Efficient constant-velocity reconfiguration of crystalline robots

Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D. Demaine, Robin Flatland, Stefan Langerman, Joseph O'Rourke, Val Pinciu, Suneeta Ramaswami, Vera Sacristán, Stefanie Wuhrer

Research output: Contribution to journalArticle

7 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)59-71
Number of pages13
Issue number1 SPEC. ISSUE
StatePublished - Jan 2011

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Mathematics(all)
  • Computer Science Applications


  • Control of robotic systems
  • Mobile robots
  • Modular robots
  • Motion planning
  • Path planning

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    Aloupis, G., Collette, S., Damian, M., Demaine, E. D., Flatland, R., Langerman, S., O'Rourke, J., Pinciu, V., Ramaswami, S., Sacristán, V., & Wuhrer, S. (2011). Efficient constant-velocity reconfiguration of crystalline robots. Robotica, 29(1 SPEC. ISSUE), 59-71. https://doi.org/10.1017/S026357471000072X