两机器人协作追踪移动目标，仅在相遇时交换信息。
Capturing a Moving Target by Two Robots in the F2F Model
- 机器人仅在面对面时通信，通过有限知识设计追踪算法
- 算法最多需三次转向，竞争比衡量效率表现
- 适用于资源受限、目标不可控的动态追踪场景
我们研究在无限实数线上由两个自主移动机器人捕捉一个移动目标的问题。两个机器人初始位于原点，最大速度为1；一个盲目的移动目标初始位于距离原点d处，以恒定速度v向远离或朝向原点方向移动。机器人可沿直线任意方向移动，但目标无法改变方向且不具通信能力。只有当两个机器人同时与目标共位时才算捕获成功。机器人仅能通过面对面（F2F）方式通信。本文针对不同先验知识（如d、运动方向、速度v）设计了高效算法，并以竞争比（算法实际捕获时间与全知模型最优时间之比）衡量效率。分析中考虑转向代价，证明可在最多三次转向内完成捕获。
原文摘要 · Abstract (English)
We study a search problem on capturing a moving target on an infinite real line. Two autonomous mobile robots (which can move with a maximum speed of 1) are initially placed at the origin, while an oblivious moving target is initially placed at a distance $d$ away from the origin. The robots can move along the line in any direction, but the target is oblivious, cannot change direction, and moves either away from or toward the origin at a constant speed $v$. Our aim is to design efficient algorithms for the two robots to capture the target. The target is captured only when both robots are co-located with it. The robots communicate with each other only face-to-face (F2F), meaning they can exchange information only when co-located, while the target remains oblivious and has no communication capabilities. We design algorithms under various knowledge scenarios, which take into account the prior knowledge the robots have about the starting distance $d$, the direction of movement (either toward or away from the origin), and the speed $v$ of the target. As a measure of the efficiency of the algorithms, we use the competitive ratio, which is the ratio of the capture time of an algorithm with limited knowledge to the capture time in the full-knowledge model. In our analysis, we are mindful of the cost of changing direction of movement, and show how to accomplish the capture of the target with at most three direction changes (turns).
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。