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Realistic Reconfiguration of Crystalline (and Telecube) Robots

  • Greg Aloupis
  • Sébastien Collette
  • Mirela Damian
  • Erik D. Demaine
  • Dania El-Khechen
  • Robin Flatland
  • Stefan Langerman
  • Joseph O’Rourke
  • Val Pinciu
  • Suneeta Ramaswami
  • Vera Sacristán
  • Stefanie Wuhrer
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 57)

Abstract

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 unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target configuration. Our algorithms involve a total of O(n 2) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n 2) parallel steps [8,10,4] or do not respect the constraints mentioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω(n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Greg Aloupis
    • 1
  • Sébastien Collette
    • 1
  • Mirela Damian
    • 2
  • Erik D. Demaine
    • 3
  • Dania El-Khechen
    • 4
  • Robin Flatland
    • 5
  • Stefan Langerman
    • 1
  • Joseph O’Rourke
    • 6
  • Val Pinciu
    • 7
  • Suneeta Ramaswami
    • 8
  • Vera Sacristán
    • 9
  • Stefanie Wuhrer
    • 10
  1. 1.Université Libre de BruxellesBelgique
  2. 2.Villanova UniversityVillanovaUSA
  3. 3.Massachusetts Institute of TechnologyCambridgeUSA
  4. 4.Concordia UniversityMontrealCanada
  5. 5.Siena CollegeLoudonvilleUSA
  6. 6.Smith CollegeNorthamptonUSA
  7. 7.Southern Connecticut State UniversityUSA
  8. 8.Rutgers UniversityCamdenUSA
  9. 9.Universitat Politècnica de CatalunyaBarcelonaSpain
  10. 10.Carleton UniversityOttawaCanada

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