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A Game Between Two Identical Dubins Cars: Evading a Conic Sensor in Minimum Time

2024-06-12 20:50:26
Ubaldo Ruiz

Abstract

A fundamental task in mobile robotics is keeping an intelligent agent under surveillance with an autonomous robot as it travels in the environment. This work studies a version of that problem involving one of the most popular vehicle platforms in robotics. In particular, we consider two identical Dubins cars moving on a plane without obstacles. One of them plays as the pursuer, and it is equipped with a limited field-of-view detection region modeled as a semi-infinite cone with its apex at the pursuer's position. The pursuer aims to maintain the other Dubins car, which plays as the evader, as much time as possible inside its detection region. On the contrary, the evader wants to escape as soon as possible. In this work, employing differential game theory, we find the time-optimal motion strategies near the game's end. The analysis of those trajectories reveals the existence of at least two singular surfaces: a Transition Surface and an Evader's Universal Surface. We also found that the barrier's standard construction produces a surface that partially lies outside the playing space and fails to define a closed region, implying that an additional procedure is required to determine all configurations where the evader escapes.

Abstract (translated)

移动机器人学的一个基本任务是在环境中将智能代理与自主机器人一起监视,以便在移动过程中保持智能代理的安全。本研究探讨了一种涉及机器人领域最受欢迎的车辆平台的问题。特别考虑两个相同的Dubins汽车在平面上没有障碍的情况。其中一个扮演追逐者,其有限的视场检测区域建模为一个半无限锥体,其尖端位于追逐者位置。追逐者试图尽可能长时间地将另一个Dubins汽车(扮演 evader)保持在检测区域内。相反,evader 希望尽快逃脱。在本研究中,我们利用微分游戏理论来寻找游戏结束时最优的运动策略。这些轨迹的分析揭示了至少两个奇点表面:一个转换表面和一个 evader 的普遍表面。我们还发现,屏障的标准结构产生了一个表面,该表面部分位于玩家的空间之外,并无法定义一个封闭的区域,这表明还需要一个额外的步骤来确定所有使 evader 逃脱的配置。

URL

https://arxiv.org/abs/2406.08637

PDF

https://arxiv.org/pdf/2406.08637.pdf


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