文章基本信息

标题：Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers
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作者：Hugo A. Akitaya ; Esther M. Arkin ; Mirela Damian 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2019
卷号：144
页码：1-14
DOI：10.4230/LIPIcs.ESA.2019.3
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra "helper" modules ("musketeers") suffice to reconfigure the remaining n modules between any two given configurations. Our algorithm uses O(n^2) pivot moves, which is worst-case optimal. Previous reconfiguration algorithms either require less restrictive "sliding" moves, do not preserve facet-connectivity, or for the setting we consider, could only handle a small subset of configurations defined by a local forbidden pattern. Configurations with the forbidden pattern do have disconnected reconfiguration graphs (discrete configuration spaces), and indeed we show that they can have an exponential number of connected components. But forbidding the local pattern throughout the configuration is far from necessary, as we show that just a constant number of added modules (placed to be freely reconfigurable) suffice for universal reconfigurability. We also classify three different models of natural pivot moves that preserve facet-connectivity, and show separations between these models.
关键词：Reconfiguration; geometric algorithm; pivoting squares; modular robots