{"id":"https://openalex.org/W4391020309","doi":"https://doi.org/10.1109/cdc49753.2023.10383230","title":"Higher-Order Retraction Maps and Construction of Numerical Methods for Optimal Control of Mechanical Systems","display_name":"Higher-Order Retraction Maps and Construction of Numerical Methods for Optimal Control of Mechanical Systems","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391020309","doi":"https://doi.org/10.1109/cdc49753.2023.10383230"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383230","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","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/A5030193701","display_name":"Alexandre Anahory Simoes","orcid":"https://orcid.org/0000-0003-4644-876X"},"institutions":[{"id":"https://openalex.org/I125068653","display_name":"IE University","ror":"https://ror.org/02jjdwm75","country_code":"ES","type":"education","lineage":["https://openalex.org/I125068653"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Alexandre Anahory Simoes","raw_affiliation_strings":["School of Science and Technology, IE University,Spain","School of Science and Technology, IE University, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science and Technology, IE University,Spain","institution_ids":["https://openalex.org/I125068653"]},{"raw_affiliation_string":"School of Science and Technology, IE University, Spain","institution_ids":["https://openalex.org/I125068653"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073767122","display_name":"Mar\u00eda Barbero-Li\u00f1\u00e1n","orcid":"https://orcid.org/0000-0001-5151-9775"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mar\u00eda Barbero Li\u00f1\u00e1n","raw_affiliation_strings":["Universidad Politécnica de Madrid,Departamento de Matemática Aplicada,Madrid,Spain,28040"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Politécnica de Madrid,Departamento de Matemática Aplicada,Madrid,Spain,28040","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011498718","display_name":"Leonardo Colombo","orcid":"https://orcid.org/0000-0003-2085-3871"},"institutions":[{"id":"https://openalex.org/I4210125392","display_name":"Centre for Automation and Robotics","ror":"https://ror.org/02wh02235","country_code":"ES","type":"facility","lineage":["https://openalex.org/I134820265","https://openalex.org/I4210125392","https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Leonardo Colombo","raw_affiliation_strings":["Centre for Automation and Robotics (CSIC-UPM), Ctra. M300 Campo Real, Km 0,200,Arganda del Rey, Madrid,Spain,28500"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Automation and Robotics (CSIC-UPM), Ctra. M300 Campo Real, Km 0,200,Arganda del Rey, Madrid,Spain,28500","institution_ids":["https://openalex.org/I4210125392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061941032","display_name":"David Mart\u0131\u0301n de Diego","orcid":"https://orcid.org/0000-0001-6762-8909"},"institutions":[{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]},{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]},{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"David Mart\u00edn de Diego","raw_affiliation_strings":["Institute of Mathematical Sciences (CSIC-UAM-UCM-UC3M),Madrid,Spain,28049"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences (CSIC-UAM-UCM-UC3M),Madrid,Spain,28049","institution_ids":["https://openalex.org/I4210157032","https://openalex.org/I50357001","https://openalex.org/I63634437"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1196,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.88174807,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"3288","last_page":"3295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9853000044822693,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9728000164031982,"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/discretization","display_name":"Discretization","score":0.7743576765060425},{"id":"https://openalex.org/keywords/tangent-bundle","display_name":"Tangent bundle","score":0.604703962802887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5528601408004761},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5419309139251709},{"id":"https://openalex.org/keywords/variational-integrator","display_name":"Variational integrator","score":0.521277904510498},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.5049589276313782},{"id":"https://openalex.org/keywords/tangent-vector","display_name":"Tangent vector","score":0.45035040378570557},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4332282245159149},{"id":"https://openalex.org/keywords/mechanical-system","display_name":"Mechanical system","score":0.42029353976249695},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38323119282722473},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36675649881362915},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34832319617271423},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.3056659698486328},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2935854494571686},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.2706165015697479},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22335490584373474},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10388723015785217},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09515038132667542}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7743576765060425},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.604703962802887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5528601408004761},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5419309139251709},{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.521277904510498},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5049589276313782},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.45035040378570557},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4332282245159149},{"id":"https://openalex.org/C171912257","wikidata":"https://www.wikidata.org/wiki/Q11019","display_name":"Mechanical system","level":2,"score":0.42029353976249695},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38323119282722473},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36675649881362915},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34832319617271423},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.3056659698486328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2935854494571686},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.2706165015697479},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22335490584373474},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10388723015785217},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09515038132667542},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc49753.2023.10383230","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W78030520","https://openalex.org/W581347801","https://openalex.org/W1408746698","https://openalex.org/W1524590822","https://openalex.org/W1973734421","https://openalex.org/W1975418576","https://openalex.org/W1982729005","https://openalex.org/W2011979132","https://openalex.org/W2015807295","https://openalex.org/W2028324955","https://openalex.org/W2030394252","https://openalex.org/W2030527848","https://openalex.org/W2116648104","https://openalex.org/W2151394936","https://openalex.org/W2162991084","https://openalex.org/W2501614392","https://openalex.org/W2892277472","https://openalex.org/W2963460487","https://openalex.org/W2963716260","https://openalex.org/W2964080211","https://openalex.org/W3098737297","https://openalex.org/W4205293427","https://openalex.org/W4213314924","https://openalex.org/W4285184769","https://openalex.org/W4287127383","https://openalex.org/W4292078513","https://openalex.org/W6603115780","https://openalex.org/W6724430050"],"related_works":["https://openalex.org/W2537694785","https://openalex.org/W2006096639","https://openalex.org/W4213445152","https://openalex.org/W340073320","https://openalex.org/W3155105888","https://openalex.org/W2946414997","https://openalex.org/W86413332","https://openalex.org/W4391020915","https://openalex.org/W2400724917","https://openalex.org/W2961659155"],"abstract_inverted_index":{"Retractions":[0],"maps":[1,30],"are":[2],"used":[3],"to":[4,35,40,87,103],"define":[5],"a":[6,36,50,66,78,84,110],"discretization":[7,29,80],"of":[8,12,19,77,95,109],"the":[9,13,20,24,45,75,92],"tangent":[10,38],"bundle":[11,39],"configuration":[14,21],"manifold":[15,22],"as":[16,65],"two":[17],"copies":[18],"where":[23],"dynamics":[25],"take":[26],"place.":[27],"Such":[28],"can":[31,62],"be":[32,63],"conveniently":[33],"lifted":[34],"higher-order":[37,46,67,79],"construct":[41,88],"geometric":[42,89],"integrators":[43,90],"for":[44,57,91,106],"Euler-Lagrange":[47],"equations.":[48],"Given":[49],"cost":[51],"function,":[52],"an":[53],"optimal":[54,93],"control":[55,94],"problem":[56],"fully":[58],"actuated":[59],"mechanical":[60,96],"systems":[61],"understood":[64],"variational":[68],"problem.":[69],"In":[70,98],"this":[71],"paper":[72],"we":[73,100],"introduce":[74],"notion":[76],"map":[81,86],"associated":[82],"with":[83],"retraction":[85],"systems.":[97],"particular,":[99],"study":[101],"applications":[102],"path":[104],"planning":[105],"obstacle":[107],"avoidance":[108],"planar":[111],"rigid":[112],"body.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}