{"id":"https://openalex.org/W7124471284","doi":"https://doi.org/10.1109/tie.2025.3645471","title":"Contact-Implicit Optimal Planning and Iterative Learning Control for Quadrupedal Robots","display_name":"Contact-Implicit Optimal Planning and Iterative Learning Control for Quadrupedal Robots","publication_year":2026,"publication_date":"2026-01-16","ids":{"openalex":"https://openalex.org/W7124471284","doi":"https://doi.org/10.1109/tie.2025.3645471"},"language":"en","primary_location":{"id":"doi:10.1109/tie.2025.3645471","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tie.2025.3645471","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Industrial Electronics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1109/tie.2025.3645471","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119219249","display_name":"Pietro Gori","orcid":"https://orcid.org/0009-0002-4989-321X"},"institutions":[{"id":"https://openalex.org/I1300504238","display_name":"Piaggio (Italy)","ror":"https://ror.org/00r254y42","country_code":"IT","type":"company","lineage":["https://openalex.org/I1300504238"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Pietro Gori","raw_affiliation_strings":["Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy"],"raw_orcid":"https://orcid.org/0009-0002-4989-321X","affiliations":[{"raw_affiliation_string":"Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I1300504238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120163031","display_name":"Vincenzo Degiacomo","orcid":null},"institutions":[{"id":"https://openalex.org/I1300504238","display_name":"Piaggio (Italy)","ror":"https://ror.org/00r254y42","country_code":"IT","type":"company","lineage":["https://openalex.org/I1300504238"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Vincenzo Degiacomo","raw_affiliation_strings":["Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I1300504238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064305562","display_name":"Michele Pierallini","orcid":"https://orcid.org/0000-0003-0547-2747"},"institutions":[{"id":"https://openalex.org/I1300504238","display_name":"Piaggio (Italy)","ror":"https://ror.org/00r254y42","country_code":"IT","type":"company","lineage":["https://openalex.org/I1300504238"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Michele Pierallini","raw_affiliation_strings":["Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0547-2747","affiliations":[{"raw_affiliation_string":"Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I1300504238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040744338","display_name":"Franco Angelini","orcid":null},"institutions":[{"id":"https://openalex.org/I1300504238","display_name":"Piaggio (Italy)","ror":"https://ror.org/00r254y42","country_code":"IT","type":"company","lineage":["https://openalex.org/I1300504238"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franco Angelini","raw_affiliation_strings":["Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2559-9569","affiliations":[{"raw_affiliation_string":"Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I1300504238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042460018","display_name":"Manolo Garabini","orcid":"https://orcid.org/0000-0002-5873-3173"},"institutions":[{"id":"https://openalex.org/I1300504238","display_name":"Piaggio (Italy)","ror":"https://ror.org/00r254y42","country_code":"IT","type":"company","lineage":["https://openalex.org/I1300504238"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Manolo Garabini","raw_affiliation_strings":["Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0002-5873-3173","affiliations":[{"raw_affiliation_string":"Centro di Ricerca “Enrico Piaggio”, Università di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I1300504238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5119219249"],"corresponding_institution_ids":["https://openalex.org/I1300504238"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08805019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"73","issue":"6","first_page":"8838","last_page":"8847"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.980400025844574,"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":0.980400025844574,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.003000000026077032,"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/T11615","display_name":"Control and Dynamics of Mobile Robots","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/iterative-learning-control","display_name":"Iterative learning control","score":0.8489000201225281},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7548999786376953},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.6808000206947327},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6414999961853027},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5827000141143799},{"id":"https://openalex.org/keywords/terrain","display_name":"Terrain","score":0.5716000199317932},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5497000217437744},{"id":"https://openalex.org/keywords/motion-planning","display_name":"Motion planning","score":0.5428000092506409},{"id":"https://openalex.org/keywords/trajectory-optimization","display_name":"Trajectory optimization","score":0.5274999737739563}],"concepts":[{"id":"https://openalex.org/C117619785","wikidata":"https://www.wikidata.org/wiki/Q6094414","display_name":"Iterative learning control","level":3,"score":0.8489000201225281},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7548999786376953},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.6808000206947327},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6414999961853027},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6098999977111816},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5827000141143799},{"id":"https://openalex.org/C161840515","wikidata":"https://www.wikidata.org/wiki/Q186131","display_name":"Terrain","level":2,"score":0.5716000199317932},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5497000217437744},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.5428000092506409},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.5274999737739563},{"id":"https://openalex.org/C145565327","wikidata":"https://www.wikidata.org/wiki/Q852514","display_name":"Motion control","level":3,"score":0.47189998626708984},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.42640000581741333},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.4090000092983246},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.38420000672340393},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3781000077724457},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C151800584","wikidata":"https://www.wikidata.org/wiki/Q2370000","display_name":"Gait","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32510000467300415},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C74222875","wikidata":"https://www.wikidata.org/wiki/Q16000312","display_name":"Robot kinematics","level":4,"score":0.32269999384880066},{"id":"https://openalex.org/C65401140","wikidata":"https://www.wikidata.org/wiki/Q7353385","display_name":"Robot control","level":4,"score":0.3206000030040741},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30790001153945923},{"id":"https://openalex.org/C60692881","wikidata":"https://www.wikidata.org/wiki/Q584529","display_name":"Humanoid robot","level":3,"score":0.2922999858856201},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.2904999852180481},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.28220000863075256},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2696000039577484},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tie.2025.3645471","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tie.2025.3645471","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Industrial Electronics","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/1347627","is_oa":false,"landing_page_url":"https://hdl.handle.net/11568/1347627","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1109/tie.2025.3645471","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tie.2025.3645471","pdf_url":null,"source":{"id":"https://openalex.org/S58031724","display_name":"IEEE Transactions on Industrial Electronics","issn_l":"0278-0046","issn":["0278-0046","1557-9948"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Industrial Electronics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.42574426531791687,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,61],"propose":[4],"a":[5,33,89],"novel":[6],"approach":[7],"for":[8,55],"motion":[9],"planning":[10,84],"and":[11,22,58,85,109,115],"control":[12,66],"in":[13,88],"quadruped":[14,102],"robots":[15],"that":[16,69],"simultaneously":[17],"optimizes":[18],"the":[19,26,50,98,101],"base":[20],"trajectory":[21,86],"contact":[23,83],"sequence":[24],"along":[25],"longitudinal":[27],"direction.":[28],"The":[29],"method":[30,99],"relies":[31],"on":[32,100],"simplified":[34],"2-D":[35],"single":[36],"rigid":[37],"body":[38],"model":[39,56],"to":[40,77,94],"compute":[41],"an":[42,63],"optimal":[43],"trajectory,":[44],"which":[45],"is":[46],"then":[47],"mapped":[48],"at":[49],"joint":[51],"level.":[52],"To":[53],"compensate":[54],"approximations":[57],"environmental":[59],"uncertainties,":[60],"introduce":[62],"iterative":[64],"learning":[65],"(ILC)":[67],"scheme":[68],"progressively":[70],"improves":[71],"tracking":[72],"performance":[73],"across":[74,112],"repetitions.":[75],"Compared":[76],"existing":[78],"approaches,":[79],"our":[80],"formulation":[81],"unifies":[82],"optimization":[87],"learning-while-doing":[90],"framework,":[91],"enhancing":[92],"robustness":[93],"disturbances.":[95],"We":[96],"validate":[97],"robot":[103],"Solo-12,":[104],"demonstrating":[105],"adaptive":[106],"gait":[107],"generation":[108],"stable":[110],"locomotion":[111],"different":[113],"terrains":[114],"perturbations.":[116]},"counts_by_year":[],"updated_date":"2026-05-05T06:06:40.768181","created_date":"2026-01-17T00:00:00"}