研究快逃者与慢追踪者在博弈中的最优移动策略，发现四类奇异曲面决定不同行为模式。
A Surveillance Game between a Differential Drive Robot and an Omnidirectional Agent: The Case of a Faster Evader
- 基于微分博弈构建追踪-逃逸模型，分析双方最优路径
- 当逃逸者更快时，存在四类奇异曲面决定策略分化
- 适用于机器人对抗、安防监控等动态追踪场景
在移动机器人领域，如何利用自主平台对目标进行持续监视是一个基础问题。本文使用微分博弈理论研究一个特定场景：一个配备有限探测范围传感器的差速驱动机器人（DDR）试图长时间保持对全向运动目标（OA）的监视。其目标是尽可能延长目标位于探测区域的时间；而目标则相反，希望尽快脱离该区域。本文将此问题建模为零和微分博弈，并求解了双方实现各自目标的时间最优运动策略。特别关注了目标速度高于机器人的场景。尽管在某些情况下，目标沿径向远离机器人可构成最优策略，但本研究揭示：根据双方速度比的不同，会出现四种类型的奇异曲面——发散面（Dispersal）、过渡面（Transition）、全域面（Universal）和聚焦面（Focal），每种曲面对应不同的最优运动策略。这些结果为复杂动态环境下的追踪决策提供了理论依据。
原文摘要 · Abstract (English)
A fundamental task in mobile robotics is to keep an agent under surveillance using an autonomous robotic platform equipped with a sensing device. Using differential game theory, we study a particular setup of the previous problem. A Differential Drive Robot (DDR) equipped with a bounded range sensor wants to keep surveillance of an Omnidirectional Agent (OA). The goal of the DDR is to maintain the OA inside its detection region for as much time as possible, while the OA, having the opposite goal, wants to leave the regions as soon as possible. We formulate the problem as a zero-sum differential game, and we compute the time-optimal motion strategies of the players to achieve their goals. We focus on the case where the OA is faster than the DDR. Given the OA's speed advantage, a winning strategy for the OA is always moving radially outwards to the DDR's position. However, this work shows that even though the previous strategy could be optimal in some cases, more complex motion strategies emerge based on the players' speed ratio. In particular, we exhibit that four classes of singular surfaces may appear in this game: Dispersal, Transition, Universal, and Focal surfaces. Each one of those surfaces implies a particular motion strategy for the players.
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