{"id":"https://openalex.org/W4416779769","doi":"https://doi.org/10.1142/s0219843625500148","title":"Nonlinear optimal control for three-link biped robots","display_name":"Nonlinear optimal control for three-link biped robots","publication_year":2025,"publication_date":"2025-11-28","ids":{"openalex":"https://openalex.org/W4416779769","doi":"https://doi.org/10.1142/s0219843625500148"},"language":"en","primary_location":{"id":"doi:10.1142/s0219843625500148","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219843625500148","pdf_url":null,"source":{"id":"https://openalex.org/S75343556","display_name":"International Journal of Humanoid Robotics","issn_l":"0219-8436","issn":["0219-8436","1793-6942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Humanoid Robotics","raw_type":"journal-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/A5068059152","display_name":"Gerasimos Rigatos","orcid":"https://orcid.org/0000-0002-2972-7030"},"institutions":[{"id":"https://openalex.org/I4210135709","display_name":"Industrial Systems Institute","ror":"https://ror.org/02sy6k521","country_code":"GR","type":"nonprofit","lineage":["https://openalex.org/I4210135709"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"G. Rigatos","raw_affiliation_strings":["Unit of Industrial Automation, Industrial Systems Institute, Athena RC 26504, Patras, Greece"],"raw_orcid":"https://orcid.org/0000-0002-2972-7030","affiliations":[{"raw_affiliation_string":"Unit of Industrial Automation, Industrial Systems Institute, Athena RC 26504, Patras, Greece","institution_ids":["https://openalex.org/I4210135709"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018683464","display_name":"Masoud Abbaszadeh","orcid":"https://orcid.org/0000-0002-9440-1563"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Abbaszadeh","raw_affiliation_strings":["Department of ECS Engineering, Rensselaer Polytechnic Institute, 12065, Troy, NY, USA"],"raw_orcid":"https://orcid.org/0000-0002-9440-1563","affiliations":[{"raw_affiliation_string":"Department of ECS Engineering, Rensselaer Polytechnic Institute, 12065, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035300094","display_name":"Pierluigi Siano","orcid":"https://orcid.org/0000-0002-0975-0241"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]},{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["IT","ZA"],"is_corresponding":false,"raw_author_name":"P. Siano","raw_affiliation_strings":["Department of Electrical Engineering, University of Johannesburg, Johannesburg 2006, South Africa","Department of Management and Innovation System, University of Salerno, Fisciano 84084, Italy"],"raw_orcid":"https://orcid.org/0000-0002-0975-0241","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Johannesburg, Johannesburg 2006, South Africa","institution_ids":["https://openalex.org/I24027795"]},{"raw_affiliation_string":"Department of Management and Innovation System, University of Salerno, Fisciano 84084, Italy","institution_ids":["https://openalex.org/I131729948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085177063","display_name":"Mohammed S. Al-Numay","orcid":"https://orcid.org/0000-0001-8576-2060"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"M. Al-Numay","raw_affiliation_strings":["Department of Electrical Engineering, King Saud University, Riyadh 11421, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-8576-2060","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, King Saud University, Riyadh 11421, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023611239","display_name":"G. Cuccurullo","orcid":"https://orcid.org/0000-0002-8360-9641"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Cuccurullo","raw_affiliation_strings":["Department of Industrial Engineering, University of Salerno, Fisciano 84084, Italy"],"raw_orcid":"https://orcid.org/0000-0002-8360-9641","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, University of Salerno, Fisciano 84084, Italy","institution_ids":["https://openalex.org/I131729948"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.30658322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"01","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":0.9642000198364258,"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":0.9642000198364258,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","score":0.01209999993443489,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.002099999925121665,"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/control-theory","display_name":"Control theory (sociology)","score":0.8079000115394592},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.595300018787384},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5781999826431274},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5241000056266785},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.503000020980835},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.49480000138282776},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4790000021457672},{"id":"https://openalex.org/keywords/feedback-linearization","display_name":"Feedback linearization","score":0.4629000127315521},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.45570001006126404}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8079000115394592},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6326000094413757},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.595300018787384},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5781999826431274},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5241000056266785},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.503000020980835},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.49480000138282776},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4790000021457672},{"id":"https://openalex.org/C85736874","wikidata":"https://www.wikidata.org/wiki/Q672139","display_name":"Feedback linearization","level":3,"score":0.4629000127315521},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.45570001006126404},{"id":"https://openalex.org/C60692881","wikidata":"https://www.wikidata.org/wiki/Q584529","display_name":"Humanoid robot","level":3,"score":0.4498000144958496},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.446399986743927},{"id":"https://openalex.org/C523889960","wikidata":"https://www.wikidata.org/wiki/Q160695","display_name":"Torso","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.414000004529953},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.3939000070095062},{"id":"https://openalex.org/C88337583","wikidata":"https://www.wikidata.org/wiki/Q7883433","display_name":"Underactuation","level":3,"score":0.3725000023841858},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.29260000586509705},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.2727999985218048},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27129998803138733},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.26249998807907104},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219843625500148","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219843625500148","pdf_url":null,"source":{"id":"https://openalex.org/S75343556","display_name":"International Journal of Humanoid Robotics","issn_l":"0219-8436","issn":["0219-8436","1793-6942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Humanoid Robotics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335726","display_name":"Deanship of Scientific Research, King Saud University","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W331599624","https://openalex.org/W1596558867","https://openalex.org/W1981690142","https://openalex.org/W1985146165","https://openalex.org/W2006065844","https://openalex.org/W2025398316","https://openalex.org/W2025517931","https://openalex.org/W2031484125","https://openalex.org/W2043709900","https://openalex.org/W2047174209","https://openalex.org/W2092367305","https://openalex.org/W2092667683","https://openalex.org/W2137547873","https://openalex.org/W2166817744","https://openalex.org/W2216740760","https://openalex.org/W2257037833","https://openalex.org/W2494257136","https://openalex.org/W2775313399","https://openalex.org/W2887272742","https://openalex.org/W2969100958","https://openalex.org/W2989484444","https://openalex.org/W2991122042","https://openalex.org/W2991263242","https://openalex.org/W3012167894","https://openalex.org/W3093749610","https://openalex.org/W3116994129","https://openalex.org/W3156911523","https://openalex.org/W3200834782","https://openalex.org/W3206546804","https://openalex.org/W3212944001","https://openalex.org/W4226039314","https://openalex.org/W4245059895","https://openalex.org/W4285505687","https://openalex.org/W4288709678","https://openalex.org/W4309445056","https://openalex.org/W4382657654","https://openalex.org/W4386038305","https://openalex.org/W4387682164","https://openalex.org/W4389169843","https://openalex.org/W4394981647","https://openalex.org/W4395069625","https://openalex.org/W4399908905"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,57,98],"nonlinear":[4,64],"optimal":[5,65,100],"control":[6,66,124,131],"approach":[7],"for":[8],"the":[9,22,26,31,40,44,47,50,62,68,72,85,90,95,108,123,130],"three-link":[10,73],"biped":[11,74,96],"robot.":[12],"In":[13],"this":[14],"humanoid":[15],"robot":[16,75,97],"there":[17],"is":[18,30,34,56,104,116],"actuation":[19],"only":[20],"in":[21,43],"two":[23],"legs":[24],"while":[25],"third":[27],"link":[28],"which":[29],"robot\u2019s":[32,45],"torso":[33,42],"unactuated.":[35],"Due":[36],"to":[37],"nonlinearities":[38],"and":[39,52,84],"unactuated":[41],"dynamics,":[46],"treatment":[48],"of":[49,71,94,122,129],"stabilization":[51],"trajectories":[53],"tracking":[54],"problem":[55],"non-trivial":[58],"task.":[59],"To":[60,106],"solve":[61],"associated":[63,86],"problem,":[67],"state-space":[69,92],"model":[70,93],"undergoes":[76],"approximate":[77],"linearization":[78],"based":[79],"on":[80],"Taylor":[81],"series":[82],"expansion":[83],"Jacobian":[87],"matrices.":[88],"For":[89],"linearized":[91],"stabilizing":[99],"(H-infinity)":[101],"feedback":[102,110],"controller":[103],"designed.":[105],"compute":[107],"controller\u2019s":[109],"gains,":[111],"an":[112],"algebraic":[113],"Riccati":[114],"equation":[115],"repetitively":[117],"solved":[118],"at":[119],"each":[120],"iteration":[121],"algorithm.":[125],"The":[126],"stability":[127],"properties":[128],"method":[132],"are":[133],"proven":[134],"through":[135],"Lyapunov":[136],"analysis.":[137]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-11-28T00:00:00"}
