研究差速机器人在圆形探测区逃逸的最短时间策略
Minimum Time Strategies for a Differential Drive Robot Escaping from a Circular Detection Region
- 将逃逸问题建模为零和追逃博弈，求解最优运动策略
- 当机器人速度优势足够时，可直接最大速度远离圆心逃脱
- 逃逸策略依赖于双方速度比和初始位置，存在多种最优路径
平面内一个差速驱动机器人（DDR）位于圆形检测区域内，目标是尽快逃出。该问题可建模为多种机器人应用场景，如无人机在固定高度飞行时，其传感器覆盖范围形成的危险区域，或机器人需快速脱离禁入区。本文研究两种情形：检测区域移动速度低于机器人且试图阻止逃逸；以及检测区域位置固定。将问题形式化为零和追逃博弈，利用微分博弈理论求解双方的时间最优运动策略。由于机器人具备速度优势，其始终可通过以最大速度远离检测区域中心实现逃脱。本文表明，此前认为的径向逃离策略在某些情况下确实最优；但实际最优策略还取决于双方速度比及初始配置，可能呈现更复杂的运动模式。
原文摘要 · Abstract (English)
A Differential Drive Robot (DDR) located inside a circular detection region in the plane wants to escape from it in minimum time. Various robotics applications can be modeled like the previous problem, such as a DDR escaping as soon as possible from a forbidden/dangerous region in the plane or running out from the sensor footprint of an unmanned vehicle flying at a constant altitude. In this paper, we find the motion strategies to accomplish its goal under two scenarios. In one, the detection region moves slower than the DDR and seeks to prevent escape; in another, its position is fixed. We formulate the problem as a zero-sum pursuit-evasion game, and using differential games theory, we compute the players' time-optimal motion strategies. Given the DDR's speed advantage, it can always escape by translating away from the center of the detection region at maximum speed. In this work, we show that the previous strategy could be optimal in some cases; however, other motion strategies emerge based on the player's speed ratio and the players' initial configurations.
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