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The controllers are decentralized in the sense that the robots do not need to exchange or know each other's state information. Instead, we assume that the robots have sensors allowing them to obtain information about relative positions of neighbors within a known range. We establish stability and convergence properties of the controllers for a certain class of simple closed curves. We illustrate our approach through simulations and consider extensions to more general planar curves.<\/jats:p>","DOI":"10.1017\/s0263574708004323","type":"journal-article","created":{"date-parts":[[2008,4,11]],"date-time":"2008-04-11T13:10:23Z","timestamp":1207919423000},"page":"691-701","source":"Crossref","is-referenced-by-count":137,"title":["Decentralized controllers for shape generation with robotic swarms"],"prefix":"10.1017","volume":"26","author":[{"given":"M. Ani","family":"Hsieh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vijay","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luiz","family":"Chaimowicz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,9,1]]},"reference":[{"key":"S0263574708004323_ref35","doi-asserted-by":"publisher","DOI":"10.1109\/70.163777"},{"key":"S0263574708004323_ref34","volume-title":"Differential Geometry of Curves and Surfaces","author":"do Carmo","year":"1976"},{"key":"S0263574708004323_ref32","unstructured":"32. Nabet B. and Leonard N. E. , \u201cShape Control of a Multi-agent System Using Tensegrity Structures,\u201d IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Nagoya, Japan (2006) pp. 329\u2013339."},{"key":"S0263574708004323_ref30","unstructured":"30. 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