{"id":"https://openalex.org/W2129541023","doi":"https://doi.org/10.1109/robot.2005.1570318","title":"Symmetric Walking Control: Invariance and Global Stability","display_name":"Symmetric Walking Control: Invariance and Global Stability","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2129541023","doi":"https://doi.org/10.1109/robot.2005.1570318","mag":"2129541023"},"language":"en","primary_location":{"id":"doi:10.1109/robot.2005.1570318","is_oa":false,"landing_page_url":"https://doi.org/10.1109/robot.2005.1570318","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 IEEE International Conference on Robotics and Automation","raw_type":"proceedings-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/A5073009713","display_name":"Sang-Ho Hyon","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"SangHo Hyon","raw_affiliation_strings":["Department of Bioengineering and Robotics Tohoku University Aramaki-Aza-Aoba 6-6-01, Sendai 980-8579, Japan sangho@ieee.org","Department of Bioengineering and Robotics, University of Tohoku, Sendai, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Bioengineering and Robotics Tohoku University Aramaki-Aza-Aoba 6-6-01, Sendai 980-8579, Japan sangho@ieee.org","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Department of Bioengineering and Robotics, University of Tohoku, Sendai, Japan","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111633599","display_name":"T. Emura","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Emura","raw_affiliation_strings":["Department of Bioengineering and Robotics, University of Tohoku, Sendai, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Bioengineering and Robotics, University of Tohoku, Sendai, Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073009713"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":4.6563,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.94836532,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1443","last_page":"1450"},"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/T12400","display_name":"Neurogenetic and Muscular Disorders Research","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2716","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.9722999930381775,"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":0.8066222667694092},{"id":"https://openalex.org/keywords/passivity","display_name":"Passivity","score":0.7670415639877319},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6131734251976013},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5125195980072021},{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.45985299348831177},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.4557371735572815},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4493822455406189},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4438934922218323},{"id":"https://openalex.org/keywords/angular-velocity","display_name":"Angular velocity","score":0.41852980852127075},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.41667473316192627},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.41664159297943115},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.36042022705078125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2962097227573395},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.20517131686210632},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17456656694412231},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15794149041175842},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.12769222259521484},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.11924475431442261},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11096999049186707},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09326612949371338}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8066222667694092},{"id":"https://openalex.org/C2778809601","wikidata":"https://www.wikidata.org/wiki/Q1045736","display_name":"Passivity","level":2,"score":0.7670415639877319},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6131734251976013},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5125195980072021},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.45985299348831177},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4557371735572815},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4493822455406189},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4438934922218323},{"id":"https://openalex.org/C5594486","wikidata":"https://www.wikidata.org/wiki/Q161635","display_name":"Angular velocity","level":2,"score":0.41852980852127075},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.41667473316192627},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.41664159297943115},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.36042022705078125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2962097227573395},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.20517131686210632},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17456656694412231},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15794149041175842},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.12769222259521484},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.11924475431442261},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11096999049186707},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09326612949371338},{"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/robot.2005.1570318","is_oa":false,"landing_page_url":"https://doi.org/10.1109/robot.2005.1570318","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2005 IEEE International Conference on Robotics and Automation","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.137.3233","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.3233","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cns.atr.jp/~sangho/hyon_icra2005_swc.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8999999761581421,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W129037336","https://openalex.org/W1487094975","https://openalex.org/W1523946546","https://openalex.org/W1578143299","https://openalex.org/W1666054468","https://openalex.org/W1803017756","https://openalex.org/W1964373008","https://openalex.org/W1979245447","https://openalex.org/W1981479913","https://openalex.org/W2049374002","https://openalex.org/W2074723184","https://openalex.org/W2118320757","https://openalex.org/W2125788595","https://openalex.org/W2126479355","https://openalex.org/W2137547873","https://openalex.org/W2142992961","https://openalex.org/W2152383438","https://openalex.org/W2163668399","https://openalex.org/W2163921174","https://openalex.org/W2167044893","https://openalex.org/W2171829106","https://openalex.org/W2331734107","https://openalex.org/W3141151088","https://openalex.org/W4205727720"],"related_works":["https://openalex.org/W4233304828","https://openalex.org/W4239268637","https://openalex.org/W2952841825","https://openalex.org/W1977819874","https://openalex.org/W2051296765","https://openalex.org/W2960878236","https://openalex.org/W153449849","https://openalex.org/W2473698078","https://openalex.org/W2010551470","https://openalex.org/W2106518784"],"abstract_inverted_index":{"This":[0],"paper":[1],"first":[2],"presents":[3],"a":[4,14,40,59,84,89,123],"novel":[5],"control":[6,11],"strategy":[7],"for":[8,110],"periodic":[9],"motion":[10],"based":[12,67],"on":[13,68],"Hamiltonian":[15,34],"system.":[16,35,74],"According":[17],"to":[18,47,83,132],"the":[19,33,49,54,69,72,142],"strategy,":[20],"hybrid":[21],"symmetric":[22,50],"orbits":[23,51],"(ideal":[24],"walking":[25,62,111],"gaits)":[26],"are":[27],"explored":[28],"using":[29,105],"reversal":[30],"symmetry":[31],"of":[32,71,104,144],"Then,":[36],"an":[37],"invariance":[38],"controller,":[39],"Symmetric":[41],"Walking":[42],"Controller,":[43],"is":[44,65,130,147],"derived":[45],"systematically":[46],"distribute":[48],"densely":[52],"throughout":[53],"entire":[55],"phase":[56],"space.":[57],"Finally,":[58],"new":[60],"robust":[61],"speed":[63],"controller":[64,94,146],"formulated":[66],"passivity":[70,97],"controlled":[73],"Consequently,":[75],"solutions":[76],"starting":[77],"from":[78],"any":[79,133],"point":[80],"globally":[81],"converge":[82],"stable":[85],"limit":[86],"cycle":[87],"having":[88],"desired":[90],"energy":[91,109],"level.":[92],"The":[93],"has":[95],"strong":[96],"and":[98,118,152],"robustness,":[99],"thereby":[100],"rendering":[101],"it":[102,129],"capable":[103],"external":[106],"disturbances":[107],"as":[108],"propulsion.":[112],"It":[113],"requires":[114],"no":[115],"model":[116],"parameters":[117],"can":[119],"be":[120],"implemented":[121],"in":[122],"very":[124],"small":[125],"program":[126],"size.":[127],"Furthermore,":[128],"applicable":[131],"biped":[134],"robot":[135],"without":[136],"major":[137],"modification.":[138],"In":[139],"this":[140,145],"report,":[141],"effectiveness":[143],"proved":[148],"mathematically,":[149],"validated":[150],"numerically,":[151],"confirmed":[153],"experimentally.":[154]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}