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Distributed Size-constrained Clustering Algorithm for Modular Robot-based Programmable Matter

Published:27 March 2023Publication History
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Abstract

Modular robots are defined as autonomous kinematic machines with variable morphology. They are composed of several thousands or even millions of modules that are able to coordinate to behave intelligently. Clustering the modules in modular robots has many benefits, including scalability, energy-efficiency, reducing communication delay, and improving the self-reconfiguration process that focuses on finding a sequence of reconfiguration actions to convert robots from an initial shape to a goal one. The main idea of clustering is to divide the modules in an initial shape into a number of groups based on the final goal shape to enhance the self-reconfiguration process by allowing clusters to reconfigure in parallel. In this work, we prove that the size-constrained clustering problem is NP-complete, and we propose a new tree-based size-constrained clustering algorithm called “SC-Clust.” To show the efficiency of our approach, we implement and demonstrate our algorithm in simulation on networks of up to 30000 modules and on the Blinky Blocks hardware with up to 144 modules.

REFERENCES

  1. [1] Adoni Hamilton Wilfried Yves, Nahhal Tarik, Krichen Moez, Aghezzaf Brahim, and Elbyed Abdeltif. 2020. A survey of current challenges in partitioning and processing of graph-structured data in parallel and distributed systems. Distrib. Parallel Databases 38 (June 2020), 495–530. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. [2] Adoni Wilfried Yves Hamilton, Nahhal Tarik, Krichen Moez, byed Abdeltif El, and Assayad Ismail. 2020. DHPV: A distributed algorithm for large-scale graph partitioning. J. Big Data 7, 1 (dec2020), 125. Google ScholarGoogle ScholarCross RefCross Ref
  3. [3] Afsar M. Mehdi and Tayarani-N Mohammad-H.. 2014. Clustering in sensor networks: A literature survey. J. Netw. Comput. Appl. 46 (2014), 198226. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. [4] Alattas Reem J., Patel Sarosh, and Sobh Tarek M.. 2019. Evolutionary modular robotics: Survey and analysis. J. Intell. Robot. Syst. 95, 3-4 (2019), 815828.Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. [5] Ansari Shahab U., Hussain Masroor, Mazhar Suleman, Manzoor Tareq, Siddiqui Khalid J., Abid Muhammad, and Jamal Habibullah. 2019. Mesh partitioning and efficient equation solving techniques by distributed finite element methods: A survey. Arch. Comput. Methods Eng. 26, 1 (2019), 116.Google ScholarGoogle ScholarCross RefCross Ref
  6. [6] Bassil Jad, Moussa Mouhamad, Makhoul Abdallah, Piranda Benoit, and Bourgeois Julien. 2020. Linear distributed clustering algorithm for modular robots-based programmable matter. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’20).Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. [7] Berenger Cedric, Niebert Peter, and Perrot Kevin. 2018. Balanced connected partitioning of unweighted grid graphs. In Leibniz International Proceedings in Informatics (LIPIcs’18), Vol. 117. Google ScholarGoogle ScholarCross RefCross Ref
  8. [8] Bhola Jyoti, Soni Surender, and Cheema Gagandeep Kaur. 2020. Genetic algorithm-based optimized leach protocol for energy efficient wireless sensor networks. J. Ambient Intell. Human. Comput. 11, 3 (2020), 12811288.Google ScholarGoogle ScholarCross RefCross Ref
  9. [9] Blin Lélia and Butelle Franck. 2001. A very fast (linear time) distributed algorithm, on general graphs, for the minimum-weight spanning tree. In Proceedings of the 5th International Conference on Principles of Distributed Systems (OPODIS’01). SUGER, 113124.Google ScholarGoogle Scholar
  10. [10] Cruz Nicolas Bulla, Nedjah Nadia, and Mourelle Luiza. 2017. Robust distributed spatial clustering for swarm robotic-based systems. Appl. Soft Comput. J. 57 (2017), 727737. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. [11] Buluç Aydın, Meyerhenke Henning, Safro Ilya, Sanders Peter, and Schulz Christian. 2016. Recent Advances in Graph Partitioning. Springer International Publishing, Cham, 117158. Google ScholarGoogle ScholarCross RefCross Ref
  12. [12] Caro Gianni Di, Ducatelle Frederick, and Gambardella Luca Maria. 2012. A fully distributed communication-based approach for spatial clustering in robotic swarms. In Proceedings of the 2nd Autonomous Robots and Multirobot Systems Workshop (ARMS’12), affiliated with the 11th International Conference on Autonomous Agents and Multiagent Systems (AAMAS’12). 153171.Google ScholarGoogle Scholar
  13. [13] Luna Giuseppe A. Di, Flocchini Paola, Santoro Nicola, Viglietta Giovanni, and Yamauchi Yukiko. 2020. Shape formation by programmable particles. Distrib. Comput. 33, 1 (2020), 69101.Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. [14] Diaz Sergio and Mendez Diego. 2019. Dynamic minimum spanning tree construction and maintenance for Wireless Sensor Networks. Revista Facultad de IngenierÃa Universidad de Antioquia (122019), 5769. Retrieved from http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-62302019000400057&nrm=iso.Google ScholarGoogle ScholarCross RefCross Ref
  15. [15] Diekmann Ralf, Preis Robert, Schlimbach Frank, and Walshaw Chris. 2000. Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM. Parallel Comput. 26, 12 (2000), 15551581.Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. [16] Dutta Ayan, Dasgupta Prithviraj, and Nelson Carl. 2016. A bottom-up search algorithm for size-constrained partitioning of modules to generate configurations in modular robots. Web Intell. 14, 1 (2016), 6782. Google ScholarGoogle ScholarCross RefCross Ref
  17. [17] Dutta Ayan, Dasgupta Raj, Baca José, and Nelson Carl A.. 2015. Spanning tree partitioning approach for configuration generation in modular robots. In Proceedings of the 28th International Florida Artificial Intelligence Research Society Conference (FLAIRS’15), Russell Ingrid and Eberle William (Eds.). AAAI Press, 360365. Retrieved from http://www.aaai.org/ocs/index.php/FLAIRS/FLAIRS15/paper/view/10447.Google ScholarGoogle Scholar
  18. [18] Dutta Ayan, Ufimtsev Vladimir, Asaithambi Asai, and Czarnecki Emily. 2019. Coalition formation for multi-robot task allocation via correlation clustering. Cybernet. Syst. 50, 8 (2019), 711728. . arXiv:https://doi.org/10.1080/01969722.2019.1677334Google ScholarGoogle ScholarCross RefCross Ref
  19. [19] Fan Neng and Pardalos Panos M.. 2010. Linear and quadratic programming approaches for the general graph partitioning problem. J. Global Optim. 48, 1 (2010), 5771.Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. [20] Feldmann Andreas Emil. 2013. Fast balanced partitioning is hard even on grids and trees. Theoret. Comput. Sci. 485 (May2013), 6168. . arxiv:1111.6745.Google ScholarGoogle ScholarCross RefCross Ref
  21. [21] Gallager R. G., Humblet P. A., and Spira P. M.. 1983. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst. 5, 1 (1983), 6677. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. [22] Garey M. R. and Johnson D. S.. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences) (1st ed.). W. H. Freeman. Retrieved from http://www.amazon.com/Computers-Intractability-NP-Completeness-Mathematical-Sciences/dp/0716710455.Google ScholarGoogle Scholar
  23. [23] Gilbert John R., Miller Gary L., and Teng Shang-Hua. 1998. Geometric mesh partitioning: Implementation and experiments. SIAM J. Sci. Comput. 19, 6 (1998), 20912110.Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. [24] Gnägi Mario and Baumann Philipp. 2021. A matheuristic for large-scale capacitated clustering. Comput. Operat. Res. 132 (2021), 105304.Google ScholarGoogle ScholarCross RefCross Ref
  25. [25] Haeupler Bernhard, Hershkowitz D. Ellis, and Wajc David. 2018. Round-and message-optimal distributed graph algorithms. In Proceedings of the ACM Symposium on Principles of Distributed Computing. 119128.Google ScholarGoogle Scholar
  26. [26] Hager William W., Phan Dzung T., and Zhang Hongchao. 2013. An exact algorithm for graph partitioning. Math. Program. 137, 1 (2013), 531556.Google ScholarGoogle ScholarCross RefCross Ref
  27. [27] Hayes Adam, Martinoli A., and Goodman Rodney. 2003. Swarm robotic odor localization: Off-line optimization and validation with real robots. Robotica 21 (072003). Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. [28] Huang Dong, Wang Chang-Dong, Wu Jian-Sheng, Lai Jian-Huang, and Kwoh Chee-Keong. 2019. Ultra-scalable spectral clustering and ensemble clustering. IEEE Trans. Knowl. Data Eng. 32, 6 (2019), 12121226.Google ScholarGoogle ScholarCross RefCross Ref
  29. [29] Kazadi Sanza, Chung M., Lee B., and Cho R.. 2004. On the dynamics of clustering systems. Robot. Auton. Syst. 46 (Jan. 2004), 127. Google ScholarGoogle ScholarCross RefCross Ref
  30. [30] Khamis Alaa, Hussein Ahmed, and Elmogy Ahmed. 2015. Multi-robot task allocation: A review of the state-of-the-art. In Cooperative Robots and Sensor Networks 2015, Anis Koubâa and J. Ramiro Martínez-de Dios (Eds.). Studies in Computational Intelligence, Vol. 607. Springer International Publishing, Cham, 31–51. Google ScholarGoogle ScholarCross RefCross Ref
  31. [31] Kim Jin, Hwang Inwook, Kim Yong-Hyuk, and Moon Byung-Ro. 2011. Genetic approaches for graph partitioning: A survey. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation. 473480.Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. [32] Liu Chao and Yim Mark. 2020. Configuration recognition with distributed information for modular robots. In Robotics Research. Springer, 967983.Google ScholarGoogle Scholar
  33. [33] Liu Jialu and Han Jiawei. 2018. Spectral clustering. In Data Clustering. Chapman and Hall/CRC, 177200.Google ScholarGoogle Scholar
  34. [34] Liu Yaoyao, Guo Ping, and Zeng Yi. 2022. MEACCP: A membrane evolutionary algorithm for capacitated clustering problem. Info. Sci. 591 (2022), 319343. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. [35] Martin C. H.. 2012. Spectral clustering: A quick overview. Ph.D. Dissertation. PhD thesis.Google ScholarGoogle Scholar
  36. [36] Mashreghi Ali and King Valerie. 2021. Broadcast and minimum spanning tree with o (m) messages in the asynchronous CONGEST model. Distrib. Comput. 34, 4 (2021), 283299.Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. [37] Mazdin Petra and Rinner Bernhard. 2021. Distributed and communication-aware coalition formation and task assignment in multi-robot systems. IEEE Access 9 (2021), 3508835100.Google ScholarGoogle Scholar
  38. [38] Meyerhenke Henning, Sanders Peter, and Schulz Christian. 2014. Partitioning complex networks via size-constrained clustering. Lecture Notes Comput. Sci. (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 8504 (2014), 351363. . arxiv:1402.3281.Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. [39] Meyerhenke Henning, Sanders Peter, and Schulz Christian. 2017. Parallel graph partitioning for complex networks. IEEE Trans. Parallel Distrib. Syst. 28, 9 (2017), 26252638.Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. [40] Moussa Mohamad, Piranda Benoit, Makhoul Abdallah, and Bourgeois Julien. 2021. Cluster-based distributed self-reconfiguration algorithm for modular robots. Lecture Notes Netw. Syst. 225 (2021), 332344. Google ScholarGoogle ScholarCross RefCross Ref
  41. [41] Mukherjee Proshikshya. 2020. LEACH-VD: A hybrid and energy-saving approach for wireless cooperative sensor networks. In IoT and WSN Applications for Modern Agricultural Advancements: Emerging Research and Opportunities. IGI Global, 7785.Google ScholarGoogle ScholarCross RefCross Ref
  42. [42] Mulvey John M. and Beck Michael P.. 1984. Solving capacitated clustering problems. Eur. J. Oper. Res. 18, 3 (1984), 339348.Google ScholarGoogle Scholar
  43. [43] Naz André, Piranda Benoît, Tucci Thadeu, Goldstein Seth Copen, and Bourgeois Julien. 2018. Network characterization of lattice-based modular robots with neighbor-to-neighbor communications. In Distributed Autonomous Robotic Systems. Springer, 415429.Google ScholarGoogle ScholarCross RefCross Ref
  44. [44] Osipov Vitaly and Sanders Peter. 2010. n-level graph partitioning. In Proceedings of the European Symposium on Algorithms. Springer, 278289.Google ScholarGoogle ScholarCross RefCross Ref
  45. [45] Pandurangan Gopal, Robinson Peter, Scquizzato Michele, et al. 2018. The distributed minimum spanning tree problem. Bull. EATCS 2, 125 (2018).Google ScholarGoogle Scholar
  46. [46] Pietrabissa A. and Liberati F.. 2019. Dynamic distributed clustering in wireless sensor networks via Voronoi tessellation control. Int. J. Control 92, 5 (2019), 10011014. . arXiv:https://doi.org/10.1080/00207179.2017.1378441Google ScholarGoogle ScholarCross RefCross Ref
  47. [47] Pinciroli C., O’Grady R., Christensen A. L., and Dorigo M.. 2009. Self-organised recruitment in a heteregeneous swarm. In Proceedings of the International Conference on Advanced Robotics. 18.Google ScholarGoogle Scholar
  48. [48] Piranda Benoît and Bourgeois Julien. 2018. Designing a quasi-spherical module for a huge modular robot to create programmable matter. Auton. Robots 42, 8 (2018), 16191633. Google ScholarGoogle ScholarCross RefCross Ref
  49. [49] Predari Maria and Esnard Aurélien. 2016. A k-way greedy graph partitioning with initial fixed vertices for parallel applications. In Proceedings of the 24th Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP’16). IEEE, 280287.Google ScholarGoogle ScholarCross RefCross Ref
  50. [50] Qi Song, Guo Hengyu, Fu Jie, Xie Yuanpeng, Zhu Mi, and Yu Miao. 2020. 3D printed shape-programmable magneto-active soft matter for biomimetic applications. Compos. Sci. Technol. 188 (2020), 107973.Google ScholarGoogle ScholarCross RefCross Ref
  51. [51] Rahimian Fatemeh, Payberah Amir H., Girdzijauskas Sarunas, Jelasity Mark, and Haridi Seif. 2015. A distributed algorithm for large-scale graph partitioning. ACM Trans. Auton. Adapt. Syst. 10, 2 (2015), 124.Google ScholarGoogle ScholarDigital LibraryDigital Library
  52. [52] Requicha A. A. G., Voelcker H. B., and Project University of Rochester. Production Automation. 1977. Constructive Solid Geometry. Production Automation Project, University of Rochester. Retrieved from https://books.google.fr/books?id=hG2lngEACAAJ.Google ScholarGoogle Scholar
  53. [53] Rolland Erik, Pirkul Hasan, and Glover Fred. 1996. Tabu search for graph partitioning. Ann. Oper. Res. 63, 2 (1996), 209232.Google ScholarGoogle ScholarCross RefCross Ref
  54. [54] Schaeffer Satu Elisa. 2007. Graph clustering. Comput. Sci. Rev. 1, 1 (2007), 2764. Google ScholarGoogle ScholarDigital LibraryDigital Library
  55. [55] Scheuerer Stephan and Wendolsky Rolf. 2006. A scatter search heuristic for the capacitated clustering problem. Eur. J. Oper. Res. 169, 2 (2006), 533547.Google ScholarGoogle Scholar
  56. [56] Shao Junming, Yang Qinli, Zhang Zhong, Liu Jinhu, and Kramer Stefan. 2018. Graph clustering with local density-cut. In Database Systems for Advanced Applications, Pei Jian, Manolopoulos Yannis, Sadiq Shazia, and Li Jianxin (Eds.). Springer International Publishing, Cham, 187202.Google ScholarGoogle Scholar
  57. [57] Simon Horst D.. 1991. Partitioning of unstructured problems for parallel processing. Comput. Syst. Eng. 2, 2-3 (1991), 135148.Google ScholarGoogle ScholarCross RefCross Ref
  58. [58] Thalamy Pierre, Piranda Benoît, and Bourgeois Julien. 2019. A survey of autonomous self-reconfiguration methods for robot-based programmable matter. Robot. Auton. Syst. 120 (2019), 103242. Google ScholarGoogle ScholarCross RefCross Ref
  59. [59] Thalamy Pierre, Piranda Benoît, Naz André, and Bourgeois Julien. 2022. VisibleSim: A behavioral simulation framework for lattice modular robots. Robotics and Autonomous Systems 147 (2022), 103913. Google ScholarGoogle ScholarDigital LibraryDigital Library
  60. [60] Tucci Thadeu, Piranda Benoît, and Bourgeois Julien. 2017. Efficient scene encoding for programmable matter self-reconfiguration algorithms. Proceedings of the ACM Symposium on Applied Computing. 256261. Google ScholarGoogle ScholarDigital LibraryDigital Library
  61. [61] Tucci Thadeu, Piranda Benoît, and Bourgeois Julien. 2018. A distributed self-assembly planning algorithm for modular robots. In Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS’18). 550558.Google ScholarGoogle ScholarDigital LibraryDigital Library
  62. [62] Wahby Mostafa, Petzold Julian, Eschke Catriona, Schmickl Thomas, and Hamann Heiko. 2019. Collective change detection: Adaptivity to dynamic swarm densities and light conditions in robot swarms. In Proceedings of the Artificial Life Conference Proceedings. Google ScholarGoogle ScholarCross RefCross Ref
  63. [63] Xiangning Fan and Yulin Song. 2007. Improvement on LEACH protocol of wireless sensor network. In Proceedings of the International Conference on Sensor Technologies and Applications (SENSORCOMM’07). IEEE, 260264.Google ScholarGoogle ScholarCross RefCross Ref
  64. [64] Yan Yaowei, Bian Yuchen, Luo Dongsheng, Lee Dongwon, and Zhang Xiang. 2019. Constrained local graph clustering by colored random walk. In Proceedings of the World Wide Web Conference. 21372146.Google ScholarGoogle ScholarDigital LibraryDigital Library
  65. [65] Zhang Yu, Parker Lynne E., and Kambhampati Subbarao. 2014. Coalition coordination for tightly coupled multirobot tasks with sensor constraints. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA’14). IEEE, 10901097.Google ScholarGoogle ScholarCross RefCross Ref
  66. [66] Zhou Qing, Benlic Una, Wu Qinghua, and Hao Jin-Kao. 2019. Heuristic search to the capacitated clustering problem. Eur. J. Oper. Res. 273, 2 (2019), 464487. Google ScholarGoogle ScholarCross RefCross Ref

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        cover image ACM Transactions on Autonomous and Adaptive Systems
        ACM Transactions on Autonomous and Adaptive Systems  Volume 18, Issue 1
        March 2023
        82 pages
        ISSN:1556-4665
        EISSN:1556-4703
        DOI:10.1145/3589019
        Issue’s Table of Contents

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        Publication History

        • Published: 27 March 2023
        • Online AM: 20 January 2023
        • Accepted: 9 January 2023
        • Revised: 6 October 2022
        • Received: 29 June 2021
        Published in taas Volume 18, Issue 1

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