹配）最大化被击败的逃逸者数量。最后通过数值算例验证了所提方法的有效性。