{"id":"https://openalex.org/W1972051539","doi":"https://doi.org/10.1109/icra.2012.6224677","title":"Approximating the stance map of the SLIP runner based on perturbation approach","display_name":"Approximating the stance map of the SLIP runner based on perturbation approach","publication_year":2012,"publication_date":"2012-05-01","ids":{"openalex":"https://openalex.org/W1972051539","doi":"https://doi.org/10.1109/icra.2012.6224677","mag":"1972051539"},"language":"en","primary_location":{"id":"doi:10.1109/icra.2012.6224677","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icra.2012.6224677","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 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/A5100708175","display_name":"Haitao Yu","orcid":"https://orcid.org/0000-0003-0155-1675"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haitao Yu","raw_affiliation_strings":["Department of Mechanical Engineering, Harbin Institute of Technology, Harbin, China","Department of Mechanical Engineering, Harbin Institute of Technology, 150001, China"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Harbin Institute of Technology, 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102985038","display_name":"Mantian Li","orcid":"https://orcid.org/0000-0003-4689-3484"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mantian Li","raw_affiliation_strings":["Department of Mechanical Engineering, Harbin Institute of Technology, Harbin, China","Department of Mechanical Engineering, Harbin Institute of Technology, 150001, China"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Harbin Institute of Technology, 150001, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100849943","display_name":"Hegao Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hegao Cai","raw_affiliation_strings":["Department of Mechanical Engineering, Harbin Institute of Technology, Harbin, China","Department of Mechanical Engineering, Harbin Institute of Technology, 150001, China"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Harbin Institute of Technology, 150001, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100708175"],"corresponding_institution_ids":["https://openalex.org/I204983213"],"apc_list":null,"apc_paid":null,"fwci":1.2102,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.77525333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"69","issue":null,"first_page":"4197","last_page":"4203"},"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/T11170","display_name":"Biomimetic flight and propulsion mechanisms","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11978","display_name":"Soil Mechanics and Vehicle Dynamics","score":0.9498000144958496,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/perturbation","display_name":"Perturbation (astronomy)","score":0.6703768968582153},{"id":"https://openalex.org/keywords/inverted-pendulum","display_name":"Inverted pendulum","score":0.6465022563934326},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5983657836914062},{"id":"https://openalex.org/keywords/slip","display_name":"Slip (aerodynamics)","score":0.5436711311340332},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5104348063468933},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.471721351146698},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4630705416202545},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4395013749599457},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.43695497512817383},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.43577301502227783},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.41559404134750366},{"id":"https://openalex.org/keywords/equations-of-motion","display_name":"Equations of motion","score":0.4145081043243408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3409537076950073},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34052202105522156},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32033878564834595},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2057446837425232}],"concepts":[{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.6703768968582153},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.6465022563934326},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5983657836914062},{"id":"https://openalex.org/C195268267","wikidata":"https://www.wikidata.org/wiki/Q1928883","display_name":"Slip (aerodynamics)","level":2,"score":0.5436711311340332},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5104348063468933},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.471721351146698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4630705416202545},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4395013749599457},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.43695497512817383},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.43577301502227783},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.41559404134750366},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.4145081043243408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3409537076950073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34052202105522156},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32033878564834595},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2057446837425232},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icra.2012.6224677","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icra.2012.6224677","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Conference on Robotics and Automation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1958809597","https://openalex.org/W1968196344","https://openalex.org/W1989796457","https://openalex.org/W2008342119","https://openalex.org/W2010650124","https://openalex.org/W2015941796","https://openalex.org/W2052683749","https://openalex.org/W2081031163","https://openalex.org/W2081115468","https://openalex.org/W2088632382","https://openalex.org/W2129287493","https://openalex.org/W2153624629","https://openalex.org/W2157826678","https://openalex.org/W2159873858","https://openalex.org/W2161427949","https://openalex.org/W2170320699","https://openalex.org/W4254676589"],"related_works":["https://openalex.org/W2056626217","https://openalex.org/W1541871911","https://openalex.org/W2050258033","https://openalex.org/W3185784018","https://openalex.org/W2184005427","https://openalex.org/W2118381768","https://openalex.org/W2148316232","https://openalex.org/W3212383242","https://openalex.org/W2079626172","https://openalex.org/W2981998189"],"abstract_inverted_index":{"The":[0,135],"Spring-Loaded":[1],"Inverted":[2],"Pendulum":[3],"(SLIP),":[4],"or":[5,77],"monopedal":[6],"runner,":[7],"is":[8,22,115,159,175],"widely":[9],"used":[10],"to":[11,60,101,117,122],"depict":[12],"running":[13,29],"and":[14,18,146],"hopping":[15],"in":[16,65,126,141,164],"mammalian":[17],"human":[19],"locomotion,":[20],"which":[21],"also":[23,176],"serving":[24],"as":[25,92,94],"a":[26,37,102,109,165],"template":[27],"for":[28,161,172],"robot":[30],"design.":[31],"This":[32],"classic":[33],"model":[34],"describes":[35],"quite":[36],"simple":[38],"mechanical":[39],"system.":[40],"Nevertheless":[41],"issue":[42],"of":[43,52,89,133],"seeking":[44],"the":[45,50,53,61,66,79,85,123,131,143,170],"accurate":[46],"analytic":[47,72,119],"solution":[48,137,158],"revealing":[49],"characteristics":[51],"motion":[54,104],"during":[55],"stance":[56,127,147,173],"remains":[57],"unsettled":[58],"due":[59],"nonintegrable":[62],"terms":[63],"contained":[64],"system":[67,91],"equations.":[68],"Moreover,":[69],"several":[70],"existing":[71,153],"approximations":[73],"by":[74,149],"simply":[75],"ignoring":[76],"linearizing":[78],"gravitational":[80],"force":[81],"can":[82,95],"not":[83],"reveal":[84],"entire":[86],"dynamical":[87],"behavior":[88],"nonlinear":[90],"well":[93],"be":[96],"breakdown":[97],"rapidly":[98],"when":[99],"applied":[100],"non-symmetric":[103,162],"case.":[105],"In":[106],"this":[107],"paper,":[108],"novel":[110],"method":[111],"with":[112,129,151],"perturbation":[113,136],"technique":[114],"proposed":[116],"obtain":[118],"approximate":[120],"solutions":[121],"SLIP":[124],"dynamics":[125],"phase":[128],"considering":[130],"effect":[132],"gravity.":[134],"achieves":[138],"higher":[139],"accuracy":[140],"predicting":[142],"apex":[144],"trajectory":[145,174],"locomotion":[148],"comparing":[150],"typical":[152],"analytical":[154],"approximations.":[155],"Particularly,":[156],"our":[157],"validated":[160],"case":[163],"large":[166],"angle":[167],"range.":[168],"Additionally,":[169],"prediction":[171],"verified":[177],"through":[178],"numerical":[179],"evaluation.":[180]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
