{"id":"https://openalex.org/W1746948350","doi":"https://doi.org/10.1109/icra.2015.7140005","title":"Analytical approximation for the double-stance phase of a walking robot","display_name":"Analytical approximation for the double-stance phase of a walking robot","publication_year":2015,"publication_date":"2015-05-01","ids":{"openalex":"https://openalex.org/W1746948350","doi":"https://doi.org/10.1109/icra.2015.7140005","mag":"1746948350"},"language":"en","primary_location":{"id":"doi:10.1109/icra.2015.7140005","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icra.2015.7140005","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Robotics and Automation (ICRA)","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/A5064041436","display_name":"Mohammad Shahbazi","orcid":"https://orcid.org/0000-0001-9479-6756"},"institutions":[{"id":"https://openalex.org/I23946033","display_name":"University of Tehran","ror":"https://ror.org/05vf56z40","country_code":"IR","type":"education","lineage":["https://openalex.org/I23946033"]},{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["IR","NL"],"is_corresponding":false,"raw_author_name":"M. Shahbazi","raw_affiliation_strings":["Department of Mechatronics Engineering, University of Tehran, Iran","Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD, the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechatronics Engineering, University of Tehran, Iran","institution_ids":["https://openalex.org/I23946033"]},{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD, the Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084264842","display_name":"Robert Babu\u0161ka","orcid":"https://orcid.org/0000-0001-9578-8598"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"R. Babuska","raw_affiliation_strings":["Delft Center for Systems and Control, Delft University of Technology, The Netherlands","Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD, the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, The Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD, the Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046652464","display_name":"Gabriel A. D. Lopes","orcid":"https://orcid.org/0000-0002-2406-9489"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"G.A.D. Lopes","raw_affiliation_strings":["Delft Center for Systems and Control, Delft University of Technology, The Netherlands","Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD, the Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, The Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628 CD, the Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"62","issue":null,"first_page":"5754","last_page":"5760"},"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":0.9865999817848206,"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":0.9800000190734863,"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/slip","display_name":"Slip (aerodynamics)","score":0.7046803832054138},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6284655332565308},{"id":"https://openalex.org/keywords/inverted-pendulum","display_name":"Inverted pendulum","score":0.5902340412139893},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5234893560409546},{"id":"https://openalex.org/keywords/double-pendulum","display_name":"Double pendulum","score":0.5084758996963501},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5063339471817017},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.42997509241104126},{"id":"https://openalex.org/keywords/bipedalism","display_name":"Bipedalism","score":0.424834668636322},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.42365872859954834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3780464231967926},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2925175428390503},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24084728956222534},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.208688884973526},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.19791486859321594},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18976935744285583},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.09847712516784668}],"concepts":[{"id":"https://openalex.org/C195268267","wikidata":"https://www.wikidata.org/wiki/Q1928883","display_name":"Slip (aerodynamics)","level":2,"score":0.7046803832054138},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6284655332565308},{"id":"https://openalex.org/C192921069","wikidata":"https://www.wikidata.org/wiki/Q550134","display_name":"Inverted pendulum","level":3,"score":0.5902340412139893},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5234893560409546},{"id":"https://openalex.org/C167183279","wikidata":"https://www.wikidata.org/wiki/Q1243208","display_name":"Double pendulum","level":4,"score":0.5084758996963501},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5063339471817017},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.42997509241104126},{"id":"https://openalex.org/C143733281","wikidata":"https://www.wikidata.org/wiki/Q372949","display_name":"Bipedalism","level":2,"score":0.424834668636322},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.42365872859954834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3780464231967926},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2925175428390503},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24084728956222534},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.208688884973526},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.19791486859321594},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18976935744285583},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.09847712516784668},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icra.2015.7140005","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icra.2015.7140005","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Robotics and Automation (ICRA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7699999809265137,"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":16,"referenced_works":["https://openalex.org/W1498336348","https://openalex.org/W1574444315","https://openalex.org/W1965348710","https://openalex.org/W1966458748","https://openalex.org/W1968196344","https://openalex.org/W1973305345","https://openalex.org/W1989796457","https://openalex.org/W2008342119","https://openalex.org/W2009317155","https://openalex.org/W2010650124","https://openalex.org/W2039583562","https://openalex.org/W2052683749","https://openalex.org/W2088632382","https://openalex.org/W2094825455","https://openalex.org/W2479798338","https://openalex.org/W6641581960"],"related_works":["https://openalex.org/W2612646280","https://openalex.org/W2008084614","https://openalex.org/W2366496871","https://openalex.org/W2041698009","https://openalex.org/W2669735925","https://openalex.org/W3216306759","https://openalex.org/W2047755970","https://openalex.org/W2378000718","https://openalex.org/W2734833709","https://openalex.org/W2204278379"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"an":[3,56,71,123],"approximate":[4,57],"analytical":[5,30],"solution":[6,31,60,118],"to":[7,32,61],"the":[8,14,21,26,28,45,62,66,86,98,130,134,139],"otherwise":[9],"non-integrable":[10],"double-stance":[11,63,77],"dynamics":[12,35,64],"of":[13,25,65,88,97,105,138],"bipedal":[15,67],"spring-loaded":[16],"inverted":[17],"pendulum":[18],"(SLIP).":[19],"Despite":[20],"apparent":[22],"structural":[23],"simplicity":[24],"SLIP,":[27],"exact":[29],"its":[33],"stance":[34],"cannot":[36],"be":[37,81],"found.":[38],"Approximate":[39],"maps":[40],"have":[41],"been":[42],"proposed":[43],"for":[44,91,122],"monoped":[46],"SLIP":[47,68,141],"runner":[48],"(encompassing":[49],"a":[50,59,76,102,112],"single-stance":[51],"phase).":[52],"Still,":[53],"even":[54],"in":[55,85],"form,":[58],"walker":[69],"remained":[70],"open":[72],"problem.":[73],"We":[74],"propose":[75],"map":[78,100],"that":[79,129],"can":[80],"readily":[82],"utilized":[83],"especially":[84],"design":[87],"control":[89,113],"systems":[90],"active":[92],"dynamic":[93],"walking.":[94],"The":[95],"accuracy":[96],"derived":[99],"over":[101],"feasible":[103],"range":[104],"locomotion":[106],"properties":[107],"is":[108,119],"analyzed":[109],"numerically,":[110],"and":[111],"application":[114],"based":[115],"on":[116],"this":[117],"presented.":[120],"Simulations":[121],"arbitrary":[124],"chosen":[125],"energy":[126],"level":[127],"reveals":[128],"devised":[131],"controller":[132],"enlarges":[133],"stable":[135],"walking":[136],"domain":[137],"standard":[140],"considerably.":[142]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
