{"id":"https://openalex.org/W3138010110","doi":"https://doi.org/10.1109/lra.2021.3065174","title":"Coupled Control Lyapunov Functions for Interconnected Systems, With Application to Quadrupedal Locomotion","display_name":"Coupled Control Lyapunov Functions for Interconnected Systems, With Application to Quadrupedal Locomotion","publication_year":2021,"publication_date":"2021-03-11","ids":{"openalex":"https://openalex.org/W3138010110","doi":"https://doi.org/10.1109/lra.2021.3065174","mag":"3138010110"},"language":"en","primary_location":{"id":"doi:10.1109/lra.2021.3065174","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2021.3065174","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766"],"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 Robotics and Automation 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, California Institute of Technology, Pasadena, California, USA"],"raw_orcid":"https://orcid.org/0000-0002-0115-5632","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, California Institute of Technology, Pasadena, California, 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, California Institute of Technology, Pasadena, California, USA"],"raw_orcid":"https://orcid.org/0000-0002-2361-1694","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, California Institute of Technology, Pasadena, California, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084523677","display_name":"Shishir Kolathaya","orcid":"https://orcid.org/0000-0001-8689-2318"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Shishir Kolathaya","raw_affiliation_strings":["Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India"],"raw_orcid":"https://orcid.org/0000-0001-8689-2318","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066501467","display_name":"Kaveh Akbari Hamed","orcid":"https://orcid.org/0000-0001-9597-1691"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kaveh Akbari Hamed","raw_affiliation_strings":["Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA"],"raw_orcid":"https://orcid.org/0000-0001-9597-1691","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"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, California Institute of Technology, Pasadena, California, USA"],"raw_orcid":"https://orcid.org/0000-0003-0848-3177","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, California Institute of Technology, Pasadena, California, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.019,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.72705165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"6","issue":"2","first_page":"3761","last_page":"3768"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9998999834060669,"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":0.9998999834060669,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9916999936103821,"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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.9829000234603882,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.8256836533546448},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6460974216461182},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5702229142189026},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.564699649810791},{"id":"https://openalex.org/keywords/quadrupedalism","display_name":"Quadrupedalism","score":0.5547741055488586},{"id":"https://openalex.org/keywords/gait","display_name":"Gait","score":0.5067687630653381},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5055642127990723},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.44024530053138733},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.41881832480430603},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.37415269017219543},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.22320204973220825},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09531909227371216},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09402844309806824},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06936752796173096}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8256836533546448},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6460974216461182},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5702229142189026},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.564699649810791},{"id":"https://openalex.org/C134181672","wikidata":"https://www.wikidata.org/wiki/Q21907045","display_name":"Quadrupedalism","level":2,"score":0.5547741055488586},{"id":"https://openalex.org/C151800584","wikidata":"https://www.wikidata.org/wiki/Q2370000","display_name":"Gait","level":2,"score":0.5067687630653381},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5055642127990723},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44024530053138733},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.41881832480430603},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.37415269017219543},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.22320204973220825},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09531909227371216},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09402844309806824},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06936752796173096},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C42407357","wikidata":"https://www.wikidata.org/wiki/Q521","display_name":"Physiology","level":1,"score":0.0},{"id":"https://openalex.org/C105702510","wikidata":"https://www.wikidata.org/wiki/Q514","display_name":"Anatomy","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lra.2021.3065174","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2021.3065174","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766"],"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 Robotics and Automation Letters","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:108777","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20210421-085752484","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W306312984","https://openalex.org/W613360614","https://openalex.org/W618254468","https://openalex.org/W1134107867","https://openalex.org/W1564897360","https://openalex.org/W1823180602","https://openalex.org/W1990993867","https://openalex.org/W1993314711","https://openalex.org/W2015084265","https://openalex.org/W2031785952","https://openalex.org/W2047174209","https://openalex.org/W2054959757","https://openalex.org/W2093627340","https://openalex.org/W2096361268","https://openalex.org/W2134078068","https://openalex.org/W2140380216","https://openalex.org/W2143729862","https://openalex.org/W2147539438","https://openalex.org/W2161427949","https://openalex.org/W2171879251","https://openalex.org/W2174809691","https://openalex.org/W2409421274","https://openalex.org/W2534895395","https://openalex.org/W2620928602","https://openalex.org/W2779458783","https://openalex.org/W2785087762","https://openalex.org/W2885116100","https://openalex.org/W2909331752","https://openalex.org/W2920812058","https://openalex.org/W3003340679","https://openalex.org/W3004116281","https://openalex.org/W3039104684","https://openalex.org/W3045789376","https://openalex.org/W3091513725","https://openalex.org/W3130192187","https://openalex.org/W3150530407","https://openalex.org/W6682089242","https://openalex.org/W6790284069"],"related_works":["https://openalex.org/W4388251424","https://openalex.org/W2008498579","https://openalex.org/W2923272690","https://openalex.org/W2559825912","https://openalex.org/W1966935220","https://openalex.org/W2064963663","https://openalex.org/W1992956164","https://openalex.org/W2775028049","https://openalex.org/W2087283056","https://openalex.org/W1536304773"],"abstract_inverted_index":{"This":[0,99],"letter":[1,74],"addresses":[2],"the":[3,8,51,66,73,93,143,147,161],"problem":[4],"of":[5,10,41,72,95],"formally":[6],"guaranteeing":[7],"stability":[9,76,97,111],"interconnected":[11,128],"systems":[12,37,43,130],"with":[13,16],"local":[14],"controllers":[15],"a":[17,30,39,105],"view":[18],"toward":[19],"stabilizing":[20,61],"quadrupeds":[21],"viewed":[22],"as":[23,38],"coupled":[24,46,53,64,87],"bipeds.":[25],"In":[26],"particular,":[27],"we":[28,136],"present":[29],"novel":[31],"framework":[32],"that":[33,44,78],"views":[34],"general":[35],"rigid-body":[36],"collection":[40],"lower-dimensional":[42],"are":[45,75],"via":[47,104],"reaction":[48],"forces.":[49],"Stabilizing":[50],"corresponding":[52],"control":[54,83,88],"system":[55],"can":[56],"thus":[57,151],"be":[58],"addressed":[59],"by":[60,85],"each":[62,82],"subsystem":[63,84],"through":[65],"passive":[67],"dynamics.":[68],"The":[69],"main":[70],"results":[71,118],"conditions":[77],"guarantee":[79],"convergence":[80],"for":[81,131],"formulating":[86],"Lyapunov":[89],"functions":[90],"(CCLFs)":[91],"using":[92,142],"notion":[94],"input-to-state":[96],"(ISS).":[98],"theoretical":[100],"result":[101],"is":[102,112,124],"illustrated":[103],"simple":[106],"cart-pole":[107],"example,":[108],"where":[109,119],"exponential":[110],"obtained.":[113],"Next,":[114],"building":[115],"on":[116,160],"previous":[117],"an":[120],"18-DOF":[121],"quadrupedal":[122,164],"robot":[123],"decomposed":[125],"into":[126],"two":[127],"bipedal":[129],"efficient":[132],"periodic":[133],"gait":[134],"generation,":[135],"design":[137],"model-free":[138],"quadratic":[139],"programs":[140],"(QPs)":[141],"CCLFs":[144],"to":[145],"stabilize":[146],"continuous":[148],"dynamics":[149],"and":[150,155,158],"achieve":[152],"experimental":[153],"walking":[154],"simulated":[156],"hopping":[157],"running":[159],"Vision":[162],"60":[163],"robot.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
