三维空间中具有四个中速局中人的可达-回避微分对策障碍的构造
Construction of the Barrier for Reach-Avoid Differential Games in Three-Dimensional Space with Four Equal-Speed Players
摘要：
本文研究了三维空间中四个等速局中人的可达回避微分对策。一个平面将游戏空间划分为一个游戏子空间和一个目标子空间。逃避者的目标是进入目标子空间，而三个追捕者合作，以防止通过捕获逃避者。为这个微分对策提供了一个完全的、封闭形式的障碍，通过这个障碍，可以在游戏开始之前完全预测游戏的获胜者。所有可能的三个追求者之间的合作被认为是，因此，每个团队的保证获胜是一个优先事项。此外，还设计了一种算法，用于计算任意数目和任意初始配置的多个追踪者的障碍。更现实地说，由于整个实现的发展是分析，他们需要一点内存没有计算负担，并允许实时更新，超出了传统的Hamilton-Jacobi-Isaacs方法的能力。
英文摘要：
This paper considers a reach-avoid differential game in three-dimensional space with four equal-speed players. A plane divides the game space into a play subspace and a goal subspace. The evader aims at entering the goal subspace while three pursuers cooperate to prevent that by capturing the evader. A complete, closed-form barrier for this differential game is provided, by which the game winner can be perfectly predicted before the game starts. All possible cooperations among three pursuers are considered and thus the guaranteed winning for each team is a prior. Furthermore, an algorithm is designed to compute the barrier for multiple pursuers of any numbers and any initial configurations. More realistically, since the whole achieved developments are analytical, they require a little memory without computational burden and allow for real-time updates, beyond the capacity of traditional Hamilton-Jacobi-Isaacs method.
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。
