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Embedded pattern formation by asynchronous robots without chirality
Distributed Computing ( IF 1.3 ) Pub Date : 2018-05-07 , DOI: 10.1007/s00446-018-0333-7
Serafino Cicerone , Gabriele Di Stefano , Alfredo Navarra

We consider the Embedded Pattern Formation (epf) problem introduced in Fujinaga et al. (SIAM J Comput 44(3):740–785, 2015). Given a set F of distinct points in the Euclidean plane (called here fixed-points) and a set R of robots such that $$|R|=|F|$$|R|=|F|, the problem asks for a distributed algorithm that moves robots so as to occupy all points in F. Initially, each robot occupies a distinct position. When active, a robot operates in standard Look-Compute-Move cycles. In one cycle, a robot perceives the current configuration in terms of the robots’ positions and the fixed-points (Look) according to its own coordinate system, decides whether to move toward some direction (Compute), and in the positive case it moves (Move). Cycles are performed asynchronously for each robot. Robots are oblivious, anonymous, silent and execute the same deterministic algorithm. In the mentioned paper, the problem has been investigated by endowing robots with chirality, that is they share a common left-right orientation. Here we consider epf without chirality, and we fully characterize when it can be solved by designing a deterministic distributed algorithm that works for all configurations but those identified as unsolvable. The algorithm has been designed according to a rigorous approach, characterized by the use of logical predicates associated to each move used by the robots. This induces a greater level of detail that provides us rigorous bases to state the correctness of the algorithm.

中文翻译:

无手性的异步机器人嵌入图案形成

我们考虑在 Fujinaga 等人中引入的嵌入模式形成 (epf) 问题。(SIAM J Comput 44(3):740–785, 2015)。给定欧几里得平面中不同点的集合 F(这里称为不动点)和机器人集合 R,使得 $$|R|=|F|$$|R|=|F|,问题要求一个移动机器人以占据 F 中所有点的分布式算法。最初,每个机器人占据不同的位置。当处于活动状态时,机器人以标准的 Look-Compute-Move 循环运行。在一个循环中,机器人根据自己的坐标系根据机器人的位置和不动点(Look)感知当前配置,决定是否向某个方向移动(Compute),在正情况下它移动(移动)。每个机器人的循环都是异步执行的。机器人是无知的,匿名的,沉默并执行相同的确定性算法。在上述论文中,通过赋予机器人手性来研究该问题,即它们具有共同的左右方向。在这里,我们考虑没有手性的 epf,并且我们完全表征了何时可以通过设计确定性分布式算法来解决它,该算法适用于所有配置,但那些被确定为无法解决的配置。该算法是根据严格的方法设计的,其特点是使用与机器人使用的每个动作相关联的逻辑谓词。这引入了更高级别的细节,为我们提供了严格的基础来说明算法的正确性。在这里,我们考虑没有手性的 epf,并且我们完全表征了何时可以通过设计确定性分布式算法来解决它,该算法适用于所有配置,但那些被确定为无法解决的配置。该算法是根据严格的方法设计的,其特点是使用与机器人使用的每个动作相关的逻辑谓词。这引入了更高级别的细节,为我们提供了严格的基础来说明算法的正确性。在这里,我们考虑没有手性的 epf,并且我们完全表征了何时可以通过设计确定性分布式算法来解决它,该算法适用于所有配置,但那些被确定为无法解决的配置。该算法是根据严格的方法设计的,其特点是使用与机器人使用的每个动作相关联的逻辑谓词。这引入了更高级别的细节,为我们提供了严格的基础来说明算法的正确性。
更新日期:2018-05-07
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