具有多边形障碍物的到达-规避博弈的追捕获胜策略
Pursuit Winning Strategies for Reach-Avoid Games with Polygonal Obstacles
AI总结：
针对含多边形障碍物的多人到达-规避微分博弈，提出MOCG追捕策略，通过三类子博弈获胜区域与滚动时域分层任务分配，给出可实现的保证击败逃避者数量递增下界。
摘要：
本文研究了在存在阻挡玩家运动的一般多边形障碍物情况下的多人到达-规避微分博弈。追捕者合作保护一个凸区域，使其免受试图到达该区域的逃避者的攻击。我们提出了一种多人现场且接近目标（MOCG）的追捕策略，该策略能够给出并实现一个不断增长的、关于保证击败的逃避者数量的下界。该追捕策略将多个追捕者对抗一个逃避者的子博弈结果与以滚动时域方式进行的分层最优任务分配相融合。为了确定谁是博弈获胜者的定性子博弈结果，我们构建了三个追捕获胜区域和策略，在这些区域和策略下，无论未知的逃避者策略如何，追捕者都能保证战胜逃避者。首先，我们利用扩展的阿波罗尼乌斯圆，提出了在有限时间内实现捕获的现场追捕获胜。其次，我们引入了凸目标覆盖多边形（GCP），并为其可见性区域包含整个受保护区域的追捕者提出了接近目标的追捕获胜，此后目标可见属性将得到保持。第三，我们采用欧几里得最短路径（ESP），为非目标可见的追捕者构建了追捕获胜区域和策略，其中追捕者首先沿ESP被引导至具有目标可见性的位置。在每个时域中，分层最优任务分配最大化被击败的逃避者数量，并由四个顺序匹配组成：捕获、增强、非支配和最近匹配。数值算例被给出以说明这些结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
