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Self-stabilizing Localization of the Middle Point of a Line Segment by an Oblivious Robot with Limited Visibility

机译:线段中点的自稳定位  一个能见度有限的无意识机器人

摘要

This paper poses a question about a simple localization problem, which isarisen from self-stabilizing location problems by oblivious mobile autonomousrobots with limited visibility. The question is if an oblivious mobile robot ona line-segment can localize the middle point of the line-segment in finitesteps observing the direction (i.e., Left or Right) and distance to the nearestend point. This problem is also akin to (a continuous version of) binarysearch, and could be closely related to computable real functions. Contrary toappearances, it is far from trivial if this simple problem is solvable or not,and unsettled yet. This paper is concerned with three variants of the originalproblem, minimally relaxing, and presents self-stabilizing algorithms for them.We also show an easy impossibility theorem for bilaterally symmetricalgorithms.
机译:本文提出了一个有关简单定位问题的问题,该问题是由可见性有限的遗忘的移动自主机器人自稳定位置问题引起的。问题是,线段上的遗忘移动机器人是否可以以有限步长定位线段的中点,从而观察方向(即左或右)和到最近端点的距离。这个问题也类似于(二进制的)连续搜索,并且可能与可计算的实函数紧密相关。与外观相反,这个简单的问题是否可以解决并且尚未解决还不是一件容易的事。本文关注原始问题的三种变体,即最小松弛,并针对它们提出了自稳定算法。我们还展示了双边对称算法的简单不可能定理。

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