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Optimal In-Place Compaction of Sliding Cubes

Authors Irina Kostitsyna , Tim Ophelders , Irene Parada , Tom Peters , Willem Sonke , Bettina Speckmann

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

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Abstract

The sliding cubes model is a well-established theoretical framework that supports the analysis of reconfiguration algorithms for modular robots consisting of face-connected cubes. As is common in the literature, we focus on reconfiguration via an intermediate canonical shape. Specifically, we present an in-place algorithm that reconfigures any n-cube configuration into a compact canonical shape using a number of moves proportional to the sum of coordinates of the input cubes. This result is asymptotically optimal and strictly improves on all prior work. Furthermore, our algorithm directly extends to dimensions higher than three.

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Irina Kostitsyna, Tim Ophelders, Irene Parada, Tom Peters, Willem Sonke, and Bettina Speckmann. Optimal In-Place Compaction of Sliding Cubes. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SWAT.2024.31

Author Details

Irina Kostitsyna
  • TU Eindhoven, The Netherlands
Tim Ophelders
  • Utrecht University, The Netherlands
  • TU Eindhoven, The Netherlands
Irene Parada
  • Universitat Politècnica de Catalunya, Barcelona, Spain
Tom Peters
  • TU Eindhoven, The Netherlands
Willem Sonke
  • TU Eindhoven, The Netherlands
Bettina Speckmann
  • TU Eindhoven, The Netherlands

Funding

  • Ophelders, Tim: partially supported by the Dutch Research Council (NWO) under project no. VI.Veni.212.260.

Supplementary Materials

References

  1. Zachary Abel and Scott Duke Kominers. Universal reconfiguration of (hyper-)cubic robots. arXiv e-Prints, 2011. URL: https://arxiv.org/abs/0802.3414v3.
  2. Hugo A. Akitaya, Esther M. Arkin, Mirela Damian, Erik D. Demaine, Vida Dujmovic, Robin Y. Flatland, Matias Korman, Belén Palop, Irene Parada, André van Renssen, and Vera Sacristán. Universal reconfiguration of facet-connected modular robots by pivots: The O(1) musketeers. Algorithmica, 83(5):1316-1351, 2021. URL: https://doi.org/10.1007/S00453-020-00784-6.
  3. Hugo A. Akitaya, Erik D. Demaine, Andrei Gonczi, Dylan H. Hendrickson, Adam Hesterberg, Matias Korman, Oliver Korten, Jayson Lynch, Irene Parada, and Vera Sacristán. Characterizing universal reconfigurability of modular pivoting robots. In Proc. 37th International Symposium on Computational Geometry (SoCG 2021), volume 189 of LIPIcs, pages 10:1-10:20, 2021. URL: https://doi.org/10.4230/LIPIcs.SoCG.2021.10.
  4. Hugo A. Akitaya, Erik D. Demaine, Matias Korman, Irina Kostitsyna, Irene Parada, Willem Sonke, Bettina Speckmann, Ryuhei Uehara, and Jules Wulms. Compacting squares: Input-sensitive in-place reconfiguration of sliding squares. In Proc. 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT), volume 227 of LIPIcs, pages 4:1-4:19, 2022. URL: https://doi.org/10.4230/LIPICS.SWAT.2022.4.
  5. Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D. Demaine, Robin Flatland, Stefan Langerman, Joseph O'Rourke, Val Pinciu, Suneeta Ramaswami, Vera Sacristán, and Stefanie Wuhrer. Efficient constant-velocity reconfiguration of crystalline robots. Robotica, 29(1):59-71, 2011. URL: https://doi.org/10.1017/S026357471000072X.
  6. 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, 42(6):652-663, 2009. URL: https://doi.org/10.1016/j.comgeo.2008.11.003.
  7. Matthew Connor and Othon Michail. Centralised connectivity-preserving transformations by rotation: 3 musketeers for all orthogonal convex shapes. In Proc. 18th International Symposium on Algorithmics of Wireless Networks (ALGOSENSORS 2022), volume 13707 of LNCS, pages 60-76. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-22050-0_5.
  8. Adrian Dumitrescu and János Pach. Pushing squares around. Graphs and Combinatorics, 22:37-50, 2006. URL: https://doi.org/10.1007/s00373-005-0640-1.
  9. Sándor P. Fekete, Phillip Keldenich, Ramin Kosfeld, Christian Rieck, and Christian Scheffer. Connected coordinated motion planning with bounded stretch. In Proc. 32nd International Symposium on Algorithms and Computation (ISAAC 2021), volume 212 of LIPIcs, pages 9:1-9:16, 2021. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2021.9.
  10. Daniel Feshbach and Cynthia Sung. Reconfiguring non-convex holes in pivoting modular cube robots. IEEE Robotics and Automation Letters, 6(4):6701-6708, 2021. URL: https://doi.org/10.1109/LRA.2021.3095030.
  11. Robert Fitch, Zack Butler, and Daniela Rus. Reconfiguration planning for heterogeneous self-reconfiguring robots. In Proc. IEEE/RSJ International Conference on Intelligent Robots and System (IROS 2003), volume 3, pages 2460-2467, 2003. URL: https://doi.org/10.1109/IROS.2003.1249239.
  12. Ferran Hurtado, Enrique Molina, Suneeta Ramaswami, and Vera Sacristán. Distributed reconfiguration of 2D lattice-based modular robotic systems. Autonomous Robots, 38:383-413, 2015. URL: https://doi.org/10.1007/s10514-015-9421-8.
  13. Othon Michail, George Skretas, and Paul G. Spirakis. On the transformation capability of feasible mechanisms for programmable matter. In Proc. 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), volume 80 of LIPIcs, pages 136:1-136:15, 2017. URL: https://doi.org/10.4230/LIPICS.ICALP.2017.136.
  14. Tillmann Miltzow, Irene Parada, Willem Sonke, Bettina Speckmann, and Jules Wulms. Hiding sliding cubes: Why reconfiguring modular robots is not easy. In Proc. 36th International Symposium on Computational Geometry, (SoCG 2020, Media Exposition), volume 164 of LIPIcs, pages 78:1-78:5, 2020. URL: https://doi.org/10.4230/LIPICS.SOCG.2020.78.
  15. Joel Moreno and Vera Sacristán. Reconfiguring sliding squares in-place by flooding. In Proc. 36th European Workshop on Computational Geometry (EuroCG), pages 32:1-32:7, 2020. Google Scholar
  16. Irene Parada, Vera Sacristán, and Rodrigo I. Silveira. A new meta-module design for efficient reconfiguration of modular robots. Autonomous Robots, 45(4):457-472, 2021. URL: https://doi.org/10.1007/s10514-021-09977-6.
  17. Frederick Stock, Hugo Akitaya, Matias Korman, Scott Kominers, and Zachary Abel. A universal in-place reconfiguration algorithm for sliding cube-shaped robots in quadratic time. In Proc. 40th International Symposium on Computational Geometry (SoCG), 2024. To appear. Google Scholar
  18. Cynthia R. Sung, James M. Bern, John Romanishin, and Daniela Rus. Reconfiguration planning for pivoting cube modular robots. In Proc. IEEE International Conference on Robotics and Automation (ICRA 2015), pages 1933-1940, 2015. URL: https://doi.org/10.1109/ICRA.2015.7139451.
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