@inproceedings{50b281a52ad242e7b9d8f4c9a1ccb1df,
title = "Universal reconfiguration of facet-connected modular robots by pivots: The O(1) musketeers",
abstract = "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(n2) 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.",
keywords = "Geometric algorithm, Modular robots, Pivoting squares, Reconfiguration",
author = "Akitaya, {Hugo A.} and Arkin, {Esther M.} and Mirela Damian and Demaine, {Erik D.} and Vida Dujmovi{\'c} and Robin Flatland and Matias Korman and Belen Palop and Irene Parada and {van Renssen}, Andr{\'e} and Vera Sacrist{\'a}n",
note = "Funding Information: Funding Hugo A. Akitaya: Supported by NSF CCF-1422311 and CCF-1423615. Esther M. Arkin: Partially funded by NSF (CCF-1526406). Erik D. Demaine: Supported in part by NSF ODISSEI grant EFRI-1240383 and NSF Expedition grant CCF-1138967. Belen Palop: Partially supported by MTM2015-63791-R (MINECO/FEDER). Irene Parada: Supported by the Austrian Science Fund (FWF): W1230. Funding Information: Andr{\'e} van Renssen: Supported by JST ERATO Grant Number JPMJER1201, Japan. Vera Sacrist{\'a}n: Partially supported by MTM2015-63791-R (MINECO/FEDER) and Gen. Cat. DGR 2017SGR1640. Funding Information: Hugo A. Akitaya: Supported by NSF CCF-1422311 and CCF-1423615. Esther M. Arkin: Partially funded by NSF (CCF-1526406). Erik D. Demaine: Supported in part by NSF ODISSEI grant EFRI-1240383 and NSF Expedition grant CCF-1138967. Belen Palop: Partially supported by MTM2015-63791-R (MINECO/FEDER). Irene Parada: Supported by the Austrian Science Fund (FWF): W1230. Publisher Copyright: {\textcopyright} Hugo A. Akitaya, Esther M. Arkin, Mirela Damian, Erik D. Demaine, Vida Dujmovi{\'c}, Robin Flatland, Matias Korman, Belen Palop, Irene Parada, Andr{\'e} van Renssen, and Vera Sacrist{\'a}n.; 27th Annual European Symposium on Algorithms, ESA 2019 ; Conference date: 09-09-2019 Through 11-09-2019",
year = "2019",
month = sep,
doi = "10.4230/LIPIcs.ESA.2019.3",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Bender, {Michael A.} and Ola Svensson and Grzegorz Herman",
booktitle = "27th Annual European Symposium on Algorithms, ESA 2019",
}