{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T10:00:18Z","timestamp":1777716018567,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"7-8","license":[{"start":{"date-parts":[[2004,8,1]],"date-time":"2004-08-01T00:00:00Z","timestamp":1091318400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2004,8]]},"abstract":"<jats:p>A metamorphic robotic system is an aggregate of homogeneous robot units which can individually and selectively locomote in such a way as to change the global shape of the system. We introduce a mathematical framework for defining and analyzing general metamorphic robots. With this formal structure, combined with ideas from geometric group theory, we define a new type of configuration space for metamorphic robots\u2014the state complex\u2014which is especially adapted to parallelization. We present an algorithm for optimizing an input reconfiguration sequence with respect to elapsed time. A universal geometric property of state complexes\u2014non-positive curvature\u2014is the key to proving convergence to the globally timeoptimal solution obtainable from the initial path.<\/jats:p>","DOI":"10.1177\/0278364904045468","type":"journal-article","created":{"date-parts":[[2004,9,13]],"date-time":"2004-09-13T20:12:22Z","timestamp":1095106342000},"page":"811-826","source":"Crossref","is-referenced-by-count":34,"title":["State Complexes for Metamorphic Robots"],"prefix":"10.1177","volume":"23","author":[{"given":"A.","family":"Abrams","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Georgia, Athens, GA 30602, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Ghrist","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Illinois, Urbana, IL 61801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2004,8,1]]},"reference":[{"key":"atypb1","unstructured":"Abrams, A. 2000.\n                      Configuration Spaces and Braid Groups of Graphs\n                      , PhD thesis, UC Berkeley."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019662529807"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"Abrams, A. and Ghrist, R. 2002. Finding topology in a factory: configuration spaces . American Mathematics Monthly(109): 140\u2013150 .","DOI":"10.1080\/00029890.2002.11919847"},{"key":"atypb4","unstructured":"Abrams, A. and Ghrist, R. 2004. The geometry and topology of reconfiguration, in press."},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"Bridson, M. and Haefliger, A. 1999. Metric Spaces of Non- Positive Curvature, Springer-Verlag, Berlin .","DOI":"10.1007\/978-3-662-12494-9"},{"key":"atypb6","unstructured":"Butler, Z., Byrnes, S., and Rus, D. 2001. Distributed motion planning for modular robots with unit-compressible modules . Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, Hawaii."},{"key":"atypb7","unstructured":"Butler, Z., Kotay, K., Rus, D., and Tomita, K. 2001. Cellular automata for decentralized control of self-reconfigurable robots . 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