Hiding Sliding Cubes: Why Reconfiguring Modular Robots Is Not Easy (Media Exposition)

Authors Tillmann Miltzow, Irene Parada , Willem Sonke , Bettina Speckmann , Jules Wulms

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Author Details

Tillmann Miltzow
  • Utrecht University, The Netherlands
Irene Parada
  • TU Eindhoven, The Netherlands
Willem Sonke
  • TU Eindhoven, The Netherlands
Bettina Speckmann
  • TU Eindhoven, The Netherlands
Jules Wulms
  • TU Eindhoven, The Netherlands


We thank Tim Ophelders for his help with the computational verification of the properties of our configuration.

Cite AsGet BibTex

Tillmann Miltzow, Irene Parada, Willem Sonke, Bettina Speckmann, and Jules Wulms. Hiding Sliding Cubes: Why Reconfiguring Modular Robots Is Not Easy (Media Exposition). In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 78:1-78:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Face-connected configurations of cubes are a common model for modular robots in three dimensions. In this abstract and the accompanying video we study reconfigurations of such modular robots using so-called sliding moves. Using sliding moves, it is always possible to reconfigure one face-connected configuration of n cubes into any other, while keeping the robot connected at all stages of the reconfiguration. For certain configurations Ω(n²) sliding moves are necessary. In contrast, the best current upper bound is O(n³). It has been conjectured that there is always a cube on the outside of any face-connected configuration of cubes which can be moved without breaking connectivity. The existence of such a cube would immediately imply a straight-forward O(n²) reconfiguration algorithm. However, we present a configuration of cubes such that no cube on the outside can move without breaking connectivity. In other words, we show that this particular avenue towards an O(n²) reconfiguration algorithm for face-connected cubes is blocked.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Sliding cubes
  • Reconfiguration
  • Modular robots


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