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：本文研究存在一般多边形障碍物阻挡玩家运动的多玩家追逃微分博弈。追逃方合作保护一个凸区域，而逃避方试图进入该区域。我们提出了一种多玩家现场及近目标（MOCG）追逃策略，该策略能够判定并实现可保证击败逃避者数量的递增下界。该追逃策略通过滚动时域方式，将多追逃者对单逃避者的子博弈结果与分层最优任务分配相融合。为判定子博弈的定性结果（即博弈胜方），我们构建了三个追逃制胜区域及相应策略，确保追逃方在逃避者策略未知的情况下仍能获胜。首先，利用扩展阿波罗尼奥斯圆提出有限时间内实现捕获的现场追逃制胜策略。其次，引入凸目标覆盖多边形（GCPs），为视野区域包含整个保护区域的追逃者提出近目标追逃制胜策略，且目标可见性在此后将得以保持。再次，采用欧几里得最短路径（ESPs）为非目标可见的追逃者构建追逃制胜区域及策略，其中追逃者首先沿ESPs被引导至具有目标可见性的位置。在每个时域内，分层最优任务分配通过四个顺序匹配（捕获匹配、增强匹配、非支配匹配和最近邻匹配）最大化被击败逃避者数量。数值算例展示了所提方法的有效性。