{"id":"https://openalex.org/W2618245409","doi":"https://doi.org/10.1109/lra.2017.2723931","title":"Fast Trajectory Optimization for Legged Robots Using Vertex-Based ZMP Constraints","display_name":"Fast Trajectory Optimization for Legged Robots Using Vertex-Based ZMP Constraints","publication_year":2017,"publication_date":"2017-07-06","ids":{"openalex":"https://openalex.org/W2618245409","doi":"https://doi.org/10.1109/lra.2017.2723931","mag":"2618245409"},"language":"en","primary_location":{"id":"doi:10.1109/lra.2017.2723931","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2017.2723931","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766","2377-3774"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Robotics and Automation Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://youtu.be/5WLeQMBuv30","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071181618","display_name":"Alexander Winkler","orcid":"https://orcid.org/0000-0003-1839-0855"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander W. Winkler","raw_affiliation_strings":["Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040208292","display_name":"Farbod Farshidian","orcid":"https://orcid.org/0000-0001-8269-6272"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Farbod Farshidian","raw_affiliation_strings":["Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075968312","display_name":"Diego Pardo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diego Pardo","raw_affiliation_strings":["Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053312475","display_name":"Michael Neunert","orcid":"https://orcid.org/0000-0003-2080-8376"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Neunert","raw_affiliation_strings":["Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077279214","display_name":"Jonas Buchli","orcid":"https://orcid.org/0000-0001-7494-8492"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jonas Buchli","raw_affiliation_strings":["Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Agile & Dexterous Robotics Laboratory, Institute of Robotics and Intelligent Systems, ETHZ Zurich, Zurich, Switzerland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2708,"has_fulltext":false,"cited_by_count":84,"citation_normalized_percentile":{"value":0.92609318,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"2","issue":"4","first_page":"2201","last_page":"2208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9800000190734863,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9764999747276306,"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/bounding-overwatch","display_name":"Bounding overwatch","score":0.6687146425247192},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6182444095611572},{"id":"https://openalex.org/keywords/kinematics","display_name":"Kinematics","score":0.5560561418533325},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5433251857757568},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.5367475748062134},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5365405678749084},{"id":"https://openalex.org/keywords/zero-moment-point","display_name":"Zero moment point","score":0.5354908108711243},{"id":"https://openalex.org/keywords/trajectory-optimization","display_name":"Trajectory optimization","score":0.52937912940979},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.49915623664855957},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4974198639392853},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4276478588581085},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.42280229926109314},{"id":"https://openalex.org/keywords/humanoid-robot","display_name":"Humanoid robot","score":0.314414918422699},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3005278408527374},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22866275906562805},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.17313003540039062},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.17280003428459167},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10962653160095215},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09273266792297363},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.08194604516029358},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.07016029953956604}],"concepts":[{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6687146425247192},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6182444095611572},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.5560561418533325},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5433251857757568},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.5367475748062134},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5365405678749084},{"id":"https://openalex.org/C19245436","wikidata":"https://www.wikidata.org/wiki/Q279038","display_name":"Zero moment point","level":4,"score":0.5354908108711243},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.52937912940979},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.49915623664855957},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4974198639392853},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4276478588581085},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42280229926109314},{"id":"https://openalex.org/C60692881","wikidata":"https://www.wikidata.org/wiki/Q584529","display_name":"Humanoid robot","level":3,"score":0.314414918422699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3005278408527374},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22866275906562805},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.17313003540039062},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.17280003428459167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10962653160095215},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09273266792297363},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.08194604516029358},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.07016029953956604},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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":2,"locations":[{"id":"doi:10.1109/lra.2017.2723931","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2017.2723931","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766","2377-3774"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Robotics and Automation Letters","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:253732","is_oa":true,"landing_page_url":"https://youtu.be/5WLeQMBuv30","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:253732","is_oa":true,"landing_page_url":"https://youtu.be/5WLeQMBuv30","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320326765","display_name":"National Centre of Competence in Research Robotics","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W276848478","https://openalex.org/W1582919213","https://openalex.org/W1592294156","https://openalex.org/W1974420726","https://openalex.org/W1985875375","https://openalex.org/W2022144657","https://openalex.org/W2037729465","https://openalex.org/W2042408133","https://openalex.org/W2043709302","https://openalex.org/W2080132051","https://openalex.org/W2086853455","https://openalex.org/W2093298840","https://openalex.org/W2094444216","https://openalex.org/W2101340954","https://openalex.org/W2110194613","https://openalex.org/W2116310395","https://openalex.org/W2123871098","https://openalex.org/W2133859362","https://openalex.org/W2144587497","https://openalex.org/W2150317946","https://openalex.org/W2153190828","https://openalex.org/W2154139861","https://openalex.org/W2162495121","https://openalex.org/W2296360731","https://openalex.org/W2326849350","https://openalex.org/W2333533581","https://openalex.org/W2413365548","https://openalex.org/W2415458238","https://openalex.org/W2491414412","https://openalex.org/W2529220408","https://openalex.org/W2539534359","https://openalex.org/W2569909268","https://openalex.org/W2617744508","https://openalex.org/W2645990732","https://openalex.org/W2739146943","https://openalex.org/W3099855898","https://openalex.org/W3105372678","https://openalex.org/W6610027523","https://openalex.org/W6739409706"],"related_works":["https://openalex.org/W2168647525","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"],"abstract_inverted_index":{"This":[0,53,83],"letter":[1],"combines":[2],"the":[3,13,40,80,90,119,122],"fast":[4],"zero-moment-point":[5],"approaches":[6],"that":[7],"work":[8],"well":[9],"in":[10,102,112],"practice":[11],"with":[12,79],"broader":[14],"range":[15],"of":[16,18,31,39,89,100,121],"capabilities":[17],"a":[19,36,86,115,126],"trajectory":[20],"optimization":[21],"formulation,":[22],"by":[23],"optimizing":[24],"over":[25],"body":[26],"motion,":[27],"footholds,":[28],"and":[29,50,68,75,96],"center":[30],"pressure":[32],"simultaneously.":[33],"We":[34,117],"introduce":[35],"vertex-based":[37],"representation":[38,88],"support-area":[41],"constraint,":[42],"which":[43,105],"can":[44],"treat":[45],"arbitrarily":[46],"oriented":[47],"point-,":[48],"line-,":[49],"area-contacts":[51],"uniformly.":[52],"generalization":[54],"allows":[55,106],"us":[56,107],"to":[57,108],"create":[58],"motions,":[59],"such":[60],"as":[61],"quadrupedal":[62],"walking,":[63,74],"trotting,":[64],"bounding,":[65],"pacing,":[66],"combinations,":[67],"transitions":[69],"between":[70],"these,":[71],"limping,":[72],"bipedal":[73],"push":[76],"recovery":[77],"all":[78],"same":[81],"approach.":[82],"formulation":[84],"constitutes":[85],"minimal":[87],"physical":[91],"laws":[92],"(unilateral":[93],"contact":[94],"forces)":[95],"kinematic":[97],"restrictions":[98],"(range":[99],"motion)":[101],"legged":[103],"locomotion,":[104],"generate":[109],"diverse":[110],"motions":[111,124],"less":[113],"than":[114],"second.":[116],"demonstrate":[118],"feasibility":[120],"generated":[123],"on":[125],"real":[127],"quadruped":[128],"robot.":[129]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
