{"id":"https://openalex.org/W2125347271","doi":"https://doi.org/10.1109/robot.1998.677020","title":"Quadratic optimization of force distribution in walking machines","display_name":"Quadratic optimization of force distribution in walking machines","publication_year":2002,"publication_date":"2002-11-27","ids":{"openalex":"https://openalex.org/W2125347271","doi":"https://doi.org/10.1109/robot.1998.677020","mag":"2125347271"},"language":"en","primary_location":{"id":"doi:10.1109/robot.1998.677020","is_oa":false,"landing_page_url":"https://doi.org/10.1109/robot.1998.677020","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146)","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/A5071582843","display_name":"Duane Marhefka","orcid":null},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D.W. Marhefka","raw_affiliation_strings":["Department of Electrical Engineering, Ohio State Uinversity, Columbus, OH, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Ohio State Uinversity, Columbus, OH, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057364155","display_name":"David E. Orin","orcid":null},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D.E. Orin","raw_affiliation_strings":["Department of Electrical Engineering, Ohio State Uinversity, Columbus, OH, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Ohio State Uinversity, Columbus, OH, USA","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":2.2404,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.88002416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"1","issue":null,"first_page":"477","last_page":"483"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.9987000226974487,"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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.9987000226974487,"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/T10784","display_name":"Muscle activation and electromyography studies","score":0.9977999925613403,"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/T10879","display_name":"Robotic Locomotion and Control","score":0.9965999722480774,"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/torque","display_name":"Torque","score":0.6893934011459351},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.6782915592193604},{"id":"https://openalex.org/keywords/hexapod","display_name":"Hexapod","score":0.6562424898147583},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.6510106325149536},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5234243869781494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5134104490280151},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.49119946360588074},{"id":"https://openalex.org/keywords/actuator","display_name":"Actuator","score":0.46381041407585144},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4637836217880249},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4608096778392792},{"id":"https://openalex.org/keywords/efficient-energy-use","display_name":"Efficient energy use","score":0.45212864875793457},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.44160833954811096},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4318380355834961},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28141409158706665},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.21322035789489746},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.11368262767791748},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07222914695739746}],"concepts":[{"id":"https://openalex.org/C144171764","wikidata":"https://www.wikidata.org/wiki/Q48103","display_name":"Torque","level":2,"score":0.6893934011459351},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.6782915592193604},{"id":"https://openalex.org/C136434205","wikidata":"https://www.wikidata.org/wiki/Q3437269","display_name":"Hexapod","level":3,"score":0.6562424898147583},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.6510106325149536},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5234243869781494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5134104490280151},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.49119946360588074},{"id":"https://openalex.org/C172707124","wikidata":"https://www.wikidata.org/wiki/Q423488","display_name":"Actuator","level":2,"score":0.46381041407585144},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4637836217880249},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4608096778392792},{"id":"https://openalex.org/C2742236","wikidata":"https://www.wikidata.org/wiki/Q924713","display_name":"Efficient energy use","level":2,"score":0.45212864875793457},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44160833954811096},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4318380355834961},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28141409158706665},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.21322035789489746},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.11368262767791748},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07222914695739746},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical 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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/robot.1998.677020","is_oa":false,"landing_page_url":"https://doi.org/10.1109/robot.1998.677020","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.9100000262260437,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320308716","display_name":"Ohio Space Grant Consortium","ror":"https://ror.org/04y65f081"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1625456515","https://openalex.org/W1643150164","https://openalex.org/W2078038590","https://openalex.org/W2091849582","https://openalex.org/W2093974551","https://openalex.org/W2106385771","https://openalex.org/W2122909244","https://openalex.org/W2139476099","https://openalex.org/W2141012854","https://openalex.org/W2154631808","https://openalex.org/W4256104700"],"related_works":["https://openalex.org/W4206704743","https://openalex.org/W4313119266","https://openalex.org/W2164807043","https://openalex.org/W4231448069","https://openalex.org/W2019128690","https://openalex.org/W2128461291","https://openalex.org/W2355907103","https://openalex.org/W2270789747","https://openalex.org/W436931041","https://openalex.org/W1495847109"],"abstract_inverted_index":{"Energy":[0,35],"efficiency":[1,13],"remains":[2],"a":[3,89,104],"problem":[4],"in":[5,72,121],"walking":[6],"machines.":[7],"One":[8],"approach":[9,113],"to":[10,28,54,62,79],"improving":[11],"energy":[12,123],"involves":[14],"solving":[15],"for":[16,100],"an":[17],"optimal":[18,57,65],"set":[19],"of":[20,92,114],"foot":[21],"forces":[22,117],"which":[23,40,85],"minimizes":[24],"the":[25,38,56,111],"power":[26,97],"supplied":[27],"DC":[29],"motor":[30],"actuators":[31],"at":[32],"each":[33],"instant.":[34],"regenerated":[36],"by":[37],"motors,":[39],"may":[41,118],"be":[42,49],"significant,":[43],"is":[44,70,108],"generally":[45],"lost":[46],"and":[47,95],"should":[48],"explicitly":[50],"taken":[51],"into":[52],"account":[53],"produce":[55,63],"force":[58],"distribution.":[59],"A":[60],"method":[61],"this":[64,73],"solution":[66],"using":[67],"quadratic":[68,82],"programming":[69,83],"developed":[71],"paper.":[74],"The":[75],"results":[76],"are":[77],"compared":[78],"three":[80],"suboptimal":[81],"approaches":[84],"minimize":[86],"internal":[87,116],"forces,":[88],"weighted":[90],"norm":[91],"joint":[93],"torques,":[94],"finally":[96],"without":[98],"accounting":[99],"regeneration,":[101],"all":[102],"on":[103],"simulated":[105],"hexapod.":[106],"It":[107],"found":[109],"that":[110],"common":[112],"minimizing":[115],"often":[119],"result":[120],"poor":[122],"efficiency.":[124]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}