Reconfiguration Algorithms for Cubic Modular Robots with Realistic Movement Constraints

Authors MIT-NASA Space Robots Team, Josh Brunner, Kenneth C. Cheung, Erik D. Demaine , Jenny Diomidova, Christine Gregg, Della H. Hendrickson, Irina Kostitsyna



PDF
Thumbnail PDF

File

LIPIcs.SWAT.2024.34.pdf
  • Filesize: 14.95 MB
  • 18 pages

Document Identifiers

Author Details

MIT-NASA Space Robots Team
  • Massachusetts Institute of Technology, Cambridge, MA, USA
  • NASA Ames Research Center, Moffett Field, CA, USA
Josh Brunner
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Kenneth C. Cheung
  • NASA Ames Research Center, Moffett Field, CA, USA
Erik D. Demaine
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Jenny Diomidova
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Christine Gregg
  • NASA Ames Research Center, Moffett Field, CA, USA
Della H. Hendrickson
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Irina Kostitsyna
  • KBR at NASA Ames Research Center, Moffett Field, CA, USA

Cite As Get BibTex

MIT-NASA Space Robots Team, Josh Brunner, Kenneth C. Cheung, Erik D. Demaine, Jenny Diomidova, Christine Gregg, Della H. Hendrickson, and Irina Kostitsyna. Reconfiguration Algorithms for Cubic Modular Robots with Realistic Movement Constraints. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SWAT.2024.34

Abstract

We introduce and analyze a model for self-reconfigurable robots made up of unit-cube modules. Compared to past models, our model aims to newly capture two important practical aspects of real-world robots. First, modules often do not occupy an exact unit cube, but rather have features like bumps extending outside the allotted space so that modules can interlock. Thus, for example, our model forbids modules from squeezing in between two other modules that are one unit distance apart. Second, our model captures the practical scenario of many passive modules assembled by a single robot, instead of requiring all modules to be able to move on their own.
We prove two universality results. First, with a supply of auxiliary modules, we show that any connected polycube structure can be constructed by a carefully aligned plane sweep. Second, without additional modules, we show how to construct any structure for which a natural notion of external feature size is at least a constant; this property largely consolidates forbidden-pattern properties used in previous works on reconfigurable modular robots.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Modular robotics
  • programmable matter
  • digital materials
  • motion planning

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Zachary Abel, Hugo Akitaya, Matias Korman, Scott Kominers, and Frederick Stock. A universal in-place reconfiguration algorithm for sliding cube-shaped robots in quadratic time. To appear at the 40th International Symposium on Computational Geometry (SoCG), 2024. Google Scholar
  2. Zachary Abel and Scott D. Kominers. Pushing hypercubes around, 2008. URL: https://arxiv.org/abs/0802.3414v2.
  3. Hugo A. Akitaya, Esther M. Arkin, Mirela Damian, Erik D. Demaine, Vida Dujmović, Robin 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.
  4. Hugo A. Akitaya, Erik D. Demaine, Andrei Gonczi, Della 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), pages 10:1-10:20, 2021. URL: https://doi.org/10.4230/LIPIcs.SoCG.2021.10.
  5. 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 Leibniz International Proceedings in Informatics (LIPIcs), pages 4:1-4:19, 2022. URL: https://doi.org/10.4230/LIPIcs.SWAT.2022.4.
  6. Greg Aloupis, Nadia Benbernou, Mirela Damian, Erik D. Demaine, Robin Flatland, John Iacono, and Stefanie Wuhrer. Efficient reconfiguration of lattice-based modular robots. Computational Geometry: Theory and Applications, 46(8):917-928, October 2013. URL: https://doi.org/10.1016/j.comgeo.2013.03.004.
  7. Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D. Demaine, Dania El-Khechen, Robin Flatland, Stefan Langerman, Joseph O'Rourke, Val Pinciu, Suneeta Ramaswami, Vera Sacristán, and Stefanie Wuhrer. Realistic reconfiguration of crystalline (and telecube) robots. In Proceedings of the 8th International Workshop on the Algorithmic Foundations of Robotics (WAFR 2008), volume 57 of Springer Tracts in Advanced Robotics, pages 433-447, Guanajuato, México, December 7-9 2008. Google Scholar
  8. 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, 42(6-7):652-663, August 2009. Google Scholar
  9. Greg Aloupis, Sébastien Collette, Erik D. Demaine, Stefan Langerman, Vera Sacristán, and Stefanie Wuhrer. Reconfiguration of cube-style modular robots using O(log n) parallel moves. In Proceedings of the 19th Annual International Symposium on Algorithms and Computation (ISAAC 2008), pages 342-353, Gold Coast, Australia, December 15-17 2008. Google Scholar
  10. 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.
  11. Byoung Kwon An. EM-Cube: Cube-shaped, self-reconfigurable robots sliding on structure surfaces. In Proc. IEEE International Conference on Robotics and Automation (ICRA), pages 3149-3155, 2008. URL: https://doi.org/10.1109/ROBOT.2008.4543690.
  12. Nora Ayanian, Paul J. White, Ádám Hálász, Mark Yim, and Vijay Kumar. Stochastic control for self-assembly of XBots. In Proc. ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC-CIE), pages 1169-1176, 2008. URL: https://doi.org/10.1115/DETC2008-49535.
  13. Nadia M. Benbernou. Geometric algorithms for reconfigurable structures. PhD thesis, Massachusetts Institute of Technology, 2011. Google Scholar
  14. Kenneth C. Cheung and Neil Gershenfeld. Reversibly assembled cellular composite materials. Science, 341(6151):1219-1221, 2013. Google Scholar
  15. Chih-Jung Chiang and Gregory S. Chirikjian. Modular robot motion planning using similarity metrics. Autonomous Robots, 10:91-106, 2001. URL: https://doi.org/10.1023/A:1026552720914.
  16. 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.
  17. 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.
  18. 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), pages 2460-2467, 2003. URL: https://doi.org/10.1109/IROS.2003.1249239.
  19. Christine E. Gregg, Damiana Catanoso, Olivia Irene B. Formoso, Irina Kostitsyna, Megan E. Ochalek, Taiwo J. Olatunde, In Won Park, Frank M. Sebastianelli, Elizabeth M. Taylor, Greenfield T. Trinh, and Kenneth C. Cheung. Ultralight, strong, and self-reprogrammable mechanical metamaterials. Science Robotics, 9(86):eadi2746, 2024. URL: https://doi.org/10.1126/scirobotics.adi2746.
  20. Christine E. Gregg, Joseph H. Kim, and Kenneth C. Cheung. Ultra-light and scalable composite lattice materials. Advanced Engineering Materials, 20(9):1800213, 2018. Google Scholar
  21. Kazuo Hosokawa, Takehito Tsujimori, Teruo Fujii, Hayato Kaetsu, Hajime Asama, Yoji Kuroda, and Isao Endo. Self-organizing collective robots with morphogenesis in a vertical plane. In Proc. IEEE International Conference on Robotics and Automation (ICRA), pages 2858-2863, 1998. URL: https://doi.org/10.1109/ROBOT.1998.680616.
  22. Benjamin Jenett, Amira Abdel-Rahman, Kenneth Cheung, and Neil Gershenfeld. Material–Robot System for Assembly of Discrete Cellular Structures. IEEE Robotics and Automation Letters, 4(4):4019-4026, October 2019. URL: https://doi.org/10.1109/LRA.2019.2930486.
  23. Irina Kostitsyna, Tim Ophelders, Irene Parada, Tom Peters, Willem Sonke, and Bettina Speckmann. Optimal in-place compaction of sliding cubes. Submission to SWAT, 2024. Google Scholar
  24. Lloyd E. Lo-Wong. Reconfiguration of pivoting modular robots. MSc thesis, Technical University Eindhoven, 2021. Google Scholar
  25. Othon Michail, George Skretas, and Paul G. Spirakis. On the transformation capability of feasible mechanisms for programmable matter. Journal of Computer and System Sciences, 102:18-39, 2019. URL: https://doi.org/10.1016/j.jcss.2018.12.001.
  26. 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), volume LIPIcs 164, pages 78:1-78:5, 2020. URL: https://doi.org/10.4230/LIPIcs.SoCG.2020.78.
  27. Joel Moreno. In-place reconfiguration of lattice-based modular robots. Bachelor’s thesis, Universitat Politècnica de Catalunya, 2019. Google Scholar
  28. 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
  29. 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.
  30. In-Won Park, Damiana Catanoso, Olivia Formoso, Christine Gregg, Megan Ochalek, Taiwo Olatunde, Frank Sebastianelli, Pascal Spino, Elizabeth Taylor, Greenfield Trinh, and Kenneth Cheung. Soll-e: A module transport and placement robot for autonomous assembly of discrete lattice structures. In 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2023. Google Scholar
  31. John Romanishin, Kyle Gilpin, and Daniela Rus. M-blocks: Momentum-driven, magnetic modular robots. In Proceedings of the 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2013), pages 4288-4295, Tokyo, Japan, November 2013. IEEE. URL: https://doi.org/10.1109/IROS.2013.6696971.
  32. Daniela Rus and Marsette Vona. A physical implementation of the self-reconfiguring crystalline robot. In Proc. IEEE International Conference on Robotics and Automation (ICRA), pages 1726-1733, 2000. URL: https://doi.org/10.1109/ROBOT.2000.844845.
  33. John W. Suh, Samuel B. Homans, and Mark Yim. Telecubes: mechanical design of a module for self-reconfigurable robotics. In Proc. 2002 IEEE International Conference on Robotics and Automation (ICRA), pages 4095-4101, 2002. URL: https://doi.org/10.1109/ROBOT.2002.1014385.
  34. Cynthia Sung, James Bern, John Romanishin, and Daniela Rus. Reconfiguration planning for pivoting cube modular robots. In Proc. 2015 IEEE International Conference on Robotics and Automation (ICRA), pages 1933-1940, 2015. URL: https://doi.org/10.1109/ICRA.2015.7139451.
  35. Yuzuru Terada and Satoshi Murata. Automatic Assembly System for Modular Structure. In Proceedings of the 22nd International Symposium on Automation and Robotics in Construction, Ferrara, Italy, September 2005. URL: https://doi.org/10.22260/ISARC2005/0028.
  36. Mark Yim, Wei-Min Shen, Behnam Salemi, Daniela Rus, Mark Moll, Hod Lipson, Eric Klavins, and Gregory S. Chirikjian. Modular self-reconfigurable robot systems. IEEE Robotics & Automation Magazine, 14(1):43-52, 2007. URL: https://doi.org/10.1109/MRA.2007.339623.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail