{"id":"https://openalex.org/W3039104684","doi":"https://doi.org/10.1109/lcsys.2020.3006963","title":"Coupled Control Systems: Periodic Orbit Generation With Application to Quadrupedal Locomotion","display_name":"Coupled Control Systems: Periodic Orbit Generation With Application to Quadrupedal Locomotion","publication_year":2020,"publication_date":"2020-07-03","ids":{"openalex":"https://openalex.org/W3039104684","doi":"https://doi.org/10.1109/lcsys.2020.3006963","mag":"3039104684"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2020.3006963","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2020.3006963","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","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/A5101641007","display_name":"Wen-Loong Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wen-Loong Ma","raw_affiliation_strings":["Department of Mechanical Engineering, and Control+Dynamical Systems, California Institute of Technology, Pasadena, USA"],"raw_orcid":"https://orcid.org/0000-0002-0115-5632","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, and Control+Dynamical Systems, California Institute of Technology, Pasadena, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064460951","display_name":"Noel Csomay-Shanklin","orcid":"https://orcid.org/0000-0002-2361-1694"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Noel Csomay-Shanklin","raw_affiliation_strings":["Department of Mechanical Engineering, and Control+Dynamical Systems, California Institute of Technology, Pasadena, USA"],"raw_orcid":"https://orcid.org/0000-0002-2361-1694","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, and Control+Dynamical Systems, California Institute of Technology, Pasadena, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039171820","display_name":"Aaron D. Ames","orcid":"https://orcid.org/0000-0003-0848-3177"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaron D. Ames","raw_affiliation_strings":["Department of Mechanical Engineering, and Control+Dynamical Systems, California Institute of Technology, Pasadena, USA"],"raw_orcid":"https://orcid.org/0000-0003-0848-3177","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, and Control+Dynamical Systems, California Institute of Technology, Pasadena, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7842,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.68485687,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"5","issue":"3","first_page":"935","last_page":"940"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9991000294685364,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9983000159263611,"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/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.6780596971511841},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6570771932601929},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5651327967643738},{"id":"https://openalex.org/keywords/holonomic-constraints","display_name":"Holonomic constraints","score":0.5501986145973206},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5351403951644897},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5057103633880615},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.469490110874176},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.37388497591018677},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2702091634273529},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25900593400001526},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17872467637062073},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1624833047389984},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.15454715490341187},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1410544514656067},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.1348293125629425}],"concepts":[{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.6780596971511841},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6570771932601929},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5651327967643738},{"id":"https://openalex.org/C116721078","wikidata":"https://www.wikidata.org/wiki/Q1048005","display_name":"Holonomic constraints","level":2,"score":0.5501986145973206},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5351403951644897},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5057103633880615},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.469490110874176},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.37388497591018677},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2702091634273529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25900593400001526},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17872467637062073},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1624833047389984},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.15454715490341187},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1410544514656067},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.1348293125629425},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lcsys.2020.3006963","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2020.3006963","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:104248","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20200707-110517874","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1351875239","display_name":null,"funder_award_id":"IIS 1724464","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W613360614","https://openalex.org/W618254468","https://openalex.org/W1504362584","https://openalex.org/W1564897360","https://openalex.org/W1990993867","https://openalex.org/W1993314711","https://openalex.org/W2096876511","https://openalex.org/W2131164291","https://openalex.org/W2140380216","https://openalex.org/W2147539438","https://openalex.org/W2169205455","https://openalex.org/W2182062983","https://openalex.org/W2409421274","https://openalex.org/W2526182054","https://openalex.org/W2770429290","https://openalex.org/W2792099719","https://openalex.org/W2971603965","https://openalex.org/W3004116281","https://openalex.org/W3091513725","https://openalex.org/W6682089242","https://openalex.org/W6768307264"],"related_works":["https://openalex.org/W763656713","https://openalex.org/W2414535689","https://openalex.org/W2558761218","https://openalex.org/W2786729812","https://openalex.org/W2983545820","https://openalex.org/W2704051639","https://openalex.org/W2248476295","https://openalex.org/W2612501290","https://openalex.org/W2181610586","https://openalex.org/W1983253151"],"abstract_inverted_index":{"A":[0],"robotic":[1,71,132],"system":[2,92,149],"can":[3,135],"be":[4,136,166],"viewed":[5],"as":[6,145],"a":[7,30,62,107,143,146,173,184],"collection":[8],"of":[9,52,58,79,88,106,128,151],"lower-dimensional":[10],"systems":[11,36,72],"that":[12,37,47,82,115],"are":[13,38],"coupled":[14,90,122,147],"via":[15,43],"reaction":[16],"forces":[17],"(Lagrange":[18],"multipliers)":[19],"enforcing":[20],"holonomic":[21],"constraints.":[22],"Inspired":[23],"by":[24],"this":[25,27,59],"viewpoint,":[26],"letter":[28,60],"presents":[29],"novel":[31],"formulation":[32,105],"for":[33,67,111,119,161,168,175],"nonlinear":[34,108],"control":[35,91,148],"subject":[39],"to":[40,131,165],"coupling":[41,80],"constraints":[42,81],"virtual":[44],"\u201ccoupling\u201d":[45],"inputs":[46],"abstractly":[48],"play":[49],"the":[50,85,89,104,112,120,126,157,169,176],"role":[51],"Lagrange":[53,68],"multipliers.":[54],"The":[55],"main":[56],"contribution":[57],"is":[61,101,181],"process":[63],"-":[64,73],"mirroring":[65],"solving":[66],"multipliers":[69],"in":[70,103],"wherein":[74,155],"we":[75,141],"isolate":[76],"subsystems":[77],"free":[78],"provably":[83],"encode":[84],"full-order":[86,121,177],"dynamics":[87],"from":[93],"which":[94,134],"it":[95],"was":[96],"derived.":[97],"This":[98,180],"dimension":[99],"reduction":[100],"leveraged":[102],"optimization":[109],"problem":[110],"isolated":[113],"subsystem":[114],"yields":[116],"periodic":[117],"orbits":[118],"system.":[123],"We":[124],"consider":[125],"application":[127],"these":[129],"ideas":[130],"systems,":[133],"decomposed":[137],"into":[138],"subsystems.":[139],"Specifically,":[140],"view":[142],"quadruped":[144],"consisting":[150],"two":[152],"bipedal":[153],"robots,":[154],"applying":[156],"framework":[158],"developed":[159],"allows":[160],"gaits":[162],"(periodic":[163],"orbits)":[164],"generated":[167],"individual":[170],"biped":[171],"yielding":[172],"gait":[174],"quadrupedal":[178,185],"dynamics.":[179],"demonstrated":[182],"on":[183,192],"robot":[186],"through":[187],"simulation":[188],"and":[189],"walking":[190],"experiments":[191],"rough":[193],"terrains.":[194]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}