{"id":"https://openalex.org/W2049080811","doi":"https://doi.org/10.1017/s0263574703005460","title":"Tracking a joint path for the walk of an underactuated biped","display_name":"Tracking a joint path for the walk of an underactuated biped","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2049080811","doi":"https://doi.org/10.1017/s0263574703005460","mag":"2049080811"},"language":"en","primary_location":{"id":"doi:10.1017/s0263574703005460","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574703005460","pdf_url":null,"source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","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/A5053183805","display_name":"Christine Chevallereau","orcid":"https://orcid.org/0000-0002-1929-5211"},"institutions":[{"id":"https://openalex.org/I4210109587","display_name":"Laboratoire de Thermique et Energie de Nantes","ror":"https://ror.org/021fdyt09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210109587","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christine Chevallereau","raw_affiliation_strings":["Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, BP 92101, 1 rue de la No\u00eb, 44321 Nantes Cedex 03 (France). E-mail:","Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, BP 92101, 1 rue de la No\u00eb, 44321 Nantes Cedex 03 (France). E-mail: Christine.Chevallereau@irccyn.ec.nantes.fr. Website: ...#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, BP 92101, 1 rue de la No\u00eb, 44321 Nantes Cedex 03 (France). E-mail:","institution_ids":["https://openalex.org/I4210109587"]},{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, BP 92101, 1 rue de la No\u00eb, 44321 Nantes Cedex 03 (France). E-mail: Christine.Chevallereau@irccyn.ec.nantes.fr. Website: ...#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073025044","display_name":"A. Formal\u2019sky","orcid":null},"institutions":[{"id":"https://openalex.org/I4210150146","display_name":"Moscow State University","ror":"https://ror.org/050a13t43","country_code":"TJ","type":"education","lineage":["https://openalex.org/I4210150146"]}],"countries":["TJ"],"is_corresponding":false,"raw_author_name":"Alexander Formal'sky","raw_affiliation_strings":["Institute of Mechanics, Moscow State Lomonosov University, 1, Michurinsky Prospect, Moscow 119899 (Russia). E-mail:","Institute of Mechanics, Moscow State Lomonosov University, 1, Michurinsky Prospect, Moscow 119899 (Russia). E-mail: formal@imec.msu.ru#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mechanics, Moscow State Lomonosov University, 1, Michurinsky Prospect, Moscow 119899 (Russia). E-mail:","institution_ids":["https://openalex.org/I4210150146"]},{"raw_affiliation_string":"Institute of Mechanics, Moscow State Lomonosov University, 1, Michurinsky Prospect, Moscow 119899 (Russia). E-mail: formal@imec.msu.ru#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015035263","display_name":"D. Djoudi","orcid":"https://orcid.org/0000-0002-5905-2740"},"institutions":[{"id":"https://openalex.org/I4210109587","display_name":"Laboratoire de Thermique et Energie de Nantes","ror":"https://ror.org/021fdyt09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210109587","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dalila Djoudi","raw_affiliation_strings":["Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, BP 92101, 1 rue de la No\u00eb, 44321 Nantes Cedex 03 (France","Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, BP 92101, 1 rue de la No\u00eb, 44321 Nantes Cedex 03  (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, BP 92101, 1 rue de la No\u00eb, 44321 Nantes Cedex 03 (France","institution_ids":["https://openalex.org/I4210109587"]},{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, BP 92101, 1 rue de la No\u00eb, 44321 Nantes Cedex 03  (France)","institution_ids":["https://openalex.org/I4210109587"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.6483,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.97637921,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"1","first_page":"15","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":1.0,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9977999925613403,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.984000027179718,"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/control-theory","display_name":"Control theory (sociology)","score":0.7543922662734985},{"id":"https://openalex.org/keywords/underactuation","display_name":"Underactuation","score":0.7473925948143005},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6501738429069519},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.6463695168495178},{"id":"https://openalex.org/keywords/inverted-pendulum","display_name":"Inverted pendulum","score":0.5444172620773315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5265576839447021},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.5183042883872986},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.49270322918891907},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.482852041721344},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4542269706726074},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4538291096687317},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36030614376068115},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2831510901451111},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.28182122111320496},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15803518891334534},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14552128314971924}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7543922662734985},{"id":"https://openalex.org/C88337583","wikidata":"https://www.wikidata.org/wiki/Q7883433","display_name":"Underactuation","level":3,"score":0.7473925948143005},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6501738429069519},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.6463695168495178},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.5444172620773315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5265576839447021},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.5183042883872986},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.49270322918891907},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.482852041721344},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4542269706726074},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4538291096687317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36030614376068115},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2831510901451111},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.28182122111320496},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15803518891334534},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14552128314971924},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","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},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0263574703005460","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574703005460","pdf_url":null,"source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8100000023841858,"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":10,"referenced_works":["https://openalex.org/W144649418","https://openalex.org/W1902344385","https://openalex.org/W1982961388","https://openalex.org/W1990353179","https://openalex.org/W1995551113","https://openalex.org/W2112829158","https://openalex.org/W2134619701","https://openalex.org/W2136605942","https://openalex.org/W2137547873","https://openalex.org/W2143804149"],"related_works":["https://openalex.org/W587013945","https://openalex.org/W4288862394","https://openalex.org/W1485310626","https://openalex.org/W33907905","https://openalex.org/W4292915238","https://openalex.org/W4285553839","https://openalex.org/W3011477119","https://openalex.org/W2371440471","https://openalex.org/W2075135955","https://openalex.org/W962423920"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,10,23,45,69,73,78,90,115,130],"control":[4,39],"law":[5,40],"for":[6],"the":[7,34,49,53,60,101,112,127,134,146],"tracking":[8,103],"of":[9,29,52,81,93,114,120,129],"cyclic":[11,131],"reference":[12,147],"path":[13,75],"by":[14],"an":[15],"under-actuated":[16],"biped":[17,54,83],"robot.":[18],"The":[19,27,38,97,150],"robot":[20],"studied":[21],"is":[22,31,41,56,76,104],"five-link":[24],"planar":[25],"biped.":[26],"degree":[28,80,92,119],"under-actuation":[30],"one":[32,91,118],"during":[33,100],"single":[35,85],"support":[36,86],"phase.":[37],"defined":[42,106,144],"in":[43,84],"such":[44],"way":[46],"that":[47],"only":[48],"geometric":[50,102],"evolution":[51,99],"configuration":[55],"controlled,":[57],"but":[58],"not":[59],"temporal":[61,98],"evolution.":[62],"To":[63],"achieve":[64],"this":[65,137],"objective,":[66],"we":[67],"consider":[68],"parametrized":[70],"control.":[71],"When":[72],"joint":[74],"given,":[77],"five":[79],"freedom":[82,94],"becomes":[87],"similar":[88],"to":[89],"inverted":[95],"pendulum.":[96],"completely":[105],"and":[107,133],"can":[108],"be":[109],"analyzed":[110],"through":[111],"study":[113],"model":[116],"with":[117,155],"freedom.":[121],"Simple":[122],"analytical":[123,151],"conditions,":[124],"which":[125],"guarantee":[126],"existence":[128],"motion":[132],"convergence":[135],"towards":[136],"motion,":[138],"are":[139,143,153],"deduced.":[140],"These":[141],"conditions":[142],"on":[145],"trajectory":[148],"path.":[149],"considerations":[152],"illustrated":[154],"some":[156],"simulation":[157],"results.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}