论文标题
两辆相同汽车的游戏：屏障的分析描述
The Game of Two Identical Cars: an Analytical Description of the Barrier
论文作者
论文摘要
在本文中，检查了两名被称为两种相同汽车的游戏的追捕游戏。假定游戏在二维飞机上进行。两位球员都有持续的速度和有限的转弯半径。第一个球员（追随者）的目标是确保确保第二个玩家（逃避者）尽快在捕获圈内。逃避者的目的是避免捕获或尽可能长时间延迟捕获。两个播放器的运动学用相同的方程式描述。因此，游戏只有一个免费参数，即捕获半径。这项工作旨在针对捕获半径的所有值对屏障表面进行完全分析的描述。以前，A.W。〜Merz分析研究了两辆相同汽车游戏的障碍。在这项工作中，发现捕获半径有一定的临界价值，在此上面，屏障与梅尔斯的示例在质量上有所不同。此外，我们获得了对屏障最佳反馈控制的分析描述。
In this paper, a pursuit-evasion game of two players known as the game of two identical cars is examined. It is assumed that the game proceeds on a two-dimensional plane. Both players have constant speeds and limited turn radii. The goal of the first player (pursuer) is to ensure that the second player (evader) is guaranteed to be within a capture circle as quickly as possible. The goal of the evader is to avoid the capture or delay it as long as possible. The kinematics of both players are described by the same equations. Thus, the game has only one free parameter, the capture radius. This work aims at a fully analytical description of the barrier surface for all values of the capture radius. Previously, A.W.~Merz analytically investigated the barrier of the game of two identical cars. In this work, it is found that there is a certain critical value of the capture radius, above which the barrier occurs qualitatively differently from Merz's example. Also, we obtained an analytical description of the optimal feedback controls on the barrier.
