{"id":"https://openalex.org/W2324080337","doi":"https://doi.org/10.1017/s0263574715000077","title":"Determination of the initial conditions by solving boundary value problem method for period-one walking of a passive biped walking robots","display_name":"Determination of the initial conditions by solving boundary value problem method for period-one walking of a passive biped walking robots","publication_year":2015,"publication_date":"2015-03-13","ids":{"openalex":"https://openalex.org/W2324080337","doi":"https://doi.org/10.1017/s0263574715000077","mag":"2324080337"},"language":"en","primary_location":{"id":"doi:10.1017/s0263574715000077","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574715000077","pdf_url":null,"source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","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/A5068424968","display_name":"Masoumeh Safartoobi","orcid":null},"institutions":[{"id":"https://openalex.org/I84248293","display_name":"Babol Noshirvani University of Technology","ror":"https://ror.org/02zc85170","country_code":"IR","type":"education","lineage":["https://openalex.org/I84248293"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Masoumeh Safartoobi","raw_affiliation_strings":["Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Postal Code: 47148-71167, Shariati Street, Babol, Mazandaran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Postal Code: 47148-71167, Shariati Street, Babol, Mazandaran, Iran","institution_ids":["https://openalex.org/I84248293"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085646461","display_name":"Morteza Dardel","orcid":"https://orcid.org/0000-0002-5206-508X"},"institutions":[{"id":"https://openalex.org/I84248293","display_name":"Babol Noshirvani University of Technology","ror":"https://ror.org/02zc85170","country_code":"IR","type":"education","lineage":["https://openalex.org/I84248293"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Morteza Dardel","raw_affiliation_strings":["Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Postal Code: 47148-71167, Shariati Street, Babol, Mazandaran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Postal Code: 47148-71167, Shariati Street, Babol, Mazandaran, Iran","institution_ids":["https://openalex.org/I84248293"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112664869","display_name":"Mohammad Hassan Ghasemi","orcid":null},"institutions":[{"id":"https://openalex.org/I84248293","display_name":"Babol Noshirvani University of Technology","ror":"https://ror.org/02zc85170","country_code":"IR","type":"education","lineage":["https://openalex.org/I84248293"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammad Hassan Ghasemi","raw_affiliation_strings":["Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Postal Code: 47148-71167, Shariati Street, Babol, Mazandaran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Postal Code: 47148-71167, Shariati Street, Babol, Mazandaran, Iran","institution_ids":["https://openalex.org/I84248293"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113732724","display_name":"Hamidreza Mohammadi Daniali","orcid":null},"institutions":[{"id":"https://openalex.org/I84248293","display_name":"Babol Noshirvani University of Technology","ror":"https://ror.org/02zc85170","country_code":"IR","type":"education","lineage":["https://openalex.org/I84248293"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Hamidreza Mohammadi Daniali","raw_affiliation_strings":["Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Postal Code: 47148-71167, Shariati Street, Babol, Mazandaran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Postal Code: 47148-71167, Shariati Street, Babol, Mazandaran, Iran","institution_ids":["https://openalex.org/I84248293"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5085646461"],"corresponding_institution_ids":["https://openalex.org/I84248293"],"apc_list":null,"apc_paid":null,"fwci":0.5311,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.68578609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"35","issue":"1","first_page":"166","last_page":"188"},"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":0.9916999936103821,"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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.972000002861023,"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/gait","display_name":"Gait","score":0.6470299363136292},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6434926986694336},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.619412362575531},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.5890008807182312},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5700964331626892},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5679623484611511},{"id":"https://openalex.org/keywords/limit-cycle","display_name":"Limit cycle","score":0.5508461594581604},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5245423913002014},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5121839046478271},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44112277030944824},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4262784421443939},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34917789697647095},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2538631558418274},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.12105622887611389},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11803844571113586},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11688265204429626},{"id":"https://openalex.org/keywords/physical-medicine-and-rehabilitation","display_name":"Physical medicine and rehabilitation","score":0.0682370662689209}],"concepts":[{"id":"https://openalex.org/C151800584","wikidata":"https://www.wikidata.org/wiki/Q2370000","display_name":"Gait","level":2,"score":0.6470299363136292},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6434926986694336},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.619412362575531},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5890008807182312},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5700964331626892},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5679623484611511},{"id":"https://openalex.org/C93357160","wikidata":"https://www.wikidata.org/wiki/Q1545916","display_name":"Limit cycle","level":3,"score":0.5508461594581604},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5245423913002014},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5121839046478271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44112277030944824},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4262784421443939},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34917789697647095},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2538631558418274},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.12105622887611389},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11803844571113586},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11688265204429626},{"id":"https://openalex.org/C99508421","wikidata":"https://www.wikidata.org/wiki/Q2678675","display_name":"Physical medicine and rehabilitation","level":1,"score":0.0682370662689209},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0263574715000077","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0263574715000077","pdf_url":null,"source":{"id":"https://openalex.org/S92163612","display_name":"Robotica","issn_l":"0263-5747","issn":["0263-5747","1469-8668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Robotica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6600000262260437,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W37667216","https://openalex.org/W50292030","https://openalex.org/W1587859748","https://openalex.org/W1639534865","https://openalex.org/W1964528398","https://openalex.org/W1968635071","https://openalex.org/W1994513760","https://openalex.org/W2004162992","https://openalex.org/W2016102421","https://openalex.org/W2018947823","https://openalex.org/W2025121834","https://openalex.org/W2030087773","https://openalex.org/W2043792506","https://openalex.org/W2074686910","https://openalex.org/W2079492494","https://openalex.org/W2116655729","https://openalex.org/W2138049089","https://openalex.org/W2141016445","https://openalex.org/W2148966638","https://openalex.org/W2161150503","https://openalex.org/W2163668399","https://openalex.org/W6651594241"],"related_works":["https://openalex.org/W2352275403","https://openalex.org/W2159885618","https://openalex.org/W1994937216","https://openalex.org/W2199313715","https://openalex.org/W2012352190","https://openalex.org/W4248087735","https://openalex.org/W4225310406","https://openalex.org/W4229560034","https://openalex.org/W4210910892","https://openalex.org/W4234512766"],"abstract_inverted_index":{"SUMMARY":[0],"With":[1],"regard":[2],"to":[3,17,50,86],"the":[4,10,31,68,88,118],"small":[5],"basin":[6],"of":[7,9,35,39,71,120],"attraction":[8],"passive":[11,32],"limit":[12,61],"cycles,":[13,62],"it":[14],"is":[15,73,84,92,108],"important":[16],"start":[18],"from":[19],"a":[20,40,63,76,105],"proper":[21,52],"initial":[22,53,82,97],"condition":[23],"for":[24,55,123],"stable":[25,56],"walking.":[26],"The":[27],"present":[28],"study":[29],"investigates":[30],"dynamic":[33],"behaviors":[34],"two-dimensional":[36],"bipedal":[37],"walkers":[38],"compass":[41],"gait":[42,60,115],"model":[43],"with":[44],"different":[45],"foot":[46],"shapes.":[47],"In":[48],"order":[49],"find":[51],"conditions":[54],"and":[57,117],"unstable":[58],"period-one":[59,114],"method":[64,107],"based":[65],"on":[66],"solving":[67,95],"nonlinear":[69],"equations":[70],"motion":[72],"presented":[74],"as":[75],"boundary":[77],"value":[78,98],"problem":[79,99],"(BVP).":[80],"An":[81],"guess":[83],"required":[85],"solve":[87],"related":[89],"BVP":[90],"that":[91],"obtained":[93],"by":[94],"an":[96],"(IVP).":[100],"For":[101],"parametric":[102],"analysis":[103],"purposes,":[104],"continuation":[106],"applied.":[109],"Simulation":[110],"results":[111],"reveal":[112],"two,":[113],"cycles":[116],"effects":[119],"parameters":[121],"variation":[122],"all":[124],"models.":[125]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
