{"id":"https://openalex.org/W2029068927","doi":"https://doi.org/10.1109/humanoids.2013.7029991","title":"Quadratic encoding of optimized humanoid walking","display_name":"Quadratic encoding of optimized humanoid walking","publication_year":2013,"publication_date":"2013-10-01","ids":{"openalex":"https://openalex.org/W2029068927","doi":"https://doi.org/10.1109/humanoids.2013.7029991","mag":"2029068927"},"language":"en","primary_location":{"id":"doi:10.1109/humanoids.2013.7029991","is_oa":false,"landing_page_url":"https://doi.org/10.1109/humanoids.2013.7029991","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 13th IEEE-RAS 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/A5101593358","display_name":"Jung-Gon Kim","orcid":"https://orcid.org/0000-0001-6951-6126"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Junggon Kim","raw_affiliation_strings":["The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA","The Robotics Institute, Carnegie Mellon University 5000 Forbes Ave., Pittsburgh, PA, 15213, USA"],"affiliations":[{"raw_affiliation_string":"The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"The Robotics Institute, Carnegie Mellon University 5000 Forbes Ave., Pittsburgh, PA, 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011046225","display_name":"Nancy S. Pollard","orcid":"https://orcid.org/0000-0001-6464-839X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nancy S. Pollard","raw_affiliation_strings":["The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA","The Robotics Institute, Carnegie Mellon University 5000 Forbes Ave., Pittsburgh, PA, 15213, USA"],"affiliations":[{"raw_affiliation_string":"The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"The Robotics Institute, Carnegie Mellon University 5000 Forbes Ave., Pittsburgh, PA, 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055330939","display_name":"Christopher G. Atkeson","orcid":"https://orcid.org/0000-0003-4265-8452"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher G. Atkeson","raw_affiliation_strings":["The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA","The Robotics Institute, Carnegie Mellon University 5000 Forbes Ave., Pittsburgh, PA, 15213, USA"],"affiliations":[{"raw_affiliation_string":"The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"The Robotics Institute, Carnegie Mellon University 5000 Forbes Ave., Pittsburgh, PA, 15213, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101593358"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":1.5149,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84752761,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"129","issue":null,"first_page":"300","last_page":"306"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12290","display_name":"Human Motion and Animation","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T12290","display_name":"Human Motion and Animation","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10812","display_name":"Human Pose and Action Recognition","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.9969000220298767,"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/humanoid-robot","display_name":"Humanoid robot","score":0.7728159427642822},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.7507374882698059},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.6489601135253906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6230035424232483},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6183227300643921},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5324949026107788},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48055651783943176},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4660898745059967},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.4646904468536377},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.4427478015422821},{"id":"https://openalex.org/keywords/trajectory-optimization","display_name":"Trajectory optimization","score":0.4185256361961365},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.408661812543869},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.38032060861587524},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37310904264450073},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3595958352088928},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3185569941997528},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.29512912034988403},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28020861744880676}],"concepts":[{"id":"https://openalex.org/C60692881","wikidata":"https://www.wikidata.org/wiki/Q584529","display_name":"Humanoid robot","level":3,"score":0.7728159427642822},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.7507374882698059},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.6489601135253906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6230035424232483},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6183227300643921},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5324949026107788},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48055651783943176},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4660898745059967},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.4646904468536377},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.4427478015422821},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.4185256361961365},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.408661812543869},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.38032060861587524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37310904264450073},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3595958352088928},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3185569941997528},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.29512912034988403},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28020861744880676},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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.2013.7029991","is_oa":false,"landing_page_url":"https://doi.org/10.1109/humanoids.2013.7029991","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4699999988079071,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W98935309","https://openalex.org/W567131581","https://openalex.org/W1646038686","https://openalex.org/W1697370532","https://openalex.org/W1962169445","https://openalex.org/W1987431312","https://openalex.org/W2007976821","https://openalex.org/W2022144657","https://openalex.org/W2027247754","https://openalex.org/W2052980659","https://openalex.org/W2083334152","https://openalex.org/W2107149337","https://openalex.org/W2122054842","https://openalex.org/W2125356896","https://openalex.org/W2163668399","https://openalex.org/W2236379170","https://openalex.org/W2293545866","https://openalex.org/W2319958627","https://openalex.org/W2336236730","https://openalex.org/W4231947169","https://openalex.org/W4249614167","https://openalex.org/W6604104294","https://openalex.org/W6637131083","https://openalex.org/W6663401431","https://openalex.org/W6690051859"],"related_works":["https://openalex.org/W1616815502","https://openalex.org/W2327610550","https://openalex.org/W2364127131","https://openalex.org/W2155888019","https://openalex.org/W4206704743","https://openalex.org/W2911254004","https://openalex.org/W2905186505","https://openalex.org/W4254843719","https://openalex.org/W2031494345","https://openalex.org/W2152773061"],"abstract_inverted_index":{"In":[0,33],"this":[1,37],"paper":[2],"we":[3,39,112],"show":[4],"that":[5,136],"optimal":[6,44,100,126,142],"stepping":[7],"trajectories":[8,46],"and":[9,30,59,62],"trajectory":[10,66],"cost":[11,121],"for":[12,47,69],"a":[13,41,48,64,114,137,147],"walking":[14,45,101,143,154],"biped":[15],"robot":[16],"on":[17],"rough":[18],"terrain":[19],"can":[20,140],"be":[21],"encoded":[22],"as":[23],"simple":[24,138],"quadratic":[25,115],"functions":[26],"of":[27,43,87,153],"initial":[28],"state":[29,58],"footstep":[31,60,107,127],"sequence.":[32],"order":[34],"to":[35,117,150],"find":[36],"encoding,":[38],"build":[40],"database":[42],"3D":[49],"humanoid":[50],"model":[51],"by":[52,78,93],"sampling":[53],"the":[54,73,80,88,95,119],"input":[55],"space":[56],"(initial":[57],"sequence)":[61],"solving":[63],"physically-based":[65],"optimization":[67,152],"problem":[68],"each":[70],"sample.":[71],"Then,":[72],"function":[74,96,116,139],"coefficients":[75],"are":[76],"obtained":[77],"fitting":[79],"data":[81,103],"using":[82],"least":[83],"squares.":[84],"The":[85],"performance":[86],"proposed":[89],"method":[90],"is":[91],"evaluated":[92],"comparing":[94],"values":[97],"with":[98,105,129,155],"other":[99],"motion":[102],"generated":[104],"different":[106],"samples.":[108],"As":[109],"an":[110,125,130],"application,":[111],"use":[113],"calculate":[118],"effort":[120],"used":[122],"in":[123],"finding":[124],"sequence":[128],"A*":[131],"algorithm.":[132],"Our":[133],"study":[134],"shows":[135],"encode":[141],"effectively,":[144],"which":[145],"provides":[146],"fast":[148],"alternative":[149],"online":[151],"full":[156],"body":[157],"dynamics.":[158]},"counts_by_year":[{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}