{"id":"https://openalex.org/W2289851065","doi":"https://doi.org/10.1109/cdc.2015.7402849","title":"Variational discretization for optimal control problems of nonholonomic mechanical systems","display_name":"Variational discretization for optimal control problems of nonholonomic mechanical systems","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2289851065","doi":"https://doi.org/10.1109/cdc.2015.7402849","mag":"2289851065"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2015.7402849","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7402849","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://zenodo.org/record/1265941","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102777647","display_name":"Leonardo Colombo","orcid":"https://orcid.org/0000-0001-6493-6113"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leonardo Colombo","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101763473","display_name":"Rohit Gupta","orcid":"https://orcid.org/0000-0002-5334-665X"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rohit Gupta","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109063322","display_name":"Anthony Bloch","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anthony Bloch","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, Michigan, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"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/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 Martin de Diego","raw_affiliation_strings":["Campus UAM, Calle Nicol\u00e1s Cabrera 15, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Campus UAM, Calle Nicol\u00e1s Cabrera 15, Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102777647"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.3403,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67602505,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"4047","last_page":"4052"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9975000023841858,"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"}},"topics":[{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9975000023841858,"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":0.9973999857902527,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/variational-integrator","display_name":"Variational integrator","score":0.8464529514312744},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.740313708782196},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7313912510871887},{"id":"https://openalex.org/keywords/nonholonomic-system","display_name":"Nonholonomic system","score":0.7148195505142212},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.6691610813140869},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.569945216178894},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4704505503177643},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.46097034215927124},{"id":"https://openalex.org/keywords/euler\u2013lagrange-equation","display_name":"Euler\u2013Lagrange equation","score":0.4455912709236145},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4269286096096039},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4194519519805908},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39515629410743713},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.331659197807312},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3038560748100281},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.2716962695121765},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.25747597217559814},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2114381194114685},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08865875005722046},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.07527020573616028}],"concepts":[{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.8464529514312744},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.740313708782196},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7313912510871887},{"id":"https://openalex.org/C138632511","wikidata":"https://www.wikidata.org/wiki/Q2478109","display_name":"Nonholonomic system","level":4,"score":0.7148195505142212},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.6691610813140869},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.569945216178894},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4704505503177643},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.46097034215927124},{"id":"https://openalex.org/C2776392105","wikidata":"https://www.wikidata.org/wiki/Q875744","display_name":"Euler\u2013Lagrange equation","level":3,"score":0.4455912709236145},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4269286096096039},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4194519519805908},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39515629410743713},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.331659197807312},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3038560748100281},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.2716962695121765},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.25747597217559814},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2114381194114685},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08865875005722046},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.07527020573616028},{"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/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2015.7402849","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7402849","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:zenodo.org:1265941","is_oa":true,"landing_page_url":"https://zenodo.org/record/1265941","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencePaper"}],"best_oa_location":{"id":"pmh:oai:zenodo.org:1265941","is_oa":true,"landing_page_url":"https://zenodo.org/record/1265941","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W200548747","https://openalex.org/W1544770838","https://openalex.org/W1989990825","https://openalex.org/W1993300073","https://openalex.org/W2000008197","https://openalex.org/W2023242456","https://openalex.org/W2086841921","https://openalex.org/W2116648104","https://openalex.org/W2148271773","https://openalex.org/W2170039048","https://openalex.org/W2333098752","https://openalex.org/W2962783108","https://openalex.org/W2964254546","https://openalex.org/W4292408540","https://openalex.org/W4300048918","https://openalex.org/W6632365957","https://openalex.org/W6766412127"],"related_works":["https://openalex.org/W1510253881","https://openalex.org/W2329610818","https://openalex.org/W589845481","https://openalex.org/W1603561442","https://openalex.org/W3001010211","https://openalex.org/W1555521844","https://openalex.org/W2013226669","https://openalex.org/W1966851594","https://openalex.org/W1953788151","https://openalex.org/W2963710483"],"abstract_inverted_index":{"This":[0],"paper":[1],"explores":[2],"the":[3,11,19,35,59,63,68,73],"construction":[4,20],"of":[5,14,21,27,51,58,62,81],"geometric":[6],"and":[7,18],"variational":[8,22,45,49],"methods":[9],"for":[10,24,72],"optimal":[12,28,36,75,79],"control":[13,29,37,76,80],"nonholonomic":[15,74],"mechanical":[16],"systems,":[17],"integrators":[23],"this":[25],"class":[26],"problems.":[30],"Given":[31],"a":[32,42,48,52,56,82],"cost":[33],"function,":[34],"problem":[38],"is":[39,85],"understood":[40],"as":[41,87],"constrained":[43],"higher-order":[44],"problem.":[46,77],"Through":[47],"discretization":[50],"Lagrangian":[53],"defined":[54],"in":[55],"submanifold":[57],"tangent":[60],"space":[61],"constraint":[64],"distribution,":[65],"we":[66],"obtain":[67],"discrete":[69],"Euler-Lagrange":[70],"equations":[71],"The":[78],"Chaplygin":[83],"sleigh":[84],"presented":[86],"an":[88],"illustrative":[89],"example.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}