{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T12:10:07Z","timestamp":1758975007128,"version":"3.44.0"},"reference-count":72,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T00:00:00Z","timestamp":1755907200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T00:00:00Z","timestamp":1755907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100008007","name":"Universit\u00e4t Paderborn","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008007","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Auton Robot"],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>We are considering the geometric amoebot model where a set of <jats:italic>n<\/jats:italic>\n            <jats:italic>amoebots<\/jats:italic> 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 <jats:inline-formula>\n              <jats:tex-math>$$\\Omega (D)$$<\/jats:tex-math>\n            <\/jats:inline-formula> where <jats:italic>D<\/jats:italic> denotes the diameter of the structure. Inspired by the nervous and muscular system, Feldmann et al. (Computat Biol 29(4):317\u2013343, 2022) have proposed the <jats:italic>reconfigurable circuit extension<\/jats:italic> and the <jats:italic>joint movement extension<\/jats:italic> 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. (Computat Biol 29(4):317\u2013343, 2022) demonstrated the power of joint movements by transforming a line of amoebots into a rhombus within <jats:inline-formula>\n              <jats:tex-math>$$O(\\log n)$$<\/jats:tex-math>\n            <\/jats:inline-formula> rounds. However, they left the details of the extension open. The goal of this paper is therefore to formalize and extend the joint movement extension. In order to provide a proof of concept for the extension, we develop centralized algorithms for two fundamental problems of modular robot systems: <jats:italic>reconfiguration<\/jats:italic> and <jats:italic>locomotion<\/jats:italic>. We approach these problems by defining meta-modules of rhombical and hexagonal shape, 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.<\/jats:p>","DOI":"10.1007\/s10514-025-10204-9","type":"journal-article","created":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T06:34:59Z","timestamp":1755930899000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reconfiguration and locomotion with joint movements in the amoebot model"],"prefix":"10.1007","volume":"49","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4601-9597","authenticated-orcid":false,"given":"Andreas","family":"Padalkin","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0620-3303","authenticated-orcid":false,"given":"Manish","family":"Kumar","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5278-528X","authenticated-orcid":false,"given":"Christian","family":"Scheideler","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,23]]},"reference":[{"issue":"3\u20134","key":"10204_CR1","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/s10846-015-0237-8","volume":"81","author":"H Ahmadzadeh","year":"2016","unstructured":"Ahmadzadeh, H., Masehian, E., & Asadpour, M. (2016). Modular robotic systems: Characteristics and applications. Journal of Intelligent & Robotic Systems, 81(3\u20134), 317\u2013357.","journal-title":"Journal of Intelligent & Robotic Systems"},{"issue":"5","key":"10204_CR2","doi-asserted-by":"publisher","first-page":"1316","DOI":"10.1007\/s00453-020-00784-6","volume":"83","author":"HA Akitaya","year":"2021","unstructured":"Akitaya, H. A., Arkin, E. M., Damian, M., Dujmovic, V., Flatland, R., Korman, M., Palop, B., Parada, I., Renssen, A. V., & Sacristan, V. (2021). Universal reconfiguration of facet-connected modular robots by pivots: The O(1) musketeers. Algorithmica, 83(5), 1316\u20131351.","journal-title":"Algorithmica"},{"key":"10204_CR3","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.tcs.2022.11.029","volume":"942","author":"A Almethen","year":"2023","unstructured":"Almethen, A., Michail, O., & Potapov, I. (2023). Distributed transformations of Hamiltonian shapes based on line moves. Theoretical Computer Science, 942, 142\u2013168.","journal-title":"Theoretical Computer Science"},{"doi-asserted-by":"crossref","unstructured":"Aloupis, G., Collette, S., Demaine, E. D., Langerman, S., Sacrist\u00e1n, V., & Wuhrer, S. (2008). Reconfiguration of cube-style modular robots using O(log n) parallel moves. In ISAAC, Lecture Notes in Computer Science (Vol. 5369, pp. 342\u2013353). Springer.","key":"10204_CR4","DOI":"10.1007\/978-3-540-92182-0_32"},{"issue":"6\u20137","key":"10204_CR5","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1016\/j.comgeo.2008.11.003","volume":"42","author":"G Aloupis","year":"2009","unstructured":"Aloupis, G., Collette, S., Damian, M., Flatland, R., Langerman, S., O\u2019Rourke, J., Ramaswami, S., Sacristan, V., & Wuhrer, S. (2009). Linear reconfiguration of cube-style modular robots. Computational Geometry, 42(6\u20137), 652\u2013663.","journal-title":"Computational Geometry"},{"issue":"8","key":"10204_CR6","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1016\/j.comgeo.2013.03.004","volume":"46","author":"G Aloupis","year":"2013","unstructured":"Aloupis, G., Benbernou, N., Damian, M., Demaine, E. D., Flatland, R., Iacono, J., & Wuhrer, S. (2013). Efficient reconfiguration of lattice-based modular robots. Computational Geometry, 46(8), 917\u2013928.","journal-title":"Computational Geometry"},{"doi-asserted-by":"publisher","unstructured":"An, B. K. (2008). Em-cube: Cube-shaped, self-reconfigurable robots sliding on structure surfaces. In 2008 IEEE International Conference on Robotics and Automation, ICRA 2008, May 19\u201323, 2008, Pasadena, California, USA (pp. 3149\u20133155). IEEE. https:\/\/doi.org\/10.1109\/ROBOT.2008.4543690","key":"10204_CR7","DOI":"10.1109\/ROBOT.2008.4543690"},{"issue":"4","key":"10204_CR8","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1016\/S1672-6529(07)60003-1","volume":"3","author":"RH Armour","year":"2006","unstructured":"Armour, R. H., & Vincent, J. F. (2006). Rolling in nature and robotics: A review. Journal of Bionic Engineering, 3(4), 195\u2013208.","journal-title":"Journal of Bionic Engineering"},{"issue":"4","key":"10204_CR9","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1007\/s11047-018-9714-x","volume":"17","author":"MA Arroyo","year":"2018","unstructured":"Arroyo, M. A., Cannon, S., Daymude, J. J., Randall, D., & Richa, A. W. (2018). A stochastic approach to shortcut bridging in programmable matter. Natural Computing, 17(4), 723\u2013741.","journal-title":"Natural Computing"},{"unstructured":"Artmann, M., Maurer, T., Padalkin, A., Warner, D., & Scheideler, C. (2025). Amoebotsim 2.0: A visual simulation environment for the amoebot model with reconfigurable circuits and joint movements. In SoCG. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik, LIPIcs (To appear).","key":"10204_CR10"},{"issue":"3","key":"10204_CR11","doi-asserted-by":"publisher","first-page":"172988141771045","DOI":"10.1177\/1729881417710457","volume":"14","author":"A Brunete","year":"2017","unstructured":"Brunete, A., Ranganath, A., Segovia, S., De Frutos, J. P., Hernando, M., & Gambao, E. (2017). Current trends in reconfigurable modular robots design. International Journal of Advanced Robotic Systems, 14(3), 1729881417710457.","journal-title":"International Journal of Advanced Robotic Systems"},{"issue":"9","key":"10204_CR12","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1177\/0278364904044409","volume":"23","author":"ZJ Butler","year":"2004","unstructured":"Butler, Z. J., Kotay, K., Rus, D., & Tomita, K. (2004). Generic decentralized control for lattice-based self-reconfigurable robots. The International Journal of Robotics Research, 23(9), 919\u2013937.","journal-title":"The International Journal of Robotics Research"},{"issue":"3\u20134","key":"10204_CR13","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1177\/0278364907085561","volume":"27","author":"J Campbell","year":"2008","unstructured":"Campbell, J., & Pillai, P. (2008). Collective actuation. The International Journal of Robotics Research, 27(3\u20134), 299\u2013314.","journal-title":"The International Journal of Robotics Research"},{"doi-asserted-by":"crossref","unstructured":"Cannon, S., Daymude, J. J., Randall, D., & Richa, A. W. (2016). A markov chain algorithm for compression in self-organizing particle systems. In PODC (pp. 279\u2013288). ACM.","key":"10204_CR14","DOI":"10.1145\/2933057.2933107"},{"doi-asserted-by":"crossref","unstructured":"Chirikjian, G. S. (1994). Kinematics of a metamorphic robotic system. In ICRA (pp. 449\u2013455). IEEE Computer Society.","key":"10204_CR15","DOI":"10.1109\/ROBOT.1994.351256"},{"doi-asserted-by":"crossref","unstructured":"Christensen, D. J., & Campbell, J. (2007). Locomotion of miniature catom chains: Scale effects on gait and velocity. In ICRA (pp. 2254\u20132260). IEEE.","key":"10204_CR16","DOI":"10.1109\/ROBOT.2007.363655"},{"doi-asserted-by":"crossref","unstructured":"Daymude, J. J., Hinnenthal, K., Richa, A. W., & Scheideler, C. (2019). Computing by programmable particles. In Distributed Computing by Mobile Entities, Lecture Notes in Computer Science (Vol. 11340, pp. 615\u2013681). Springer.","key":"10204_CR17","DOI":"10.1007\/978-3-030-11072-7_22"},{"issue":"2","key":"10204_CR18","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s00446-023-00443-3","volume":"36","author":"JJ Daymude","year":"2023","unstructured":"Daymude, J. J., Richa, A. W., & Scheideler, C. (2023). The canonical amoebot model: Algorithms and concurrency control. Distributed Computing, 36(2), 159\u2013192.","journal-title":"Distributed Computing"},{"doi-asserted-by":"crossref","unstructured":"Derakhshandeh, Z., Dolev, S., Gmyr, R., Richa, A. W., Scheideler, C., & Strothmann, T. (2014). Brief announcement: Amoebot\u2014a new model for programmable matter. In SPAA (pp. 220\u2013222). ACM.","key":"10204_CR19","DOI":"10.1145\/2612669.2612712"},{"doi-asserted-by":"crossref","unstructured":"Derakhshandeh, Z., Gmyr, R., Richa, A. W., Scheideler, C., & Strothmann, T. (2015). An algorithmic framework for shape formation problems in self-organizing particle systems. In NANOCOM (pp. 1\u20132). ACM.","key":"10204_CR20","DOI":"10.1145\/2800795.2800829"},{"doi-asserted-by":"crossref","unstructured":"Derakhshandeh, Z., Gmyr, R., Richa, A. W., Scheideler, C., & Strothmann, T. (2016). Universal shape formation for programmable matter. In SPAA (pp. 289\u2013299). ACM.","key":"10204_CR21","DOI":"10.1145\/2935764.2935784"},{"doi-asserted-by":"crossref","unstructured":"Dewey, D. J., Ashley-Rollman, M. P., De Rosa, M., Goldstein, S. C., Mowry, T. C., Srinivasa, S. S., Pillai, P., & Campbell, J. (2008). Generalizing metamodules to simplify planning in modular robotic systems. In IROS (pp. 1338\u20131345). IEEE.","key":"10204_CR22","DOI":"10.1109\/IROS.2008.4651094"},{"issue":"1","key":"10204_CR23","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s00446-019-00350-6","volume":"33","author":"GA Di Luna","year":"2020","unstructured":"Di Luna, G. A., Flocchini, P., Santoro, N., Viglietta, G., & Yamauchi, Y. (2020). Shape formation by programmable particles. Distributed Computing, 33(1), 69\u2013101.","journal-title":"Distributed Computing"},{"doi-asserted-by":"crossref","unstructured":"Dolev, S., Frenkel, S., Rosenblit, M., Narayanan, R. P., & Venkateswarlu, K. M. (2016). In-vivo energy harvesting nano robots. In 2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE) (pp. 1\u20135).","key":"10204_CR24","DOI":"10.1109\/ICSEE.2016.7806107"},{"doi-asserted-by":"crossref","unstructured":"Dufoulon, F., Kutten, S., & Moses Jr, W. K. (2021) Efficient deterministic leader election for programmable matter. In PODC (pp. 103\u2013113). ACM.","key":"10204_CR25","DOI":"10.1145\/3465084.3467900"},{"issue":"3","key":"10204_CR26","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1109\/TRA.2004.824936","volume":"20","author":"A Dumitrescu","year":"2004","unstructured":"Dumitrescu, A., Suzuki, I., & Yamashita, M. (2004). Motion planning for metamorphic systems: Feasibility, decidability, and distributed reconfiguration. IEEE Transactions on Robotics and Automation, 20(3), 409\u2013418.","journal-title":"IEEE Transactions on Robotics and Automation"},{"issue":"4","key":"10204_CR27","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1089\/cmb.2021.0363","volume":"29","author":"M Feldmann","year":"2022","unstructured":"Feldmann, M., Padalkin, A., Scheideler, C., & Dolev, S. (2022). Coordinating amoebots via reconfigurable circuits. Computational Biology, 29(4), 317\u2013343.","journal-title":"Computational Biology"},{"issue":"3\u20134","key":"10204_CR28","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1177\/0278364907085097","volume":"27","author":"R Fitch","year":"2008","unstructured":"Fitch, R., & Butler, Z. J. (2008). Million module march: Scalable locomotion for large self-reconfiguring robots. The International Journal of Robotics Research, 27(3\u20134), 331\u2013343.","journal-title":"The International Journal of Robotics Research"},{"issue":"2","key":"10204_CR29","doi-asserted-by":"publisher","first-page":"026003","DOI":"10.1088\/1748-3190\/abbdcc","volume":"16","author":"A Garcia","year":"2020","unstructured":"Garcia, A., Krummel, G., & Priya, S. (2020). Fundamental understanding of millipede morphology and locomotion dynamics. Bioinspiration & Biomimetics, 16(2), 026003.","journal-title":"Bioinspiration & Biomimetics"},{"doi-asserted-by":"crossref","unstructured":"Gupta, S., van Kreveld, M., Michail, O., & Padalkin, A. (2024). Collision detection for modular robots\u2014it is easy to cause collisions and hard to avoid them. In ALGOWIN, Lecture Notes in Computer Science (Vol. 15026, pp. 76\u201390). Springer.","key":"10204_CR30","DOI":"10.1007\/978-3-031-74580-5_6"},{"doi-asserted-by":"crossref","unstructured":"Hirose, S. (1991). Three basic types of locomotion in mobile robots. In Fifth International Conference on Advanced Robotics\u2019 Robots in Unstructured Environments (pp. 12\u201317). IEEE.","key":"10204_CR31","DOI":"10.1109\/ICAR.1991.240483"},{"issue":"4","key":"10204_CR32","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s10514-015-9421-8","volume":"38","author":"F Hurtado","year":"2015","unstructured":"Hurtado, F., Molina, E., Ramaswami, S., & Sacrist\u00e1n, V. (2015). Distributed reconfiguration of 2d lattice-based modular robotic systems. Autonomous Robots, 38(4), 383\u2013413.","journal-title":"Autonomous Robots"},{"doi-asserted-by":"crossref","unstructured":"Inou, N., Kobayashi, H., & Koseki, M. (2002). Development of pneumatic cellular robots forming a mechanical structure. In ICARCV (pp. 63\u201368). IEEE.","key":"10204_CR33","DOI":"10.1109\/ICARCV.2002.1234791"},{"doi-asserted-by":"crossref","unstructured":"Jing, G., Tosun, T., Yim, M., & Kress-Gazit, H. (2016). An end-to-end system for accomplishing tasks with modular robots. In Robotics: Science and Systems.","key":"10204_CR34","DOI":"10.24963\/ijcai.2017\/686"},{"issue":"7","key":"10204_CR35","doi-asserted-by":"publisher","first-page":"1337","DOI":"10.1007\/s10514-018-9738-1","volume":"42","author":"G Jing","year":"2018","unstructured":"Jing, G., Tosun, T., Yim, M., & Kress-Gazit, H. (2018). Accomplishing high-level tasks with modular robots. Autonomous Robots, 42(7), 1337\u20131354.","journal-title":"Autonomous Robots"},{"issue":"2","key":"10204_CR36","doi-asserted-by":"publisher","first-page":"59","DOI":"10.3311\/PPme.7047","volume":"57","author":"Z Juh\u00e1sz","year":"2013","unstructured":"Juh\u00e1sz, Z., & Zelei, A. (2013). Analysis of worm-like locomotion. Periodica Polytechnica Mechanical Engineering, 57(2), 59\u201364.","journal-title":"Periodica Polytechnica Mechanical Engineering"},{"issue":"4","key":"10204_CR37","doi-asserted-by":"publisher","first-page":"118","DOI":"10.3390\/robotics10040118","volume":"10","author":"M Sivaperuman Kalairaj","year":"2021","unstructured":"Sivaperuman Kalairaj, M., Cai, C. J., Pavitra, S., & Ren, H. (2021). Untethered origami worm robot with diverse multi-leg attachments and responsive motions under magnetic actuation. Robotics, 10(4), 118.","journal-title":"Robotics"},{"doi-asserted-by":"crossref","unstructured":"Kehoe, M., & Piovesan, D. (2019). Taxonomy of two dimensional bio-inspired locomotion systems. In EMBC (pp. 3703\u20133706). IEEE.","key":"10204_CR38","DOI":"10.1109\/EMBC.2019.8857565"},{"unstructured":"Kirby, B., Campbell, J., Aksak, B., Pillai, P., Hoburg, J., Mowry, T. C., & Goldstein, S. C. (2005). Catoms: Moving robots without moving parts. In AAAI (pp. 1730\u20131731). AAAI Press\/The MIT Press.","key":"10204_CR39"},{"unstructured":"Kostitsyna, I., Scheideler, C., & Warner, D. (2022). Fault-tolerant shape formation in the amoebot model. In DNA, LIPIcs, vol 238. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (pp 1\u201322).","key":"10204_CR40"},{"doi-asserted-by":"crossref","unstructured":"Kotay, K., Rus, D., & Vona, M. (2000). Using modular self-reconfiguring robots for locomotion. In ISER, Lecture Notes in Control and Information Sciences (Vol. 271, pp. 259\u2013269). Springer.","key":"10204_CR41","DOI":"10.1007\/3-540-45118-8_27"},{"issue":"2","key":"10204_CR42","doi-asserted-by":"publisher","first-page":"026005","DOI":"10.1088\/1748-3190\/ac482d","volume":"17","author":"S Kuroda","year":"2022","unstructured":"Kuroda, S., Uchida, N., & Nakagaki, T. (2022). Gait switching with phase reversal of locomotory waves in the centipede scolopocryptops rubiginosus. Bioinspiration & Biomimetics, 17(2), 026005.","journal-title":"Bioinspiration & Biomimetics"},{"issue":"2","key":"10204_CR43","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.robot.2005.09.023","volume":"54","author":"H Kurokawa","year":"2006","unstructured":"Kurokawa, H., Yoshida, E., Tomita, K., Kamimura, A., Murata, S., & Kokaji, S. (2006). Self-reconfigurable M-TRAN structures and walker generation. Robotics and Autonomous Systems, 54(2), 142\u2013149.","journal-title":"Robotics and Autonomous Systems"},{"issue":"3","key":"10204_CR44","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1086\/284068","volume":"121","author":"M LaBarbera","year":"1983","unstructured":"LaBarbera, M. (1983). Why the wheels won\u2019t go. The American Naturalist, 121(3), 395\u2013408.","journal-title":"The American Naturalist"},{"doi-asserted-by":"crossref","unstructured":"Mellinger, D., Kumar, V., & Yim, M. (2009). Control of locomotion with shape-changing wheels. In ICRA (pp. 1750\u20131755). IEEE.","key":"10204_CR45","DOI":"10.1109\/ROBOT.2009.5152478"},{"doi-asserted-by":"crossref","unstructured":"Murata, S., Kurokawa, H., & Kokaji, S. (1994). Self-assembling machine. In ICRA (pp. 441\u2013448). IEEE Computer Society.","key":"10204_CR46","DOI":"10.1109\/ROBOT.1995.525759"},{"unstructured":"Nguyen, A., Guibas, L.J., & Yim, M. (2001). Controlled module density helps reconfiguration planning. In Workshop on the Algorithmic Foundations of Robotics (pp. TH15\u2013TH27).","key":"10204_CR47"},{"doi-asserted-by":"crossref","unstructured":"Omori, H., Hayakawa, T., & Nakamura, T. (2008). Locomotion and turning patterns of a peristaltic crawling earthworm robot composed of flexible units. In IROS (pp. 1630\u20131635). IEEE.","key":"10204_CR48","DOI":"10.1109\/IROS.2008.4650980"},{"doi-asserted-by":"crossref","unstructured":"Padalkin, A., & Scheideler, C. (2024). Polylogarithmic time algorithms for shortest path forests in programmable matter. In PODC (pp. 65\u201375). ACM,","key":"10204_CR49","DOI":"10.1145\/3662158.3662776"},{"issue":"4","key":"10204_CR50","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1007\/s11047-024-09981-6","volume":"23","author":"A Padalkin","year":"2024","unstructured":"Padalkin, A., Scheideler, C., & Warner, D. (2024). The structural power of reconfigurable circuits in the amoebot model. Natural Computing, 23(4), 603\u2013625.","journal-title":"Natural Computing"},{"doi-asserted-by":"crossref","unstructured":"Parada, I., Sacrist\u00e1n, V., & Silveira, R. I. (2016). A new meta-module for efficient reconfiguration of hinged-units modular robots. In ICRA (pp. 5197\u20135202). IEEE.","key":"10204_CR51","DOI":"10.1109\/ICRA.2016.7487726"},{"doi-asserted-by":"crossref","unstructured":"Romanishin, J., Gilpin, K., & Rus, D. (2013). M-blocks: Momentum-driven, magnetic modular robots. In IROS (pp. 4288\u20134295). IEEE.","key":"10204_CR52","DOI":"10.1109\/IROS.2013.6696971"},{"doi-asserted-by":"crossref","unstructured":"Rus, D., & Vona, M. (1999). Self-reconfiguration planning with compressible unit modules. In ICRA (pp. 2513\u20132520). IEEE Robotics and Automation Society","key":"10204_CR53","DOI":"10.1109\/ROBOT.1999.773975"},{"issue":"1","key":"10204_CR54","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1023\/A:1026504804984","volume":"10","author":"D Rus","year":"2001","unstructured":"Rus, D., & Vona, M. (2001). Crystalline robots: Self-reconfiguration with compressible unit modules. Autonomous Robots, 10(1), 107\u2013124.","journal-title":"Autonomous Robots"},{"issue":"7","key":"10204_CR55","doi-asserted-by":"publisher","first-page":"2281","DOI":"10.1016\/j.jfranklin.2011.05.022","volume":"349","author":"H Sadjadi","year":"2012","unstructured":"Sadjadi, H., Mohareri, O., Al-Jarrah, M. A., & Assaleh, K. (2012). Design and implementation of hexbot: A modular self-reconfigurable robotic system. Journal of the Franklin Institute, 349(7), 2281\u20132293.","journal-title":"Journal of the Franklin Institute"},{"issue":"6","key":"10204_CR56","doi-asserted-by":"publisher","first-page":"758","DOI":"10.1177\/0278364908099463","volume":"28","author":"J Sastra","year":"2009","unstructured":"Sastra, J., Chitta, S., & Yim, M. (2009). Dynamic rolling for a modular loop robot. The International Journal of Robotics Research, 28(6), 758\u2013773.","journal-title":"The International Journal of Robotics Research"},{"issue":"4","key":"10204_CR57","doi-asserted-by":"publisher","first-page":"12142","DOI":"10.1109\/LRA.2022.3213137","volume":"7","author":"Q Shao","year":"2022","unstructured":"Shao, Q., Dong, X., Lin, Z., Tang, C., Sun, H., Liu, X. J., & Zhao, H. (2022). Untethered robotic millipede driven by low-pressure microfluidic actuators for multi-terrain exploration. IEEE Robotics and Automation Letters, 7(4), 12142\u201312149.","journal-title":"IEEE Robotics and Automation Letters"},{"doi-asserted-by":"crossref","unstructured":"Suh, J. W., Homans, S. B., & Yim, M. (2002). Telecubes: Mechanical design of a module for self-reconfigurable robotics. In ICRA (pp. 4095\u20134101). IEEE","key":"10204_CR58","DOI":"10.1109\/ROBOT.2002.1014385"},{"doi-asserted-by":"crossref","unstructured":"Suzuki, Y., Inou, N., Koseki, M., & Kimura, H. (2008). Reconfigurable modular robots adaptively transforming a mechanical structure (numerical expression of transformation criteria of \u201cchobie ii\u201d and motion experiments). In DARS (pp. 393\u2013403). Springer.","key":"10204_CR59","DOI":"10.1007\/978-3-642-00644-9_35"},{"issue":"2","key":"10204_CR60","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1142\/S0129053393000086","volume":"5","author":"T Toffoli","year":"1993","unstructured":"Toffoli, T., & Margolus, N. (1993). Programmable matter: Concepts and realization. International Journal of High Speed Computing, 5(2), 155\u2013170.","journal-title":"International Journal of High Speed Computing"},{"doi-asserted-by":"crossref","unstructured":"Vassilvitskii, S., Kubica, J., Rieffel, E., Suh, J., & Yim, M. (2002a). On the general reconfiguration problem for expanding cube style modular robots. In ICRA (pp. 801\u2013808). IEEE","key":"10204_CR61","DOI":"10.1109\/ROBOT.2002.1013456"},{"doi-asserted-by":"crossref","unstructured":"Vassilvitskii, S., Yim, M., & Suh, J.W. (2002b). A complete, local and parallel reconfiguration algorithm for cube style modular robots. In ICRA (pp. 117\u2013122). IEEE.","key":"10204_CR62","DOI":"10.1109\/ROBOT.2002.1013348"},{"doi-asserted-by":"crossref","unstructured":"Weller, M. P., Kirby, B. T., Brown, H. B., Gross, M. D., & Goldstein, S. C. (2009). Design of prismatic cube modules for convex corner traversal in 3D. In IROS (pp. 1490\u20131495). IEEE.","key":"10204_CR63","DOI":"10.1109\/IROS.2009.5354320"},{"doi-asserted-by":"crossref","unstructured":"White, P. J., & Yim, M. (2007). Scalable modular self-reconfigurable robots using external actuation. In IROS (pp. 2773\u20132778). IEEE.","key":"10204_CR64","DOI":"10.1109\/IROS.2007.4399606"},{"doi-asserted-by":"crossref","unstructured":"Woods, D., Chen, H. L., Goodfriend, S., Dabby, N., Winfree, E., & Yin, P. (2013). Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In ITCS (pp. 353\u2013354). ACM.","key":"10204_CR65","DOI":"10.1145\/2422436.2422476"},{"doi-asserted-by":"crossref","unstructured":"Yim, M. (1994). New locomotion gaits. In ICRA (pp. 2508\u20132514). IEEE Computer Society.","key":"10204_CR66","DOI":"10.1109\/ROBOT.1994.351134"},{"doi-asserted-by":"crossref","unstructured":"Yim, M., Duff, D., & Roufas, K. (2000). Polybot: A modular reconfigurable robot. In ICRA (pp. 514\u2013520). IEEE.","key":"10204_CR67","DOI":"10.1109\/ROBOT.2000.844106"},{"issue":"2","key":"10204_CR68","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1109\/6.981854","volume":"39","author":"M Yim","year":"2002","unstructured":"Yim, M., Zhang, Y., & Duff, D. (2002). Modular robots. IEEE Spectrum, 39(2), 30\u201334.","journal-title":"IEEE Spectrum"},{"issue":"2\u20133","key":"10204_CR69","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1023\/A:1022287820808","volume":"14","author":"M Yim","year":"2003","unstructured":"Yim, M., Roufas, K., Duff, D., Zhang, Y., Eldershaw, C., & Homans, S. (2003). Modular reconfigurable robots in space applications. Autonomous Robots, 14(2\u20133), 225\u2013237.","journal-title":"Autonomous Robots"},{"doi-asserted-by":"crossref","unstructured":"Yim, M., White, P., Park, M., & Sastra, J. (2009). Modular self-reconfigurable robots. In Encyclopedia of Complexity and Systems Science (pp. 5618\u20135631). Springer.","key":"10204_CR70","DOI":"10.1007\/978-0-387-30440-3_334"},{"doi-asserted-by":"crossref","unstructured":"Yoshida, E., Murata, S., Kamimura, A., Tomita, K., Kurokawa, H., & Kokaji, S. (2003). Evolutionary synthesis of dynamic motion and reconfiguration process for a modular robot M-TRAN. In CIRA (pp. 1004\u20131010). IEEE.","key":"10204_CR71","DOI":"10.1109\/CIRA.2003.1222317"},{"doi-asserted-by":"crossref","unstructured":"Zhang, Y., Yim, M., Eldershaw, C., Duff, D., & Roufas, K. (2003). Scalable and reconfigurable configurations and locomotion gaits for chain-type modular reconfigurable robots. In CIRA (pp. 893\u2013899). IEEE.","key":"10204_CR72","DOI":"10.1109\/CIRA.2003.1222298"}],"container-title":["Autonomous Robots"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10514-025-10204-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10514-025-10204-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10514-025-10204-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T11:30:22Z","timestamp":1758972622000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10514-025-10204-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,23]]},"references-count":72,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10204"],"URL":"https:\/\/doi.org\/10.1007\/s10514-025-10204-9","relation":{},"ISSN":["0929-5593","1573-7527"],"issn-type":[{"type":"print","value":"0929-5593"},{"type":"electronic","value":"1573-7527"}],"subject":[],"published":{"date-parts":[[2025,8,23]]},"assertion":[{"value":"10 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 August 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"22"}}