Reconfiguration of Cube-Style Modular Robots Using O(logn) Parallel Moves

Authors:
Greg Aloupis;Sébastien Collette;Erik D. Demaine;Stefan Langerman;Vera Sacristán;Stefanie Wuhrer
Affiliations:
Université Libre de Bruxelles,;Université Libre de Bruxelles,;Massachusetts Institute of Technology,;Université Libre de Bruxelles,;Universitat Politècnica de Catalunya,;Carleton University,
Venue:
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Year:
2008

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Abstract

We consider a model of reconfigurable robot, introduced andprototyped by the robotics community. The robot consists ofindependently manipulable unit-square atoms that canextend/contract arms on each side and attach/detach from neighbors.The optimal worst-case number of sequential moves required totransform one connected configuration to another was shown to beθ(n) at ISAAC 2007. However, in principle,atoms can all move simultaneously. We develop a parallel algorithmfor reconfiguration that runs in only O(logn)parallel steps, although the total number of operations increasesslightly to θ(n logn). The resultis the first (theoretically) almost-instantaneous universallyreconfigurable robot built from simple units.