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.
- [1] . 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 Scholar
Digital Library
- [2] . 2020. DHPV: A distributed algorithm for large-scale graph partitioning. J. Big Data 7, 1 (
dec 2020), 1–25. Google ScholarCross Ref
- [3] . 2014. Clustering in sensor networks: A literature survey. J. Netw. Comput. Appl. 46 (2014), 198–226. Google Scholar
Digital Library
- [4] . 2019. Evolutionary modular robotics: Survey and analysis. J. Intell. Robot. Syst. 95, 3-4 (2019), 815–828.Google Scholar
Digital Library
- [5] . 2019. Mesh partitioning and efficient equation solving techniques by distributed finite element methods: A survey. Arch. Comput. Methods Eng. 26, 1 (2019), 1–16.Google Scholar
Cross Ref
- [6] . 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 Scholar
Digital Library
- [7] . 2018. Balanced connected partitioning of unweighted grid graphs. In Leibniz International Proceedings in Informatics (LIPIcs’18), Vol. 117. Google Scholar
Cross Ref
- [8] . 2020. Genetic algorithm-based optimized leach protocol for energy efficient wireless sensor networks. J. Ambient Intell. Human. Comput. 11, 3 (2020), 1281–1288.Google Scholar
Cross Ref
- [9] . 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, 113–124.Google Scholar
- [10] . 2017. Robust distributed spatial clustering for swarm robotic-based systems. Appl. Soft Comput. J. 57 (2017), 727–737. Google Scholar
Digital Library
- [11] . 2016. Recent Advances in Graph Partitioning. Springer International Publishing, Cham, 117–158. Google Scholar
Cross Ref
- [12] . 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). 153–171.Google Scholar
- [13] . 2020. Shape formation by programmable particles. Distrib. Comput. 33, 1 (2020), 69–101.Google Scholar
Digital Library
- [14] . 2019. Dynamic minimum spanning tree construction and maintenance for Wireless Sensor Networks. Revista Facultad de IngenierÃa Universidad de Antioquia (
12 2019), 57–69. Retrieved from http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-62302019000400057&nrm=iso.Google ScholarCross Ref
- [15] . 2000. Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM. Parallel Comput. 26, 12 (2000), 1555–1581.Google Scholar
Digital Library
- [16] . 2016. A bottom-up search algorithm for size-constrained partitioning of modules to generate configurations in modular robots. Web Intell. 14, 1 (2016), 67–82. Google Scholar
Cross Ref
- [17] . 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), and (Eds.). AAAI Press, 360–365. Retrieved from http://www.aaai.org/ocs/index.php/FLAIRS/FLAIRS15/paper/view/10447.Google Scholar
- [18] . 2019. Coalition formation for multi-robot task allocation via correlation clustering. Cybernet. Syst. 50, 8 (2019), 711–728. .
arXiv:https://doi.org/10.1080/01969722.2019.1677334 Google ScholarCross Ref
- [19] . 2010. Linear and quadratic programming approaches for the general graph partitioning problem. J. Global Optim. 48, 1 (2010), 57–71.Google Scholar
Digital Library
- [20] . 2013. Fast balanced partitioning is hard even on grids and trees. Theoret. Comput. Sci. 485 (
May 2013), 61–68. .arxiv:1111.6745 .Google ScholarCross Ref
- [21] . 1983. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Program. Lang. Syst. 5, 1 (1983), 66–77. Google Scholar
Digital Library
- [22] . 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 Scholar
- [23] . 1998. Geometric mesh partitioning: Implementation and experiments. SIAM J. Sci. Comput. 19, 6 (1998), 2091–2110.Google Scholar
Digital Library
- [24] . 2021. A matheuristic for large-scale capacitated clustering. Comput. Operat. Res. 132 (2021), 105304.Google Scholar
Cross Ref
- [25] . 2018. Round-and message-optimal distributed graph algorithms. In Proceedings of the ACM Symposium on Principles of Distributed Computing. 119–128.Google Scholar
- [26] . 2013. An exact algorithm for graph partitioning. Math. Program. 137, 1 (2013), 531–556.Google Scholar
Cross Ref
- [27] . 2003. Swarm robotic odor localization: Off-line optimization and validation with real robots. Robotica 21 (
07 2003). Google ScholarDigital Library
- [28] . 2019. Ultra-scalable spectral clustering and ensemble clustering. IEEE Trans. Knowl. Data Eng. 32, 6 (2019), 1212–1226.Google Scholar
Cross Ref
- [29] . 2004. On the dynamics of clustering systems. Robot. Auton. Syst. 46 (Jan. 2004), 1–27. Google Scholar
Cross Ref
- [30] . 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 Scholar
Cross Ref
- [31] . 2011. Genetic approaches for graph partitioning: A survey. In Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation. 473–480.Google Scholar
Digital Library
- [32] . 2020. Configuration recognition with distributed information for modular robots. In Robotics Research. Springer, 967–983.Google Scholar
- [33] . 2018. Spectral clustering. In Data Clustering. Chapman and Hall/CRC, 177–200.Google Scholar
- [34] . 2022. MEACCP: A membrane evolutionary algorithm for capacitated clustering problem. Info. Sci. 591 (2022), 319–343. Google Scholar
Digital Library
- [35] . 2012. Spectral clustering: A quick overview. Ph.D. Dissertation. PhD thesis.Google Scholar
- [36] . 2021. Broadcast and minimum spanning tree with o (m) messages in the asynchronous CONGEST model. Distrib. Comput. 34, 4 (2021), 283–299.Google Scholar
Digital Library
- [37] . 2021. Distributed and communication-aware coalition formation and task assignment in multi-robot systems. IEEE Access 9 (2021), 35088–35100.Google Scholar
- [38] . 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), 351–363. .
arxiv:1402.3281 .Google ScholarDigital Library
- [39] . 2017. Parallel graph partitioning for complex networks. IEEE Trans. Parallel Distrib. Syst. 28, 9 (2017), 2625–2638.Google Scholar
Digital Library
- [40] . 2021. Cluster-based distributed self-reconfiguration algorithm for modular robots. Lecture Notes Netw. Syst. 225 (2021), 332–344. Google Scholar
Cross Ref
- [41] . 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, 77–85.Google Scholar
Cross Ref
- [42] . 1984. Solving capacitated clustering problems. Eur. J. Oper. Res. 18, 3 (1984), 339–348.Google Scholar
- [43] . 2018. Network characterization of lattice-based modular robots with neighbor-to-neighbor communications. In Distributed Autonomous Robotic Systems. Springer, 415–429.Google Scholar
Cross Ref
- [44] . 2010. n-level graph partitioning. In Proceedings of the European Symposium on Algorithms. Springer, 278–289.Google Scholar
Cross Ref
- [45] . 2018. The distributed minimum spanning tree problem. Bull. EATCS 2, 125 (2018).Google Scholar
- [46] . 2019. Dynamic distributed clustering in wireless sensor networks via Voronoi tessellation control. Int. J. Control 92, 5 (2019), 1001–1014. .
arXiv:https://doi.org/10.1080/00207179.2017.1378441 Google ScholarCross Ref
- [47] . 2009. Self-organised recruitment in a heteregeneous swarm. In Proceedings of the International Conference on Advanced Robotics. 1–8.Google Scholar
- [48] . 2018. Designing a quasi-spherical module for a huge modular robot to create programmable matter. Auton. Robots 42, 8 (2018), 1619–1633. Google Scholar
Cross Ref
- [49] . 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, 280–287.Google Scholar
Cross Ref
- [50] . 2020. 3D printed shape-programmable magneto-active soft matter for biomimetic applications. Compos. Sci. Technol. 188 (2020), 107973.Google Scholar
Cross Ref
- [51] . 2015. A distributed algorithm for large-scale graph partitioning. ACM Trans. Auton. Adapt. Syst. 10, 2 (2015), 1–24.Google Scholar
Digital Library
- [52] . 1977. Constructive Solid Geometry. Production Automation Project, University of Rochester. Retrieved from https://books.google.fr/books?id=hG2lngEACAAJ.Google Scholar
- [53] . 1996. Tabu search for graph partitioning. Ann. Oper. Res. 63, 2 (1996), 209–232.Google Scholar
Cross Ref
- [54] . 2007. Graph clustering. Comput. Sci. Rev. 1, 1 (2007), 27–64. Google Scholar
Digital Library
- [55] . 2006. A scatter search heuristic for the capacitated clustering problem. Eur. J. Oper. Res. 169, 2 (2006), 533–547.Google Scholar
- [56] . 2018. Graph clustering with local density-cut. In Database Systems for Advanced Applications, , , , and (Eds.). Springer International Publishing, Cham, 187–202.Google Scholar
- [57] . 1991. Partitioning of unstructured problems for parallel processing. Comput. Syst. Eng. 2, 2-3 (1991), 135–148.Google Scholar
Cross Ref
- [58] . 2019. A survey of autonomous self-reconfiguration methods for robot-based programmable matter. Robot. Auton. Syst. 120 (2019), 103242. Google Scholar
Cross Ref
- [59] . 2022. VisibleSim: A behavioral simulation framework for lattice modular robots. Robotics and Autonomous Systems 147 (2022), 103913. Google Scholar
Digital Library
- [60] . 2017. Efficient scene encoding for programmable matter self-reconfiguration algorithms. Proceedings of the ACM Symposium on Applied Computing. 256–261. Google Scholar
Digital Library
- [61] . 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). 550–558.Google Scholar
Digital Library
- [62] . 2019. Collective change detection: Adaptivity to dynamic swarm densities and light conditions in robot swarms. In Proceedings of the Artificial Life Conference Proceedings. Google Scholar
Cross Ref
- [63] . 2007. Improvement on LEACH protocol of wireless sensor network. In Proceedings of the International Conference on Sensor Technologies and Applications (SENSORCOMM’07). IEEE, 260–264.Google Scholar
Cross Ref
- [64] . 2019. Constrained local graph clustering by colored random walk. In Proceedings of the World Wide Web Conference. 2137–2146.Google Scholar
Digital Library
- [65] . 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, 1090–1097.Google Scholar
Cross Ref
- [66] . 2019. Heuristic search to the capacitated clustering problem. Eur. J. Oper. Res. 273, 2 (2019), 464–487. Google Scholar
Cross Ref
Index Terms
Distributed Size-constrained Clustering Algorithm for Modular Robot-based Programmable Matter
Recommendations
Designing a quasi-spherical module for a huge modular robot to create programmable matter
There are many ways to implement programmable matter. One is to build it as a huge modular self-reconfigurable robot composed of a large set of spherical micro-robots, like in the Claytronics project. These micro-robots must be able to stick to each ...
A Distributed Self-Assembly Planning Algorithm for Modular Robots
AAMAS '18: Proceedings of the 17th International Conference on Autonomous Agents and MultiAgent SystemsA distributed modular robot is composed of many autonomous modules, capable of organizing the overall robot into a specific goal structure. There are two possibilities to change the morphology of such a robot. The first one, self-reconfiguration, moves ...
Efficient collective shape shifting and locomotion of massively-modular robotic structures
We propose a methodology of planning effective shape shifting and locomotion of large-ensemble modular robots based on a cubic lattice. The modules are divided into two groups: fixed ones, that build a rigid porous frame, and mobile ones, that flow ...






Comments