{"id":"https://openalex.org/W1919563466","doi":"https://doi.org/10.1109/cdc.2003.1271708","title":"Steering laws and continuum models for planar formations","display_name":"Steering laws and continuum models for planar formations","publication_year":2004,"publication_date":"2004-04-23","ids":{"openalex":"https://openalex.org/W1919563466","doi":"https://doi.org/10.1109/cdc.2003.1271708","mag":"1919563466"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2003.1271708","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2003.1271708","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5077434413","display_name":"Eric W. Justh","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E.W. Justh","raw_affiliation_strings":["Institute for Systems Research, University of Maryland, College Park, MD, USA","Inst. for Syst. Res., Maryland Univ., College Park, MD, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Research, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Inst. for Syst. Res., Maryland Univ., College Park, MD, USA#TAB#","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103154670","display_name":"P. S. Krishnaprasad","orcid":"https://orcid.org/0000-0003-4557-158X"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P.S. Krishnaprasad","raw_affiliation_strings":["Institute for Systems Research and Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA","University of Maryland, College Park"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Systems Research and Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"University of Maryland, College Park","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":4.3423,"has_fulltext":false,"cited_by_count":89,"citation_normalized_percentile":{"value":0.95181601,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"3609","last_page":"3614"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9991000294685364,"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":0.9991000294685364,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9825000166893005,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9812999963760376,"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/lyapunov-function","display_name":"Lyapunov function","score":0.6508240699768066},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6254751682281494},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5743735432624817},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5697395205497742},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.5282389521598816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48935312032699585},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.47809574007987976},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4527474045753479},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.44695693254470825},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.44276756048202515},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.410230815410614},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3905639052391052},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3849417567253113},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.36330753564834595},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3134396970272064},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2897532880306244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2620023488998413},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18107491731643677},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.14249420166015625},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12005403637886047},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11339670419692993}],"concepts":[{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6508240699768066},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6254751682281494},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5743735432624817},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5697395205497742},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5282389521598816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48935312032699585},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.47809574007987976},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4527474045753479},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.44695693254470825},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.44276756048202515},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.410230815410614},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3905639052391052},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3849417567253113},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.36330753564834595},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3134396970272064},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2897532880306244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2620023488998413},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18107491731643677},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.14249420166015625},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12005403637886047},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11339670419692993},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2003.1271708","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2003.1271708","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.392.6826","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.392.6826","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isr.umd.edu/Labs/ISL/BAIL/JusthKrishnaCDC03_1609.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.75,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1533117844","https://openalex.org/W1540059687","https://openalex.org/W1584141004","https://openalex.org/W1805843217","https://openalex.org/W1837437011","https://openalex.org/W1978040684","https://openalex.org/W2015410655","https://openalex.org/W2026892575","https://openalex.org/W2029364999","https://openalex.org/W2049817674","https://openalex.org/W2060203271","https://openalex.org/W2089724372","https://openalex.org/W2130647107","https://openalex.org/W2152916654","https://openalex.org/W2165744313","https://openalex.org/W2176984061","https://openalex.org/W2565631288","https://openalex.org/W4235548700","https://openalex.org/W4241590110","https://openalex.org/W6631817498","https://openalex.org/W6634990043","https://openalex.org/W6638170506","https://openalex.org/W6638704798"],"related_works":["https://openalex.org/W2901496727","https://openalex.org/W3048854954","https://openalex.org/W4296944280","https://openalex.org/W3128450063","https://openalex.org/W2002590892","https://openalex.org/W2952839596","https://openalex.org/W1983947117","https://openalex.org/W1982525352","https://openalex.org/W2084224265","https://openalex.org/W2105113683"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,66,77,87],"Lie":[3,43],"group":[4,44,68],"formulation":[5,103],"for":[6,34,58,69,80,91],"the":[7,18,26,51,70,105],"problem":[8],"of":[9,11,22,28,53,104],"control":[10,71],"formations.":[12],"Vehicle":[13],"trajectories":[14],"are":[15],"described":[16],"using":[17,86],"planar":[19],"Frenet-Serret":[20],"equations":[21,107],"motion,":[23],"which":[24,90],"capture":[25],"evolution":[27],"both":[29],"vehicle":[30],"position":[31],"and":[32],"orientation":[33],"unit-speed":[35],"motion":[36],"subject":[37],"to":[38,49,97],"curvature":[39,61],"(steering)":[40],"control.":[41],"The":[42,73],"structure":[45],"can":[46],"be":[47],"exploited":[48],"determine":[50],"set":[52],"all":[54],"possible":[55],"(relative)":[56],"equilibria":[57],"arbitrary":[59],"G-invariant":[60],"controls,":[62],"where":[63],"G=SE(2)":[64],"is":[65,76,108],"symmetry":[67],"law.":[72],"main":[74],"result":[75,79],"convergence":[78],"n":[81],"vehicles":[82],"(for":[83],"finite":[84],"n),":[85],"Lyapunov":[88],"function":[89],"n=2,":[92],"has":[93],"been":[94],"previously":[95],"shown":[96],"yield":[98],"global":[99],"convergence.":[100],"A":[101],"continuum":[102],"basic":[106],"also":[109],"presented.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":9}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
