Reconfiguration and Locomotion with Joint Movements in the Amoebot Model

Authors Andreas Padalkin , Manish Kumar , Christian Scheideler



PDF
Thumbnail PDF

File

LIPIcs.SAND.2024.18.pdf
  • Filesize: 1.2 MB
  • 20 pages

Document Identifiers

Author Details

Andreas Padalkin
  • Paderborn University, Germany
Manish Kumar
  • Bar-Ilan University, Israel
Christian Scheideler
  • Paderborn University, Germany

Cite As Get BibTex

Andreas Padalkin, Manish Kumar, and Christian Scheideler. Reconfiguration and Locomotion with Joint Movements in the Amoebot Model. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SAND.2024.18

Abstract

We are considering the geometric amoebot model where a set of n amoebots is placed on the triangular grid. An amoebot is able to send information to its neighbors, and to move via expansions and contractions. Since amoebots and information can only travel node by node, most problems have a natural lower bound of Ω(D) where D denotes the diameter of the structure. Inspired by the nervous and muscular system, Feldmann et al. have proposed the reconfigurable circuit extension and the joint movement extension of the amoebot model with the goal of breaking this lower bound.
In the joint movement extension, the way amoebots move is altered. Amoebots become able to push and pull other amoebots. Feldmann et al. demonstrated the power of joint movements by transforming a line of amoebots into a rhombus within O(log n) rounds. However, they left the details of the extension open. The goal of this paper is therefore to formalize the joint movement extension. In order to provide a proof of concept for the extension, we consider two fundamental problems of modular robot systems: reconfiguration and locomotion.
We approach these problems by defining meta-modules of rhombical and hexagonal shapes, respectively. The meta-modules are capable of movement primitives like sliding, rotating, and tunneling. This allows us to simulate reconfiguration algorithms of various modular robot systems. Finally, we construct three amoebot structures capable of locomotion by rolling, crawling, and walking, respectively.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Cooperation and coordination
  • Theory of computation → Computational geometry
Keywords
  • programmable matter
  • modular robot system
  • reconfiguration
  • locomotion

Metrics

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

References

  1. Hossein Ahmadzadeh, Ellips Masehian, and Masoud Asadpour. Modular robotic systems: Characteristics and applications. J. Intell. Robotic Syst., 81(3-4):317-357, 2016. Google Scholar
  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. Google Scholar
  3. Abdullah Almethen, Othon Michail, and Igor Potapov. Distributed transformations of hamiltonian shapes based on line moves. Theor. Comput. Sci., 942:142-168, 2023. Google Scholar
  4. Greg Aloupis, Nadia M. Benbernou, Mirela Damian, Erik D. Demaine, Robin Y. Flatland, John Iacono, and Stefanie Wuhrer. Efficient reconfiguration of lattice-based modular robots. Comput. Geom., 46(8):917-928, 2013. Google Scholar
  5. Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D. Demaine, Robin Y. Flatland, Stefan Langerman, Joseph O'Rourke, Suneeta Ramaswami, Vera Sacristán Adinolfi, and Stefanie Wuhrer. Linear reconfiguration of cube-style modular robots. Comput. Geom., 42(6-7):652-663, 2009. Google Scholar
  6. Greg Aloupis, Sébastien Collette, Erik D. Demaine, Stefan Langerman, Vera Sacristán Adinolfi, and Stefanie Wuhrer. Reconfiguration of cube-style modular robots using O(log n) parallel moves. In ISAAC, volume 5369 of Lecture Notes in Computer Science, pages 342-353. Springer, 2008. Google Scholar
  7. Byoung Kwon An. Em-cube: cube-shaped, self-reconfigurable robots sliding on structure surfaces. In 2008 IEEE International Conference on Robotics and Automation, ICRA 2008, May 19-23, 2008, Pasadena, California, USA, pages 3149-3155. IEEE, 2008. URL: https://doi.org/10.1109/ROBOT.2008.4543690.
  8. Rhodri H Armour and Julian FV Vincent. Rolling in nature and robotics: A review. Journal of Bionic Engineering, 3(4):195-208, 2006. Google Scholar
  9. Alberto Brunete, Avinash Ranganath, Sergio Segovia, Javier Perez De Frutos, Miguel Hernando, and Ernesto Gambao. Current trends in reconfigurable modular robots design. International Journal of Advanced Robotic Systems, 14(3):1729881417710457, 2017. Google Scholar
  10. Zack J. Butler, Keith Kotay, Daniela Rus, and Kohji Tomita. Generic decentralized control for lattice-based self-reconfigurable robots. Int. J. Robotics Res., 23(9):919-937, 2004. Google Scholar
  11. Jason Campbell and Padmanabhan Pillai. Collective actuation. Int. J. Robotics Res., 27(3-4):299-314, 2008. Google Scholar
  12. Gregory S. Chirikjian. Kinematics of a metamorphic robotic system. In ICRA, pages 449-455. IEEE Computer Society, 1994. Google Scholar
  13. David Johan Christensen and Jason Campbell. Locomotion of miniature catom chains: Scale effects on gait and velocity. In ICRA, pages 2254-2260. IEEE, 2007. Google Scholar
  14. Joshua J. Daymude, Kristian Hinnenthal, Andréa W. Richa, and Christian Scheideler. Computing by programmable particles. In Distributed Computing by Mobile Entities, volume 11340 of Lecture Notes in Computer Science, pages 615-681. Springer, 2019. Google Scholar
  15. Joshua J. Daymude, Andréa W. Richa, and Christian Scheideler. The canonical amoebot model: Algorithms and concurrency control. In DISC, volume 209 of LIPIcs, pages 20:1-20:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. Google Scholar
  16. Zahra Derakhshandeh, Shlomi Dolev, Robert Gmyr, Andréa W. Richa, Christian Scheideler, and Thim Strothmann. Brief announcement: amoebot - a new model for programmable matter. In SPAA, pages 220-222. ACM, 2014. Google Scholar
  17. Zahra Derakhshandeh, Robert Gmyr, Andréa W. Richa, Christian Scheideler, and Thim Strothmann. An algorithmic framework for shape formation problems in self-organizing particle systems. In NANOCOM, pages 21:1-21:2. ACM, 2015. Google Scholar
  18. Zahra Derakhshandeh, Robert Gmyr, Andréa W. Richa, Christian Scheideler, and Thim Strothmann. Universal shape formation for programmable matter. In SPAA, pages 289-299. ACM, 2016. Google Scholar
  19. Daniel J. Dewey, Michael P. Ashley-Rollman, Michael DeRosa, Seth Copen Goldstein, Todd C. Mowry, Siddhartha S. Srinivasa, Padmanabhan Pillai, and Jason Campbell. Generalizing metamodules to simplify planning in modular robotic systems. In IROS, pages 1338-1345. IEEE, 2008. Google Scholar
  20. Shlomi Dolev, Sergey Frenkel, Michael Rosenblit, Ram Prasadh Narayanan, and K Muni Venkateswarlu. In-vivo energy harvesting nano robots. In 2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE), pages 1-5, 2016. Google Scholar
  21. Fabien Dufoulon, Shay Kutten, and William K. Moses Jr. Efficient deterministic leader election for programmable matter. In PODC, pages 103-113. ACM, 2021. Google Scholar
  22. Adrian Dumitrescu, Ichiro Suzuki, and Masafumi Yamashita. Motion planning for metamorphic systems: feasibility, decidability, and distributed reconfiguration. IEEE Trans. Robotics, 20(3):409-418, 2004. Google Scholar
  23. Michael Feldmann, Andreas Padalkin, Christian Scheideler, and Shlomi Dolev. Coordinating amoebots via reconfigurable circuits. J. Comput. Biol., 29(4):317-343, 2022. Google Scholar
  24. Robert Fitch and Zack J. Butler. Million module march: Scalable locomotion for large self-reconfiguring robots. Int. J. Robotics Res., 27(3-4):331-343, 2008. Google Scholar
  25. Anthony Garcia, Gregory Krummel, and Shashank Priya. Fundamental understanding of millipede morphology and locomotion dynamics. Bioinspiration & Biomimetics, 16(2):026003, December 2020. Google Scholar
  26. Shigeo Hirose. Three basic types of locomotion in mobile robots. In Fifth International Conference on Advanced Robotics' Robots in Unstructured Environments, pages 12-17. IEEE, 1991. Google Scholar
  27. Ferran Hurtado, Enrique Molina, Suneeta Ramaswami, and Vera Sacristán Adinolfi. Distributed reconfiguration of 2d lattice-based modular robotic systems. Auton. Robots, 38(4):383-413, 2015. Google Scholar
  28. Norio Inou, Hisato Kobayashi, and Michihiko Koseki. Development of pneumatic cellular robots forming a mechanical structure. In ICARCV, pages 63-68. IEEE, 2002. Google Scholar
  29. Gangyuan Jing, Tarik Tosun, Mark Yim, and Hadas Kress-Gazit. An end-to-end system for accomplishing tasks with modular robots. In Robotics: Science and Systems, 2016. Google Scholar
  30. Gangyuan Jing, Tarik Tosun, Mark Yim, and Hadas Kress-Gazit. Accomplishing high-level tasks with modular robots. Auton. Robots, 42(7):1337-1354, 2018. Google Scholar
  31. Zoltán Juhász and Ambrus Zelei. Analysis of worm-like locomotion. Periodica Polytechnica Mechanical Engineering, 57(2):59-64, 2013. Google Scholar
  32. Manivannan Sivaperuman Kalairaj, Catherine Jiayi Cai, Pavitra S, and Hongliang Ren. Untethered origami worm robot with diverse multi-leg attachments and responsive motions under magnetic actuation. Robotics, 10(4):118, 2021. Google Scholar
  33. Matthew Kehoe and Davide Piovesan. Taxonomy of two dimensional bio-inspired locomotion systems. In EMBC, pages 3703-3706. IEEE, 2019. Google Scholar
  34. Brian T. Kirby, Jason Campbell, Burak Aksak, Padmanabhan Pillai, James F. Hoburg, Todd C. Mowry, and Seth Copen Goldstein. Catoms: Moving robots without moving parts. In AAAI, pages 1730-1731. AAAI Press / The MIT Press, 2005. Google Scholar
  35. Irina Kostitsyna, Christian Scheideler, and Daniel Warner. Fault-tolerant shape formation in the amoebot model. In DNA, volume 238 of LIPIcs, pages 9:1-9:22. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  36. Keith Kotay, Daniela Rus, and Marsette Vona. Using modular self-reconfiguring robots for locomotion. In ISER, volume 271 of Lecture Notes in Control and Information Sciences, pages 259-269. Springer, 2000. Google Scholar
  37. Shigeru Kuroda, Nariya Uchida, and Toshiyuki Nakagaki. Gait switching with phase reversal of locomotory waves in the centipede scolopocryptops rubiginosus. Bioinspiration & Biomimetics, 17(2):026005, March 2022. Google Scholar
  38. Haruhisa Kurokawa, Eiichi Yoshida, Kohji Tomita, Akiya Kamimura, Satoshi Murata, and Shigeru Kokaji. Self-reconfigurable M-TRAN structures and walker generation. Robotics Auton. Syst., 54(2):142-149, 2006. Google Scholar
  39. Michael LaBarbera. Why the wheels won't go. The American Naturalist, 121(3):395-408, 1983. Google Scholar
  40. Giuseppe Antonio Di Luna, Paola Flocchini, Nicola Santoro, Giovanni Viglietta, and Yukiko Yamauchi. Shape formation by programmable particles. Distributed Comput., 33(1):69-101, 2020. Google Scholar
  41. Daniel Mellinger, Vijay Kumar, and Mark Yim. Control of locomotion with shape-changing wheels. In ICRA, pages 1750-1755. IEEE, 2009. Google Scholar
  42. Satoshi Murata, Haruhisa Kurokawa, and Shigeru Kokaji. Self-assembling machine. In ICRA, pages 441-448. IEEE Computer Society, 1994. Google Scholar
  43. An Nguyen, Leonidas J Guibas, and Mark Yim. Controlled module density helps reconfiguration planning. In Workshop on the Algorithmic Foundations of Robotics, pages TH15-TH27, 2001. Google Scholar
  44. Hayato Omori, Takeshi Hayakawa, and Taro Nakamura. Locomotion and turning patterns of a peristaltic crawling earthworm robot composed of flexible units. In IROS, pages 1630-1635. IEEE, 2008. Google Scholar
  45. Andreas Padalkin, Manish Kumar, and Christian Scheideler. Reconfiguration and locomotion with joint movements in the amoebot model. CoRR, abs/2305.06146, 2023. Google Scholar
  46. Andreas Padalkin, Manish Kumar, and Christian Scheideler. Reconfiguration and locomotion with joint movements in the amoebot model. 40th European Workshop on Computational Geometry, 2024. Google Scholar
  47. Andreas Padalkin, Christian Scheideler, and Daniel Warner. The structural power of reconfigurable circuits in the amoebot model. In DNA, volume 238 of LIPIcs, pages 8:1-8:22. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  48. Irene Parada, Vera Sacristán, and Rodrigo I. Silveira. A new meta-module for efficient reconfiguration of hinged-units modular robots. In ICRA, pages 5197-5202. IEEE, 2016. Google Scholar
  49. John Romanishin, Kyle Gilpin, and Daniela Rus. M-blocks: Momentum-driven, magnetic modular robots. In IROS, pages 4288-4295. IEEE, 2013. Google Scholar
  50. Daniela Rus and Marsette Vona. Self-reconfiguration planning with compressible unit modules. In ICRA, pages 2513-2520. IEEE Robotics and Automation Society, 1999. Google Scholar
  51. Daniela Rus and Marsette Vona. Crystalline robots: Self-reconfiguration with compressible unit modules. Auton. Robots, 10(1):107-124, 2001. Google Scholar
  52. Hossein Sadjadi, Omid Mohareri, Mohammad Amin Al-Jarrah, and Khaled Assaleh. Design and implementation of hexbot: A modular self-reconfigurable robotic system. J. Frankl. Inst., 349(7):2281-2293, 2012. Google Scholar
  53. Jimmy Sastra, Sachin Chitta, and Mark Yim. Dynamic rolling for a modular loop robot. Int. J. Robotics Res., 28(6):758-773, 2009. Google Scholar
  54. Qi Shao, Xuguang Dong, Zhonghan Lin, Chao Tang, Hao Sun, Xin-Jun Liu, and Huichan Zhao. Untethered robotic millipede driven by low-pressure microfluidic actuators for multi-terrain exploration. IEEE Robotics Autom. Lett., 7(4):12142-12149, 2022. Google Scholar
  55. John W. Suh, Samuel B. Homans, and Mark Yim. Telecubes: Mechanical design of a module for self-reconfigurable robotics. In ICRA, pages 4095-4101. IEEE, 2002. Google Scholar
  56. Yosuke Suzuki, Norio Inou, Michihiko Koseki, and Hitoshi Kimura. Reconfigurable modular robots adaptively transforming a mechanical structure (numerical expression of transformation criteria of "chobie ii" and motion experiments). In DARS, pages 393-403. Springer, 2008. Google Scholar
  57. Tommaso Toffoli and Norman Margolus. Programmable matter: Concepts and realization. Int. J. High Speed Comput., 5(2):155-170, 1993. Google Scholar
  58. Sergei Vassilvitskii, Jeremy Kubica, Eleanor Gilbert Rieffel, John W. Suh, and Mark Yim. On the general reconfiguration problem for expanding cube style modular robots. In ICRA, pages 801-808. IEEE, 2002. Google Scholar
  59. Sergei Vassilvitskii, Mark Yim, and John W. Suh. A complete, local and parallel reconfiguration algorithm for cube style modular robots. In ICRA, pages 117-122. IEEE, 2002. Google Scholar
  60. Michael Philetus Weller, Brian T. Kirby, H. Benjamin Brown, Mark D. Gross, and Seth Copen Goldstein. Design of prismatic cube modules for convex corner traversal in 3d. In IROS, pages 1490-1495. IEEE, 2009. Google Scholar
  61. Paul J. White and Mark Yim. Scalable modular self-reconfigurable robots using external actuation. In IROS, pages 2773-2778. IEEE, 2007. Google Scholar
  62. Damien Woods, Ho-Lin Chen, Scott Goodfriend, Nadine Dabby, Erik Winfree, and Peng Yin. Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In ITCS, pages 353-354. ACM, 2013. Google Scholar
  63. Mark Yim. New locomotion gaits. In ICRA, pages 2508-2514. IEEE Computer Society, 1994. Google Scholar
  64. Mark Yim, David Duff, and Kimon Roufas. Polybot: A modular reconfigurable robot. In ICRA, pages 514-520. IEEE, 2000. Google Scholar
  65. Mark Yim, Kimon Roufas, David Duff, Ying Zhang, Craig Eldershaw, and Samuel B. Homans. Modular reconfigurable robots in space applications. Auton. Robots, 14(2-3):225-237, 2003. Google Scholar
  66. Mark Yim, Paul J. White, Michael Park, and Jimmy Sastra. Modular self-reconfigurable robots. In Encyclopedia of Complexity and Systems Science, pages 5618-5631. Springer, 2009. Google Scholar
  67. Mark Yim, Ying Zhang, and David Duff. Modular robots. IEEE Spectrum, 39(2):30-34, 2002. Google Scholar
  68. Eiichi Yoshida, Satoshi Murata, Akiya Kamimura, Kohji Tomita, Haruhisa Kurokawa, and Shigeru Kokaji. Evolutionary synthesis of dynamic motion and reconfiguration process for a modular robot M-TRAN. In CIRA, pages 1004-1010. IEEE, 2003. Google Scholar
  69. Ying Zhang, Mark Yim, Craig Eldershaw, Dave Duff, and Kimon Roufas. Scalable and reconfigurable configurations and locomotion gaits for chain-type modular reconfigurable robots. In CIRA, pages 893-899. IEEE, 2003. Google Scholar
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