Universal reconfiguration of facet-connected modular robots by pivots: The O(1) musketeers
Name
LIPIcs-ESA-2019-3.pdf
Description
Published version
Size
1.31 MB
Format
Adobe PDF
Checksum (MD5)
5733a1625730e624763a8f32958ef411
Author(s)
Demaine, Erik D
Date Issued
September 2019
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Publisher
Schloss Dagstuhl, Leibniz Center for Informatics
Citation
Akitaya, Hugo A. et al. “Universal reconfiguration of facet-connected modular robots by pivots: The O(1) musketeers.” Leibniz International Proceedings in Informatics, LIPIcs, 144, 3 (September 2019): 1-14 © 2019 The Author(s)
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution 3.0 unported license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.ESA.2019.3
