{"id":"https://openalex.org/W2199168279","doi":"https://doi.org/10.1109/humanoids.2015.7363473","title":"A closed-form solution for real-time ZMP gait generation and feedback stabilization","display_name":"A closed-form solution for real-time ZMP gait generation and feedback stabilization","publication_year":2015,"publication_date":"2015-11-01","ids":{"openalex":"https://openalex.org/W2199168279","doi":"https://doi.org/10.1109/humanoids.2015.7363473","mag":"2199168279"},"language":"en","primary_location":{"id":"doi:10.1109/humanoids.2015.7363473","is_oa":false,"landing_page_url":"https://doi.org/10.1109/humanoids.2015.7363473","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids)","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/A5074291890","display_name":"Russ Tedrake","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Russ Tedrake","raw_affiliation_strings":["Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA"],"affiliations":[{"raw_affiliation_string":"Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049981830","display_name":"Scott Kuindersma","orcid":"https://orcid.org/0000-0003-0645-6626"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott Kuindersma","raw_affiliation_strings":["Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA"],"affiliations":[{"raw_affiliation_string":"Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036513591","display_name":"Robin Deits","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robin Deits","raw_affiliation_strings":["Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA"],"affiliations":[{"raw_affiliation_string":"Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109094932","display_name":"Kanako Miura","orcid":null},"institutions":[{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kanako Miura","raw_affiliation_strings":["Humanoid Research Group, National Institute of Advanced Industrial Science & Technology (AIST), Tsukuba, Ibaraki, Japan"],"affiliations":[{"raw_affiliation_string":"Humanoid Research Group, National Institute of Advanced Industrial Science & Technology (AIST), Tsukuba, Ibaraki, Japan","institution_ids":["https://openalex.org/I73613424"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5074291890"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":7.2581,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.97760394,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.9965000152587891,"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":0.9858999848365784,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/zero-moment-point","display_name":"Zero moment point","score":0.8135416507720947},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7782618403434753},{"id":"https://openalex.org/keywords/humanoid-robot","display_name":"Humanoid robot","score":0.7033083438873291},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6390916109085083},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6173204779624939},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.532459557056427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5232462286949158},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5110098123550415},{"id":"https://openalex.org/keywords/gait","display_name":"Gait","score":0.5075956583023071},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4611847996711731},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.44472891092300415},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4376488924026489},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4242258667945862},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4131855368614197},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.41277170181274414},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.41184067726135254},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.3999940752983093},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35876214504241943},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2283710241317749},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.21440601348876953},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15691176056861877},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13880741596221924}],"concepts":[{"id":"https://openalex.org/C19245436","wikidata":"https://www.wikidata.org/wiki/Q279038","display_name":"Zero moment point","level":4,"score":0.8135416507720947},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7782618403434753},{"id":"https://openalex.org/C60692881","wikidata":"https://www.wikidata.org/wiki/Q584529","display_name":"Humanoid robot","level":3,"score":0.7033083438873291},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6390916109085083},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6173204779624939},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.532459557056427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5232462286949158},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5110098123550415},{"id":"https://openalex.org/C151800584","wikidata":"https://www.wikidata.org/wiki/Q2370000","display_name":"Gait","level":2,"score":0.5075956583023071},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4611847996711731},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.44472891092300415},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4376488924026489},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4242258667945862},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4131855368614197},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.41277170181274414},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.41184067726135254},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.3999940752983093},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35876214504241943},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2283710241317749},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.21440601348876953},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15691176056861877},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13880741596221924},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C42407357","wikidata":"https://www.wikidata.org/wiki/Q521","display_name":"Physiology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/humanoids.2015.7363473","is_oa":false,"landing_page_url":"https://doi.org/10.1109/humanoids.2015.7363473","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W205259702","https://openalex.org/W1030513622","https://openalex.org/W1661823234","https://openalex.org/W1945123189","https://openalex.org/W1969752069","https://openalex.org/W1994275787","https://openalex.org/W2015149365","https://openalex.org/W2072241589","https://openalex.org/W2098561496","https://openalex.org/W2127763473","https://openalex.org/W2133859362","https://openalex.org/W2991542025","https://openalex.org/W3102051120","https://openalex.org/W3150530246","https://openalex.org/W6626973494","https://openalex.org/W6642513403"],"related_works":["https://openalex.org/W1829175078","https://openalex.org/W2133801610","https://openalex.org/W2130383927","https://openalex.org/W2606527650","https://openalex.org/W2120357486","https://openalex.org/W2151003079","https://openalex.org/W2170918662","https://openalex.org/W2163503851","https://openalex.org/W2034988786","https://openalex.org/W2220923292"],"abstract_inverted_index":{"Here":[0],"we":[1],"present":[2],"a":[3,31],"closed-form":[4],"solution":[5],"to":[6],"the":[7,35,41,45,58,65,73,84],"continuous":[8],"time-varying":[9,47],"linear-quadratic":[10],"regulator":[11],"problem":[12],"for":[13,23,44],"zero-moment":[14],"point":[15],"(ZMP)":[16],"tracking.":[17],"This":[18,50],"generalizes":[19],"previous":[20],"analytical":[21],"solutions":[22],"gait":[24],"generation":[25],"by":[26,39,82],"allowing":[27],"\"soft\"":[28],"tracking":[29],"(with":[30],"quadratic":[32],"cost)":[33],"of":[34,60],"desired":[36,66],"ZMP,":[37],"and":[38],"providing":[40],"feedback":[42],"gains":[43],"resulting":[46],"optimal":[48,85],"controller.":[49],"enables":[51],"very":[52],"fast":[53],"O(n)":[54],"computation,":[55],"with":[56],"n":[57],"number":[59],"piecewise":[61],"polynomial":[62],"segments":[63],"in":[64],"ZMP":[67],"trajectory.":[68],"Results":[69],"are":[70],"presented":[71],"using":[72],"Atlas":[74],"humanoid":[75],"robot":[76],"where":[77],"dynamic":[78],"walking":[79],"is":[80],"achieved":[81],"recomputing":[83],"controller":[86],"online.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
