Paper by Erik D. Demaine

Reference:

Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D. Demaine, Robin Flatland, Stefan Langerman, Joseph O'Rourke, Suneeta Ramaswami, Vera Sacristán, and Stefanie Wuhrer, “Linear Reconfiguration of Cube-Style Modular Robots”, in Abstracts from the 12th Encuentros de Geometría Computacional (EGC 2007), June 25–27, 2007, pages 19–34.

BibTeX

@InProceedings{Crystalline_EGC2007,
  AUTHOR        = {Greg Aloupis and S{\'e}bastien Collette and Mirela Damian
                   and Erik D. Demaine and Robin Flatland and Stefan Langerman
                   and Joseph O'Rourke and Suneeta Ramaswami and
                   Vera Sacrist{\'a}n and Stefanie Wuhrer},
  TITLE         = {Linear Reconfiguration of Cube-Style Modular Robots},
  BOOKTITLE     = {Abstracts from the 12th Encuentros de Geometr{\'\i}a
                   Computacional (EGC 2007)},
  bookurl       = {http://www.infor.uva.es/egc07/},
  MONTH         = {June 25--27},
  YEAR          = 2007,
  PAGES         = {19--34},

  paperkind     = {abstract},
  unrefereed    = 1,
  papers        = {Crystalline_CGTA; Crystalline_ISAAC2007},
}

Abstract:

In this paper we propose a novel algorithm for both contracting and expanding cube-style modular robots which reconfigures any given source robot composed of n atoms into any given target robot with O(n) basic actions, improving on previous O(n²) algorithms. During reconfiguration, the robot forms one connected component at all times, and the reconfiguration takes place within the union of the bounding boxes of the initial and final robot configurations. The algorithm can be implemented using distributed control and allowing massive simultaneous parallel moves of the atoms.

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Related papers:

Crystalline_CGTA (Linear Reconfiguration of Cube-Style Modular Robots)

Crystalline_ISAAC2007 (Linear Reconfiguration of Cube-Style Modular Robots)