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A Continuous, Local Strategy for Constructing a Short Chain of Mobile Robots

机译：构建移动机器人短链的连续局部策略

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摘要

We are given an arbitrarily shaped chain of n robots with fixed end points in the plane. We assume that each robot can only see its two neighbors in the chain, which have to be within its viewing range. The goal is to move the robots to the straight line between the end points. Each robot has to base the decision where to move on the relative positions of its neighbors only. Such local strategies considered until now are based on discrete rounds, where a round consists of a movement of each robot. In this paper, we initiate the study of continuous local strategies: The robots may perpetually observe the relative positions of their neighbors, and may perpetually adjust their speed and direction in response to these observations. We assume a speed limit for the robots, that we normalize to one, which corresponds to the viewing range. Our contribution is a continuous, local strategy that needs time O(min{n, (OPT + d)log(n)}). Here d is the distance between the two stationary end points, and OPT is the time needed by an optimal global strategy. Our strategy has the property that the robot which reaches its destination last always moves with maximum speed. Thus, the same bound as above also holds for the distance travelled.
机译：我们得到了n个机器人的任意形状的链，在平面中具有固定的端点。我们假设每个机器人只能看到链中的两个邻居，这两个邻居必须在其可视范围内。目标是将机器人移至端点之间的直线。每个机器人都必须根据其邻居的相对位置来决定要移动的位置。到现在为止考虑的这种局部策略是基于离散的回合，其中回合由每个机器人的运动组成。在本文中，我们开始研究连续的局部策略：机器人可以永久观察其邻居的相对位置，并可以根据这些观察永久地调整其速度和方向。我们假定机器人的速度极限，我们将其归一化为一个视场范围。我们的贡献是需要时间O（min {n，（OPT + d）log（n）}）的连续局部策略。 d是两个固定端点之间的距离，OPT是最佳全局策略所需的时间。我们的策略具有以下特性：最后到达目的地的机器人始终以最大速度运动。因此，对于行进的距离也保持与上述相同的界限。

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