{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T11:04:08Z","timestamp":1790247848486,"version":"4.1.0"},"reference-count":24,"publisher":"Emerald","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,10,12]]},"abstract":"<jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>Rigidity of formation is an important concept in multi-agent localization and control problems. The purpose of this paper is to design the control laws to enable the group to asymptotically exhibit the flocking motion while preserving the network rigidity at all times.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Design\/methodology\/approach<\/jats:title>\n                    <jats:p>The novel approach for designing control laws is derived from a smooth artificial potential function based on an undirected infinitesimally rigid formation which specifies the target formation. Then the potential function is used to specify a gradient control law, under which the original system then becomes an orderly infinitesimally rigid formation.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Findings<\/jats:title>\n                    <jats:p>The strong relationship between the stability of the target formation and the gradient control protocol are utilized to design the control laws which can be proved to make the target formation stable. However, the rigidity matrix is not utilized in the design of control law. Future research will mainly focus on formation control with the relationship of rigidity matrix.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Originality\/value<\/jats:title>\n                    <jats:p>The value of this paper is focused on the control laws design and the control laws could enable the group to asymptotically exhibit the flocking motion while preserving the network rigidity at all times. Also the detailed simulations and experiments are given to prove that the novel approach is available.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1108\/03684921211276819","type":"journal-article","created":{"date-parts":[[2013,3,25]],"date-time":"2013-03-25T14:02:45Z","timestamp":1364220165000},"page":"1650-1661","source":"Crossref","is-referenced-by-count":7,"title":["Distributed rigid formation control algorithm for multi-agent systems"],"prefix":"10.1108","volume":"41","author":[{"given":"Hu","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Institute of Technology, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongqiang","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Institute of Technology, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huagang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Automation, Beijing Institute of Technology, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"140","reference":[{"issue":"6","key":"2026092406170331200_b1","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1109\/MCS.2008.929280","article-title":"Rigid graph control architectures for autonomous formations","volume":"28","author":"Anderson","year":"2008","journal-title":"IEEE Control Systems Magazine"},{"key":"2026092406170331200_b2","doi-asserted-by":"crossref","unstructured":"Asimow, L.\n           and Roth, B. (1978), \u201cRigidity of graphs\u201d, Transactions of the American Mathematical Society, Vol. 245, pp. 279-89.","DOI":"10.1090\/S0002-9947-1978-0511410-9"},{"issue":"12","key":"2026092406170331200_b4","doi-asserted-by":"crossref","first-page":"1663","DOI":"10.1109\/TMC.2006.174","article-title":"A theory of network localization","volume":"5","author":"Aspnes","year":"2006","journal-title":"IEEE Transactions on Mobile Computing"},{"issue":"3","key":"2026092406170331200_b5","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1016\/j.automatica.2007.07.022","article-title":"Distributed algorithms for reaching consensus on general functions","volume":"44","author":"Cortes","year":"2008","journal-title":"Automatica"},{"key":"2026092406170331200_b6","doi-asserted-by":"crossref","unstructured":"Dimarogonas, D.V.\n           and Johansson, K.H. (2008), \u201cOn the stability of distance based formation control\u201d, Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, pp. 1200-5.","DOI":"10.1109\/CDC.2008.4739215"},{"key":"2026092406170331200_b7","doi-asserted-by":"crossref","unstructured":"Dimarogonas, D.V.\n           and Johansson, K.H. (2009), \u201cFurther results on the stability of distance-based multi-robot formations\u201d, American Control Conference, St Louis, MO, pp. 2972-7.","DOI":"10.1109\/ACC.2009.5160238"},{"issue":"1","key":"2026092406170331200_b8","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1108\/03684920110363860","article-title":"The genic agent: a hybrid approach for multi-agent problem solving","volume":"30","author":"Emilie","year":"2001","journal-title":"Kybernetes"},{"key":"2026092406170331200_b9","doi-asserted-by":"crossref","unstructured":"Fang, J.\n           and Morse, A. (2008), \u201cNetwork localization using graph decomposition and rigidity\u201d, Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, pp. 1091-6.","DOI":"10.1109\/CDC.2008.4738795"},{"issue":"2","key":"2026092406170331200_b10","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1049\/iet-cta:20050409","article-title":"Acquiring and maintaining persistence of autonomous multi-vehicle formations","volume":"1","author":"Fidan","year":"2007","journal-title":"IET Control Theory and Applications"},{"issue":"5","key":"2026092406170331200_b11","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1108\/03684920610662403","article-title":"Mobile agent system framework suitable for scalable networks","volume":"35","author":"Francisco","year":"2006","journal-title":"Kybernetes"},{"key":"2026092406170331200_b12","doi-asserted-by":"crossref","unstructured":"Hur, H.\n           and Ahn, H. (2010), Active Localization in Distributed Networks: A Framework, Control Automation and Systems (ICCAS), Gyeonggi-do, pp. 1586-91.","DOI":"10.1109\/ICCAS.2010.5669676"},{"issue":"1","key":"2026092406170331200_b13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jctb.2004.11.002","article-title":"Connected rigidity mastoids and unique realizations of graphs","volume":"94","author":"Jackson","year":"2005","journal-title":"Journal of Combinatorial Theory, Series B"},{"key":"2026092406170331200_b14","doi-asserted-by":"crossref","unstructured":"Krick, L.\n          , Broucke, M.E. and Francis, B.A. (2008), \u201cStabilization of infinitesimally rigid formations of multi-robot networks\u201d, Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, pp. 477-82.","DOI":"10.1109\/CDC.2008.4738760"},{"key":"2026092406170331200_b15","doi-asserted-by":"crossref","unstructured":"Laman, G.\n           (1970), \u201cOn graphs and the rigidity of plane skeletal structures\u201d, Journal of Engineering Mathematics, Vol. 4, pp. 331-40.","DOI":"10.1007\/BF01534980"},{"key":"2026092406170331200_b16","unstructured":"Lee, D.\n           and Spong, M. (2006), \u201cStable flocking of inertial agents on balanced communication graphs\u201d, Proceedings of the American Control Conference 2006, Minneapolis, MN, pp. 2136-41."},{"issue":"3","key":"2026092406170331200_b17","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/TAC.2005.864190","article-title":"Flocking for multi-agent dynamic systems: algorithms and theory","volume":"51","author":"Olfati-Saber","year":"2006","journal-title":"IEEE Transactions on Automatic Control"},{"key":"2026092406170331200_b18","doi-asserted-by":"crossref","unstructured":"Olfati-Saber, R.\n           and Murray, R. (2002), \u201cGraph rigidity and distributed formation stabilization of multi-vehicle systems\u201d, Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, USA, pp. 2965-71.","DOI":"10.1109\/CDC.2002.1184307"},{"key":"2026092406170331200_b19","doi-asserted-by":"crossref","unstructured":"Schneider, F.E.\n           and Wildermuth, D. (2005), \u201cExperimental comparison of a directed and a nondirected potential field approach to formation navigation\u201d, Proceedings of IEEE International Symposium on Computational Intelligence in Robotics and Automation, Espoo, Finland, pp. 21-6.","DOI":"10.1109\/CIRA.2005.1554249"},{"key":"2026092406170331200_b20","doi-asserted-by":"crossref","unstructured":"Tanner, H.G.\n          , Jadbabaie, A. and Pappas, G.J. (2003a), \u201cStable flocking of mobile agents, part I: fixed topology\u201d, Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, pp. 2010-15.","DOI":"10.1109\/CDC.2003.1272910"},{"key":"2026092406170331200_b21","doi-asserted-by":"crossref","unstructured":"Tanner, H.G.\n          , Jadbabaie, A. and Pappas, G.J. (2003b), \u201cStable flocking of mobile agents, part II: dynamic topology\u201d, Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, pp. 2016-21.","DOI":"10.1109\/CDC.2003.1272911"},{"issue":"8","key":"2026092406170331200_b22","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1108\/03684921011063592","article-title":"Multi-robot object tracking and docking systems based on networked control frames","volume":"39","author":"Wen","year":"2010","journal-title":"Kybernetes"},{"key":"2026092406170331200_b23","doi-asserted-by":"crossref","unstructured":"Zhang, F.\n           and Leonard, N.E. (2006), \u201cCoordinated patterns on smooth curves\u201d, Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, Fort Lauderdale, FL, USA, pp. 434-9.","DOI":"10.1109\/ICNSC.2006.1673185"},{"key":"2026092406170331200_b24","doi-asserted-by":"crossref","unstructured":"Zhu, G.\n           and Hu, J. (2009), \u201cStiffness matrix and quantitative measure of formation rigidity\u201d, Proceeding of the 48th IEEE Conference on Decision and Control, Shanghai, China, pp. 3057-61.","DOI":"10.1109\/CDC.2009.5400387"},{"issue":"1","key":"2026092406170331200_frd1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0022-247X(79)90108-2","article-title":"The rigidity of graphs, II","volume":"68","author":"Asimow","year":"1979","journal-title":"Journal of Mathematical Analysis and Applications"}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/03684921211276819","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684921211276819\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/k\/article-pdf\/41\/10\/1650\/1840227\/03684921211276819.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/k\/article-pdf\/41\/10\/1650\/1840227\/03684921211276819.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T10:17:13Z","timestamp":1790245033000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/k\/article\/41\/10\/1650\/273223\/Distributed-rigid-formation-control-algorithm-for"}},"subtitle":[],"editor":[{"given":"Desheng","family":"Dash Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2012,10,12]]},"references-count":24,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2012,10,12]]}},"URL":"https:\/\/doi.org\/10.1108\/03684921211276819","relation":{},"ISSN":["0368-492X","1758-7883"],"issn-type":[{"value":"0368-492X","type":"print"},{"value":"1758-7883","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,12]]}}}