{"id":"https://openalex.org/W2019815646","doi":"https://doi.org/10.1109/cdc.2011.6160972","title":"Rank deficiency and superstability of hybrid systems with application to bipedal robots","display_name":"Rank deficiency and superstability of hybrid systems with application to bipedal robots","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2019815646","doi":"https://doi.org/10.1109/cdc.2011.6160972","mag":"2019815646"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6160972","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160972","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","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/A5089141072","display_name":"Eric Wendel","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Wendel","raw_affiliation_strings":["Department of AeroSpace Engineering, Texas A and M University, College Station, TX, USA","Department of Aerospace Engineering, Texas A&M University, College Station 77840, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of AeroSpace Engineering, Texas A and M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Department of Aerospace Engineering, Texas A&M University, College Station 77840, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"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/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaron D. Ames","raw_affiliation_strings":["Faculty of the Department of Mechanical Engineering, Texas A and M University, College Station, TX, USA","Faculty of the Department of Mechanical Engineering, Texas A&M University, College Station, 77840, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of the Department of Mechanical Engineering, Texas A and M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Faculty of the Department of Mechanical Engineering, Texas A&M University, College Station, 77840, USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"5469","issue":null,"first_page":"7422","last_page":"7427"},"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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.9923999905586243,"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":0.9866999983787537,"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/rank","display_name":"Rank (graph theory)","score":0.84284508228302},{"id":"https://openalex.org/keywords/hybrid-system","display_name":"Hybrid system","score":0.7002310156822205},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.58664470911026},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5795437693595886},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5269877314567566},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4954632520675659},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.44255369901657104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3877433240413666},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3313278555870056},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30878961086273193},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24773570895195007},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12814202904701233},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11618191003799438},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.10105094313621521},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0838986337184906}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.84284508228302},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.7002310156822205},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.58664470911026},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5795437693595886},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5269877314567566},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4954632520675659},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.44255369901657104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3877433240413666},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3313278555870056},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30878961086273193},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24773570895195007},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12814202904701233},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11618191003799438},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.10105094313621521},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0838986337184906},{"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.2011.6160972","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6160972","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European Control Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:authors.library.caltech.edu:93007","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/93007/","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":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W50292030","https://openalex.org/W1504362584","https://openalex.org/W1521821198","https://openalex.org/W1558079603","https://openalex.org/W1779583466","https://openalex.org/W1893209994","https://openalex.org/W1977106683","https://openalex.org/W2015689071","https://openalex.org/W2029030701","https://openalex.org/W2101956251","https://openalex.org/W2112640448","https://openalex.org/W2115497059","https://openalex.org/W2117631239","https://openalex.org/W2122171303","https://openalex.org/W2128198426","https://openalex.org/W2129231075","https://openalex.org/W2137547873","https://openalex.org/W2152871707","https://openalex.org/W2160649180","https://openalex.org/W2166972647","https://openalex.org/W2171178105","https://openalex.org/W2605543710","https://openalex.org/W3101117696","https://openalex.org/W4232056870","https://openalex.org/W4292994524","https://openalex.org/W4300506249","https://openalex.org/W6602037555","https://openalex.org/W6638171340","https://openalex.org/W6677402884"],"related_works":["https://openalex.org/W4297787022","https://openalex.org/W2015540166","https://openalex.org/W1666143004","https://openalex.org/W78494858","https://openalex.org/W2949126640","https://openalex.org/W2071370397","https://openalex.org/W4321242394","https://openalex.org/W1968813561","https://openalex.org/W1201114281","https://openalex.org/W2154236742"],"abstract_inverted_index":{"The":[0,162],"objectives":[1],"of":[2,11,13,24,35,46,62,86,106,129,139],"this":[3],"paper":[4],"are":[5,19,123,164],"to":[6,49,93,125,150,157,168],"study":[7],"the":[8,33,44,60,63,84,104,126,137],"rank":[9,45,101,120,148],"properties":[10],"flows":[12],"hybrid":[14,51,54,111,131],"systems,":[15,27,43],"show":[16],"that":[17,31],"they":[18],"fundamentally":[20],"different":[21],"from":[22],"those":[23],"smooth":[25,41],"dynamical":[26,42],"and":[28,69,73,77,152],"consider":[29],"applications":[30],"emphasize":[32],"importance":[34,105],"these":[36,119],"differences.":[37],"In":[38],"contrast":[39],"with":[40],"a":[47,50,53,144,169],"solution":[48],"system,":[52],"execution,":[55],"is":[56,83,100,136,153],"always":[57],"less":[58],"than":[59],"dimension":[61],"space":[64],"on":[65],"which":[66],"it":[67,99],"evolves":[68],"falls":[70],"within":[71],"easily-computed":[72],"possibly":[74],"distinct":[75],"upper":[76],"lower":[78],"bounds.":[79],"Our":[80,133],"main":[81],"contribution":[82,135],"derivation":[85,138],"conditions":[87,122,141],"for":[88,114,142],"when":[89,98,143],"an":[90],"execution":[91,146],"fails":[92],"have":[94],"maximal":[95],"rank,":[96],"i.e.,":[97],"deficient.":[102],"Given":[103],"periodic":[107,130,145],"behavior":[108],"in":[109,116,159,166],"many":[110],"systems":[112],"applications,":[113],"example":[115],"bipedal":[117],"robots,":[118],"deficiency":[121],"applied":[124],"special":[127],"case":[128],"executions.":[132],"secondary":[134],"superstability":[140],"has":[147],"equal":[149],"0":[151],"therefore":[154],"completely":[155],"insensitive":[156],"perturbations":[158],"initial":[160],"conditions.":[161],"results":[163],"illustrated":[165],"application":[167],"planar":[170],"kneed":[171],"biped.":[172]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
