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Efficient constant-velocity reconfiguration of crystalline robots**

Published online by Cambridge University Press:  14 January 2011

Greg Aloupis ,
Sébastien Collette ,
Mirela Damian ,
Erik D. Demaine ,
Robin Flatland ,
Stefan Langerman ,
Joseph O'Rourke ,
Val Pinciu ,
Suneeta Ramaswami  and
Vera Sacristán
...Show all authors
Greg Aloupis*
Affiliation:
Université Libre de Bruxelles, Belgique. E-mail: aloupis.greg@gmail.com (Supported by the Communauté française de Belgique - ARC)
Sébastien Collette
Affiliation:
Chargé de Recherches du FRS-FNRS, Université Libre de Bruxelles, Belgique. E-mail: sebastien.collette@ulb.ac.be
Mirela Damian
Affiliation:
Villanova University, Villanova, PA, USA. E-mail: mirela.damian@villanova.edu
Erik D. Demaine
Affiliation:
Massachusetts Institute of Technology, Cambridge, MA, USA. E-mail: edemaine@mit.edu (Partially supported by NSF CAREER award CCF-0347776, DOE grant DE-FG02-04ER25647, and AFOSR grant FA9550-07-1-0538)
Robin Flatland
Affiliation:
Siena College, Loudonville, NY, USA. E-mail: flatland@siena.edu
Stefan Langerman
Affiliation:
Maítre de Recherches du FRS-FNRS, Université Libre de Bruxelles, Belgique. E-mail: stefan.langerman@ulb.ac.be
Joseph O'Rourke
Affiliation:
Smith College, Northampton, MA, USA. E-mail: orourke@cs.smith.edu
Val Pinciu
Affiliation:
Southern Connecticut State University, New Haven, CT, USA. E-mail: pinciu@scsu.ctstateu.edu
Suneeta Ramaswami
Affiliation:
Rutgers University, Camden, NJ, USA. E-mail: rsuneeta@camden.rutgers.edu. (Partially supported by NSF grant CCR-0204293)
Vera Sacristán
Affiliation:
Universitat Politècnica de Catalunya, Barcelona, Spain. E-mail: vera.sacristan@upc.edu (Partially supported by projects MCI MTM2009-07242 and Gen. Cat. DGR 2009SGR1040)
Stefanie Wuhrer
Affiliation:
Carleton University, Ottawa, Canada. E-mail: swuhrer@scs.carleton.ca
*
*Corresponding author. E-mail: aloupis.greg@gmail.com
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Summary

In this paper, we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most constant velocity and can displace at most a constant number of other atoms. We assume that one of the atoms has access to the coordinates of atoms in the target configuration.

Our algorithms involve a total of O(n2) atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n2) parallel steps or do not respect the constraints mentioned above. In fact, in the settings considered, our algorithms are optimal. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configuration space, and only requires local communication.

Keywords

Control of robotic systemsMobile robotsModular robotsMotion planningPath planning
Type
Article
Information
Robotica , Volume 29 , Special Issue 1: Robotic Self-X Systems , January 2011 , pp. 59 - 71
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

**

A short version appeared at WAFR 2008,2 with title Realistic reconfiguration of crystalline (and telecube) robots

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