{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T19:16:09Z","timestamp":1789586169577,"version":"build-2803163510"},"reference-count":17,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,3,12]],"date-time":"2015-03-12T00:00:00Z","timestamp":1426118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Institut Mines Telecom","award":["Futur et Ruptures"],"award-info":[{"award-number":["Futur et Ruptures"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We present an application of distributed consensus algorithms to metamorphic systems. A metamorphic system is a set of identical units that can self-assemble to form a rigid structure. For instance, one can think of a robotic arm composed of multiple links connected by joints. The system can change its shape in order to adapt to different environments via reconfiguration of its constituting units. We assume in this work that several metamorphic systems form a network: two systems are connected whenever they are able to communicate with each other. The aim of this paper is to propose a distributed algorithm that synchronizes all of the systems in the network. Synchronizing means that all of the systems should end up having the same configuration. This aim is achieved in two steps: (i) we cast the problem as a consensus problem on a metric space; and (ii) we use a recent distributed consensus algorithm that only makes use of metrical notions.<\/jats:p>","DOI":"10.3390\/e17031165","type":"journal-article","created":{"date-parts":[[2015,3,12]],"date-time":"2015-03-12T11:30:24Z","timestamp":1426159824000},"page":"1165-1180","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Distributed Consensus for Metamorphic Systems Using a GossipAlgorithm for CAT(0) Metric Spaces"],"prefix":"10.3390","volume":"17","author":[{"given":"Anass","family":"Bellachehab","sequence":"first","affiliation":[{"name":"Telecom SudParis, Institut Mines-T\u00e9l\u00e9com, UMR CNRS 5157 SAMOVAR, 9 Rue Charles Fourier, 91000 \u00c9vry, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Dashchenko, A. 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Max-Consensus in a Max-Plus Algebraic Setting: The Case of Fixed Communication Topologies, Sarajevo, Bosnia and Herzegovina.","DOI":"10.1109\/ICAT.2009.5348437"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1177\/0278364904045468","article-title":"State complexes for metamorphic robots","volume":"23","author":"Abrams","year":"2004","journal-title":"Int. J. Robot. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.aam.2005.08.009","article-title":"The geometry and topology of reconfiguration","volume":"38","author":"Ghrist","year":"2007","journal-title":"Adv. Appl. Math."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bellachehab, A., and Jakubowicz, J. (Random Pairwise Gossip on CAT (\u03ba) Metric Spaces, 2014). Random Pairwise Gossip on CAT (\u03ba) Metric Spaces, arXiv preprint arXiv:1405.4190.","DOI":"10.1109\/CDC.2014.7040264"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s10514-006-8546-1","article-title":"Design of the ATRON lattice-based self-reconfigurable robot","volume":"21","author":"Kassow","year":"2006","journal-title":"Auton. Robots."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bacak, M. (2014). Convex Analysis and Optimization in Hadamard Spaces, De Gruyter.","DOI":"10.1515\/9783110361629"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Jost, J. (1997). Nonpositive Curvature: Geometric and Analytic Aspects, ETH Zurich; Springer.","DOI":"10.1007\/978-3-0348-8918-6"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.aam.2011.06.004","article-title":"Geodesics in CAT (0) cubical complexes","volume":"48","author":"Ardila","year":"2012","journal-title":"Adv. Appl. Math."},{"key":"ref_15","unstructured":"Grohs, P. (2012). Wolfowitz\u2019s Theorem and Convergence of Consensus Algorithms in Hadamard Spaces, ETH."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1137\/140953393","article-title":"Computing medians and means in Hadamard spaces","volume":"24","author":"Bacak","year":"2014","journal-title":"SIAM J. Optim."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bridson, M., and Haefliger, A. (1999). Metric Spaces of Non-Positive Curvature, Springer.","DOI":"10.1007\/978-3-662-12494-9"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/3\/1165\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:43:25Z","timestamp":1760215405000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/3\/1165"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,12]]},"references-count":17,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,3]]}},"alternative-id":["e17031165"],"URL":"https:\/\/doi.org\/10.3390\/e17031165","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,12]]}}}