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”, Computational Geometry: Theory and Applications, volume 42, number 6–7, August 2009, pages 652–663.

BibTeX

@Article{Crystalline_CGTA,
  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},
  JOURNAL       = {Computational Geometry: Theory and Applications},
  journalurl    = {https://www.sciencedirect.com/journal/computational-geometry},
  VOLUME        = 42,
  NUMBER        = {6--7},
  MONTH         = {August},
  YEAR          = 2009,
  PAGES         = {652--663},

  length        = {20 pages},
  replaces      = {Crystalline_ISAAC2007},
  papers        = {Crystalline_WAFR2008; Crystalline_ISAAC2008; Crystalline_ISAAC2007; Crystalline_EGC2007},
  doi           = {https://dx.doi.org/10.1016/J.COMGEO.2008.11.003},
  dblp          = {https://dblp.org/rec/journals/comgeo/AloupisCDDFLORAW09},
  comments      = {This paper is also available from <A HREF="https://doi.org/10.1016/J.COMGEO.2008.11.003">ScienceDirect</A>.},
}

Abstract:

In this paper we propose a novel algorithm that, given a source robot S and a target robot T, reconfigures S into T. Both S and T are robots composed of n atoms arranged in 2 × 2 × 2 meta-modules. The reconfiguration involves a total of O(n) atomic operations (expand, contract, attach, detach) and is performed in O(n) parallel steps. This improves on previous reconfiguration algorithms [1, 2, 3], which require O(n²) parallel steps. Our algorithm is in-place; that is, the reconfiguration takes place within the union of the bounding boxes of the source and target robots. We show that the algorithm can also be implemented in a synchronous, distributed fashion.

Comments:

This paper is also available from ScienceDirect.

Length:

The paper is 20 pages.

Availability:

The paper is available in PDF (3178k).

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Crystalline_ISAAC2008 (Reconfiguration of Cube-Style Modular Robots Using O(log n) Parallel Moves)

Crystalline_ISAAC2007 (Linear Reconfiguration of Cube-Style Modular Robots)

Crystalline_EGC2007 (Linear Reconfiguration of Cube-Style Modular Robots)