A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in a Quadratic Number of Moves

Abel, Zachary; A. Akitaya, Hugo; Kominers, Scott Duke; Korman, Matias; Stock, Frederick

doi:10.4230/LIPIcs.SoCG.2024.1

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Document Identifiers

DOI: 10.4230/LIPIcs.SoCG.2024.1
URN: urn:nbn:de:0030-drops-199468

Author Details

Zachary Abel

Massachusetts Institute of Technology, Cambridge, MA, USA

Hugo A. Akitaya

University of Massachusetts Lowell, MA, USA

Scott Duke Kominers

Harvard University, Cambridge, MA, USA
a16z crypto, New York, NY, USA

Matias Korman

Siemens Electronic Design Automation, Wilsonville, OR, USA

Frederick Stock

University of Massachusetts Lowell, MA, USA

Acknowledgements

The authors would like to thank Maarten Löffler and for his contributions during early discussions as well as the authors of [Irina Kostitsyna et al., 2024] and the anonymous reviewers for their valuable comments. Finally, we would like to thank Kevin Li and Colton Wolk for implementing preliminary versions of the algorithms proposed in this paper.

Cite AsGet BibTex

Zachary Abel, Hugo A. Akitaya, Scott Duke Kominers, Matias Korman, and Frederick Stock. A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in a Quadratic Number of Moves. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SoCG.2024.1

Abstract

In the modular robot reconfiguration problem, we are given n cube-shaped modules (or robots) as well as two configurations, i.e., placements of the n modules so that their union is face-connected. The goal is to find a sequence of moves that reconfigures the modules from one configuration to the other using "sliding moves," in which a module slides over the face or edge of a neighboring module, maintaining connectivity of the configuration at all times. For many years it has been known that certain module configurations in this model require at least Ω(n²) moves to reconfigure between them. In this paper, we introduce the first universal reconfiguration algorithm - i.e., we show that any n-module configuration can reconfigure itself into any specified n-module configuration using just sliding moves. Our algorithm achieves reconfiguration in O(n²) moves, making it asymptotically tight. We also present a variation that reconfigures in-place, it ensures that throughout the reconfiguration process, all modules, except for one, will be contained in the union of the bounding boxes of the start and end configuration.

Subject Classification

ACM Subject Classification

Theory of computation → Computational geometry

Keywords

modular reconfigurable robots
sliding cube model
reconfiguration

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References

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