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oai:drops-oai.dagstuhl.de:11124 2024-03-06T10:47:30Z ddc:004 open_access

Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers Akitaya, Hugo A. Arkin, Esther M. Damian, Mirela Demaine, Erik D. Dujmović, Vida Flatland, Robin Korman, Matias Palop, Belen Parada, Irene van Renssen, André Sacristán, Vera Reconfiguration geometric algorithm pivoting squares modular robots 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hugo A. Akitaya and Esther M. Arkin and Mirela Damian and Erik D. Demaine and Vida Dujmović and Robin Flatland and Matias Korman and Belen Palop and Irene Parada and André van Renssen and Vera Sacristán 2019 Is Part Of LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2019.3 urn:nbn:de:0030-drops-111247 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.3 eng https://creativecommons.org/licenses/by/3.0/legalcode