Universal reconfiguration of facet-connected modular robots by pivots: The O(1) musketeers

Hugo A. Akitaya, Esther M. Arkin, Mirela Damian, Erik D. Demaine, Vida Dujmović, Robin Flatland, Matias Korman, Belen Palop, Irene Parada, André van Renssen, Vera Sacristán

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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.

Original languageEnglish
Title of host publication27th Annual European Symposium on Algorithms, ESA 2019
EditorsMichael A. Bender, Ola Svensson, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771245
DOIs
Publication statusPublished - 2019 Sep
Event27th Annual European Symposium on Algorithms, ESA 2019 - Munich/Garching, Germany
Duration: 2019 Sep 92019 Sep 11

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume144
ISSN (Print)1868-8969

Conference

Conference27th Annual European Symposium on Algorithms, ESA 2019
CountryGermany
CityMunich/Garching
Period19/9/919/9/11

Keywords

  • Geometric algorithm
  • Modular robots
  • Pivoting squares
  • Reconfiguration

ASJC Scopus subject areas

  • Software

Fingerprint Dive into the research topics of 'Universal reconfiguration of facet-connected modular robots by pivots: The O(1) musketeers'. Together they form a unique fingerprint.

Cite this