{"id":"https://openalex.org/W4416214752","doi":"https://doi.org/10.1109/lra.2025.3632610","title":"Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robots","display_name":"Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robots","publication_year":2025,"publication_date":"2025-11-14","ids":{"openalex":"https://openalex.org/W4416214752","doi":"https://doi.org/10.1109/lra.2025.3632610"},"language":"en","primary_location":{"id":"doi:10.1109/lra.2025.3632610","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2025.3632610","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766"],"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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.07823","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080191249","display_name":"Lorenzo Amatucci","orcid":"https://orcid.org/0009-0006-6764-8102"},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lorenzo Amatucci","raw_affiliation_strings":["Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy"],"raw_orcid":"https://orcid.org/0009-0006-6764-8102","affiliations":[{"raw_affiliation_string":"Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy","institution_ids":["https://openalex.org/I30771326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029470639","display_name":"Jo\u00e3o Sousa-Pinto","orcid":"https://orcid.org/0000-0003-2469-2809"},"institutions":[{"id":"https://openalex.org/I4210107260","display_name":"Apple (United Kingdom)","ror":"https://ror.org/01vpeym60","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210107260"]},{"id":"https://openalex.org/I4210153776","display_name":"Apple (United States)","ror":"https://ror.org/059hsda18","country_code":"US","type":"company","lineage":["https://openalex.org/I4210153776"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Jo\u00e3o Sousa-Pinto","raw_affiliation_strings":["Apple, Cupertino, USA","Apple"],"raw_orcid":"https://orcid.org/0000-0003-2469-2809","affiliations":[{"raw_affiliation_string":"Apple, Cupertino, USA","institution_ids":["https://openalex.org/I4210153776"]},{"raw_affiliation_string":"Apple","institution_ids":["https://openalex.org/I4210107260"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090269671","display_name":"Giulio Turrisi","orcid":"https://orcid.org/0000-0003-3007-3553"},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giulio Turrisi","raw_affiliation_strings":["Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy"],"raw_orcid":"https://orcid.org/0000-0003-3007-3553","affiliations":[{"raw_affiliation_string":"Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy","institution_ids":["https://openalex.org/I30771326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027758717","display_name":"Dominique Orban","orcid":"https://orcid.org/0000-0002-8017-7687"},"institutions":[{"id":"https://openalex.org/I45683168","display_name":"Polytechnique Montr\u00e9al","ror":"https://ror.org/05f8d4e86","country_code":"CA","type":"education","lineage":["https://openalex.org/I45683168"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Dominique Orban","raw_affiliation_strings":["GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montr&#x00E9;al, Montreal, Canada"],"raw_orcid":"https://orcid.org/0000-0002-8017-7687","affiliations":[{"raw_affiliation_string":"GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montr&#x00E9;al, Montreal, Canada","institution_ids":["https://openalex.org/I45683168"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086426608","display_name":"Victor Barasuol","orcid":"https://orcid.org/0000-0003-4966-5743"},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Victor Barasuol","raw_affiliation_strings":["Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy"],"raw_orcid":"https://orcid.org/0000-0003-4966-5743","affiliations":[{"raw_affiliation_string":"Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy","institution_ids":["https://openalex.org/I30771326"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010033061","display_name":"Claudio Semini","orcid":"https://orcid.org/0000-0002-3034-4686"},"institutions":[{"id":"https://openalex.org/I30771326","display_name":"Italian Institute of Technology","ror":"https://ror.org/042t93s57","country_code":"IT","type":"facility","lineage":["https://openalex.org/I30771326"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Claudio Semini","raw_affiliation_strings":["Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy"],"raw_orcid":"https://orcid.org/0000-0002-3034-4686","affiliations":[{"raw_affiliation_string":"Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy","institution_ids":["https://openalex.org/I30771326"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4208,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82649791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"11","issue":"1","first_page":"1010","last_page":"1017"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10879","display_name":"Robotic Locomotion and Control","score":0.930400013923645,"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":0.930400013923645,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.019899999722838402,"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":0.00860000029206276,"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/solver","display_name":"Solver","score":0.6757000088691711},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.590499997138977},{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.5679000020027161},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5454999804496765},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5371999740600586},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5069000124931335},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.46880000829696655},{"id":"https://openalex.org/keywords/legged-robot","display_name":"Legged robot","score":0.4675000011920929},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.44699999690055847}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7613999843597412},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6757000088691711},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.590499997138977},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.5679000020027161},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5454999804496765},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5371999740600586},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5069000124931335},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.46880000829696655},{"id":"https://openalex.org/C2779908020","wikidata":"https://www.wikidata.org/wiki/Q1424704","display_name":"Legged robot","level":3,"score":0.4675000011920929},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.44699999690055847},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.39890000224113464},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3736000061035156},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.35989999771118164},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C172707124","wikidata":"https://www.wikidata.org/wiki/Q423488","display_name":"Actuator","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.3190999925136566},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.296099990606308},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.2937999963760376},{"id":"https://openalex.org/C145565327","wikidata":"https://www.wikidata.org/wiki/Q852514","display_name":"Motion control","level":3,"score":0.27790001034736633},{"id":"https://openalex.org/C150415221","wikidata":"https://www.wikidata.org/wiki/Q40687","display_name":"Robotic arm","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C65401140","wikidata":"https://www.wikidata.org/wiki/Q7353385","display_name":"Robot control","level":4,"score":0.25999999046325684},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/lra.2025.3632610","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2025.3632610","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766"],"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:publications.polymtl.ca:70296","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:arXiv.org:2506.07823","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.07823","pdf_url":"https://arxiv.org/pdf/2506.07823","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.07823","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.07823","pdf_url":"https://arxiv.org/pdf/2506.07823","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,28,116,127,158],"novel":[4],"Model":[5],"Predictive":[6],"Control":[7],"(MPC)":[8],"implementation":[9,105],"for":[10,121,130,161],"legged":[11,165],"robot":[12],"locomotion":[13],"that":[14,167],"leverages":[15],"GPU":[16],"parallelization.":[17],"Our":[18],"approach":[19],"enables":[20],"both":[21],"temporal":[22],"and":[23,78,92,111,126],"state-space":[24],"parallelization":[25,186],"by":[26],"incorporating":[27],"parallel":[29],"associative":[30],"scan":[31],"to":[32,115,163,178],"solve":[33],"the":[34,42,84,87,93,96,101,138,148,155,179,182,191,197,200],"primal-dual":[35],"Karush-Kuhn-Tucker":[36],"(KKT)":[37],"system.":[38],"In":[39],"this":[40,104,209],"way,":[41],"optimal":[43],"control":[44,90],"problem":[45,149],"is":[46],"solved":[47],"in":[48,119,171,199,203],"<inline-formula":[49,62,70,74,79],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[50,63,71,75,80,216],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[51,64,72,76,81],"notation=\"LaTeX\">$\\mathcal":[52,65],"{O}(\\log":[53],"^{2}(n)\\log":[54],"{N}":[55],"+":[56,67],"\\log":[57],"^{2}(m))$</tex-math></inline-formula>":[58],"complexity,":[59],"instead":[60],"of":[61,86,95,103,157,193],"{O}(N(n":[66],"m)^{3})$</tex-math></inline-formula>,":[68],"where":[69],"notation=\"LaTeX\">$n$</tex-math></inline-formula>,":[73],"notation=\"LaTeX\">$m$</tex-math></inline-formula>,":[77],"notation=\"LaTeX\">$N$</tex-math></inline-formula>":[82],"are":[83],"dimension":[85],"system":[88],"state,":[89],"vector,":[91],"length":[94],"prediction":[97,139],"horizon.":[98],"We":[99],"demonstrate":[100],"advantages":[102],"over":[106],"two":[107],"state-of-the-art":[108],"solvers":[109],"(acados":[110],"crocoddyl),":[112],"achieving":[113],"up":[114,162],"60%":[117],"improvement":[118,129],"runtime":[120],"Whole":[122],"Body":[123,133],"Dynamics":[124,134],"(WB)-MPC":[125],"700%":[128],"Single":[131],"Rigid":[132],"(SRBD)-MPC":[135],"when":[136],"varying":[137],"horizon":[140],"length.":[141],"The":[142,205],"presented":[143],"formulation":[144],"scales":[145],"efficiently":[146],"with":[147,196,208],"state":[150],"dimensions":[151],"as":[152],"well,":[153],"enabling":[154],"definition":[156],"centralized":[159],"controller":[160],"16":[164],"robots":[166],"can":[168,211],"be":[169,212],"computed":[170],"less":[172],"than":[173],"25":[174],"ms.":[175],"Furthermore,":[176],"thanks":[177],"JAX":[180],"implementation,":[181],"solver":[183],"supports":[184],"large-scale":[185],"across":[187],"multiple":[188],"environments,":[189],"allowing":[190],"possibility":[192],"performing":[194],"learning":[195],"MPC":[198],"loop":[201],"directly":[202],"GPU.":[204],"code":[206],"associated":[207],"work":[210],"found":[213],"at":[214],"<uri":[215],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">https://github.com/iit-DLSLab/mpx</uri>.":[217]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}