{"id":"https://openalex.org/W2138296912","doi":"https://doi.org/10.1080/00207170802108441","title":"Stabilisation of infinitesimally rigid formations of multi-robot networks","display_name":"Stabilisation of infinitesimally rigid formations of multi-robot networks","publication_year":2008,"publication_date":"2008-12-08","ids":{"openalex":"https://openalex.org/W2138296912","doi":"https://doi.org/10.1080/00207170802108441","mag":"2138296912"},"language":"en","primary_location":{"id":"doi:10.1080/00207170802108441","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170802108441","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024544170","display_name":"Laura Krick","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Laura Krick","raw_affiliation_strings":["a Edward S. Rogers Sr. Department of Electrical and Computer Engineering , University of Toronto , Toronto, Canada","Edward S. Rogers Sr.Department of Electrical and Computer Engineering, University of Toronto, Toronto, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"a Edward S. Rogers Sr. Department of Electrical and Computer Engineering , University of Toronto , Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Edward S. Rogers Sr.Department of Electrical and Computer Engineering, University of Toronto, Toronto, Canada#TAB#","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016807277","display_name":"Mireille E. Broucke","orcid":"https://orcid.org/0000-0001-8275-3716"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Mireille E. Broucke","raw_affiliation_strings":["a Edward S. Rogers Sr. Department of Electrical and Computer Engineering , University of Toronto , Toronto, Canada","Edward S. Rogers Sr.Department of Electrical and Computer Engineering, University of Toronto, Toronto, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"a Edward S. Rogers Sr. Department of Electrical and Computer Engineering , University of Toronto , Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Edward S. Rogers Sr.Department of Electrical and Computer Engineering, University of Toronto, Toronto, Canada#TAB#","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103692639","display_name":"Bruce A. Francis","orcid":null},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bruce A. Francis","raw_affiliation_strings":["a Edward S. Rogers Sr. Department of Electrical and Computer Engineering , University of Toronto , Toronto, Canada","Edward S. Rogers Sr.Department of Electrical and Computer Engineering, University of Toronto, Toronto, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"a Edward S. Rogers Sr. Department of Electrical and Computer Engineering , University of Toronto , Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Edward S. Rogers Sr.Department of Electrical and Computer Engineering, University of Toronto, Toronto, Canada#TAB#","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016807277"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":18.4871,"has_fulltext":false,"cited_by_count":546,"citation_normalized_percentile":{"value":0.99372183,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"82","issue":"3","first_page":"423","last_page":"439"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9753999710083008,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.972000002861023,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.8330053091049194},{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.6527523994445801},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5675289034843445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5021371841430664},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49009573459625244},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.4429767429828644},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4264720380306244},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.425496369600296},{"id":"https://openalex.org/keywords/polygon","display_name":"Polygon (computer graphics)","score":0.4198572337627411},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.41676628589630127},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.385686457157135},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3349058926105499},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.25540369749069214},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23624151945114136},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2176072597503662},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1779630482196808},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13505181670188904}],"concepts":[{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.8330053091049194},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.6527523994445801},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5675289034843445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5021371841430664},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49009573459625244},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.4429767429828644},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4264720380306244},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.425496369600296},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.4198572337627411},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.41676628589630127},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.385686457157135},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3349058926105499},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.25540369749069214},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23624151945114136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2176072597503662},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1779630482196808},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13505181670188904},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207170802108441","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170802108441","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1509448450","https://openalex.org/W1515707356","https://openalex.org/W1561704653","https://openalex.org/W1574347413","https://openalex.org/W1964537835","https://openalex.org/W1983176609","https://openalex.org/W2002347650","https://openalex.org/W2008995486","https://openalex.org/W2027312585","https://openalex.org/W2053741158","https://openalex.org/W2066603407","https://openalex.org/W2067461601","https://openalex.org/W2099660631","https://openalex.org/W2105039030","https://openalex.org/W2105850748","https://openalex.org/W2111638077","https://openalex.org/W2137642864","https://openalex.org/W2140947684","https://openalex.org/W2167485994","https://openalex.org/W2487739765","https://openalex.org/W2623837311","https://openalex.org/W3005347161","https://openalex.org/W4213264637","https://openalex.org/W4243082658","https://openalex.org/W4249151328","https://openalex.org/W4294967943"],"related_works":["https://openalex.org/W2370598571","https://openalex.org/W2355499472","https://openalex.org/W2349230259","https://openalex.org/W2948176890","https://openalex.org/W1827844156","https://openalex.org/W2068360468","https://openalex.org/W2201246509","https://openalex.org/W2599583908","https://openalex.org/W4302569442","https://openalex.org/W2949837591"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"article":[2],"considers":[3],"the":[4,35,44,56,65,83,90,93,109,146,156,162],"design":[5],"of":[6,62,82,89,92,158],"a":[7,23,48,60,75,126],"formation":[8,58,96],"control":[9,19,50],"for":[10,64,78,101,125],"multivehicle":[11,66],"systems":[12],"that":[13,33,71],"uses":[14],"only":[15],"local":[16,79],"information.":[17],"The":[18,120,136],"is":[20,41,51,69,74,97,111,140],"derived":[21],"from":[22,43,46],"potential":[24,39],"function":[25,40],"based":[26],"on":[27,129],"an":[28,151],"undirected":[29],"infinitesimally":[30],"rigid":[31],"graph":[32],"specifies":[34],"target":[36,57],"formation.":[37],"A":[38,86],"obtained":[42],"graph,":[45],"which":[47],"gradient":[49],"derived.":[52],"Under":[53],"this":[54],"controller":[55,110],"becomes":[59],"manifold":[61,131],"equilibria":[63],"system.":[67],"It":[68],"shown":[70],"infinitesimal":[72],"rigidity":[73,118],"sufficient":[76],"condition":[77],"asymptotical":[80],"stability":[81,91],"equilibrium":[84],"manifold.":[85],"complete":[87],"study":[88],"regular":[94],"polygon":[95],"presented":[98,105],"and":[99,149],"results":[100],"directed":[102],"graphs":[103],"are":[104],"as":[106,150],"well.":[107],"Finally,":[108],"validated":[112],"experimentally.":[113],"Keywords:":[114],"cooperative":[115],"controlmultiagent":[116],"formationsgraph":[117],"Acknowledgements":[119],"authors":[121],"thank":[122],"Manfredi":[123],"Maggiore":[124],"helpful":[127],"discussion":[128],"centre":[130],"theory.":[132],"Notes":[133],"Note":[134],"1.":[135],"notation":[137],"e":[138],"i":[139,148,160],"used":[141],"to":[142,145],"refer":[143],"both":[144],"edge":[147,159],"error":[152],"vector":[153],"pointing":[154],"in":[155,161],"direction":[157],"framework.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":31},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":26},{"year":2021,"cited_by_count":30},{"year":2020,"cited_by_count":33},{"year":2019,"cited_by_count":48},{"year":2018,"cited_by_count":68},{"year":2017,"cited_by_count":51},{"year":2016,"cited_by_count":46},{"year":2015,"cited_by_count":45},{"year":2014,"cited_by_count":34},{"year":2013,"cited_by_count":30},{"year":2012,"cited_by_count":17}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}