{"id":"https://openalex.org/W2043357744","doi":"https://doi.org/10.1137/130950793","title":"Complexity of Control-Affine Motion Planning","display_name":"Complexity of Control-Affine Motion Planning","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2043357744","doi":"https://doi.org/10.1137/130950793","mag":"2043357744"},"language":"en","primary_location":{"id":"doi:10.1137/130950793","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130950793","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1309.2571","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013119422","display_name":"Fr\u00e9d\u00e9ric Jean","orcid":"https://orcid.org/0000-0001-8170-076X"},"institutions":[{"id":"https://openalex.org/I4210132720","display_name":"Laboratoire d'Optique Appliqu\u00e9e","ror":"https://ror.org/03czns913","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I201181511","https://openalex.org/I4210098836","https://openalex.org/I4210132720","https://openalex.org/I4210145102","https://openalex.org/I4210145102","https://openalex.org/I4405258625"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"F. Jean","raw_affiliation_strings":["OC - Optimisation et commande (828, boulevard des Mar\u00e9chaux 91120 Palaiseau - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"OC - Optimisation et commande (828, boulevard des Mar\u00e9chaux 91120 Palaiseau - France)","institution_ids":["https://openalex.org/I4210132720"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049756010","display_name":"Dario Prandi","orcid":"https://orcid.org/0000-0002-8156-5526"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es de l'\u00c9cole polytechnique","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210114274","display_name":"Laboratoire d\u2019Informatique et Syst\u00e8mes","ror":"https://ror.org/0257sgk90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274"]}],"countries":["FR","IT"],"is_corresponding":false,"raw_author_name":"D. Prandi","raw_affiliation_strings":["GECO - Geometric Control Design (CMAP - Centre de Math\u00e9matiques Appliqu\u00e9es \u00c9cole Polytechnique Route de Saclay 91128 Palaiseau Cedex - France)","LSIS - Laboratoire des Sciences de l'Information et des Syst\u00e8mes (Domaine Universitaire de Saint-J\u00e9r\u00f4me\r\nBatiment Polytech\r\nAvenue Escadrille Normandie-Niemen\r\n13397 MARSEILLE CEDEX 20 - France)","SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (via Bonomea, 265 - 34136 Trieste - Italy - Italy)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"GECO - Geometric Control Design (CMAP - Centre de Math\u00e9matiques Appliqu\u00e9es \u00c9cole Polytechnique Route de Saclay 91128 Palaiseau Cedex - France)","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210107641"]},{"raw_affiliation_string":"LSIS - Laboratoire des Sciences de l'Information et des Syst\u00e8mes (Domaine Universitaire de Saint-J\u00e9r\u00f4me\r\nBatiment Polytech\r\nAvenue Escadrille Normandie-Niemen\r\n13397 MARSEILLE CEDEX 20 - France)","institution_ids":["https://openalex.org/I4210114274"]},{"raw_affiliation_string":"SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (via Bonomea, 265 - 34136 Trieste - Italy - Italy)","institution_ids":["https://openalex.org/I138549579"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2001,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.68266345,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"53","issue":"2","first_page":"816","last_page":"844"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.8095213770866394},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7434310913085938},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.5405847430229187},{"id":"https://openalex.org/keywords/nonholonomic-system","display_name":"Nonholonomic system","score":0.5091621279716492},{"id":"https://openalex.org/keywords/motion-planning","display_name":"Motion planning","score":0.47665029764175415},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.41554003953933716},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4064429700374603},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3418787717819214},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2571371793746948},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15700048208236694},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.12990009784698486},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1085963249206543}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8095213770866394},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7434310913085938},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.5405847430229187},{"id":"https://openalex.org/C138632511","wikidata":"https://www.wikidata.org/wiki/Q2478109","display_name":"Nonholonomic system","level":4,"score":0.5091621279716492},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.47665029764175415},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.41554003953933716},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4064429700374603},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3418787717819214},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2571371793746948},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15700048208236694},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.12990009784698486},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1085963249206543},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/130950793","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130950793","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1309.2571","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1309.2571","pdf_url":"https://arxiv.org/pdf/1309.2571","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.753.6279","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.753.6279","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1309.2571.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00909748v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00909748","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2015, 53 (2), pp.816-844. &#x27E8;10.1137/130950793&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1309.2571","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1309.2571","pdf_url":"https://arxiv.org/pdf/1309.2571","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W19908240","https://openalex.org/W20444823","https://openalex.org/W101508493","https://openalex.org/W168467620","https://openalex.org/W1486223302","https://openalex.org/W1510199534","https://openalex.org/W1595765050","https://openalex.org/W1633338931","https://openalex.org/W1643902510","https://openalex.org/W1864105480","https://openalex.org/W1969916170","https://openalex.org/W1980388405","https://openalex.org/W1984309625","https://openalex.org/W1988978140","https://openalex.org/W2005873971","https://openalex.org/W2014373684","https://openalex.org/W2016159918","https://openalex.org/W2033013465","https://openalex.org/W2056700074","https://openalex.org/W2060233727","https://openalex.org/W2076487845","https://openalex.org/W2078255209","https://openalex.org/W2091697047","https://openalex.org/W2096118742","https://openalex.org/W2100021086","https://openalex.org/W2116995996","https://openalex.org/W2134061953","https://openalex.org/W2138137563","https://openalex.org/W2166662778","https://openalex.org/W2168626685","https://openalex.org/W2501142942","https://openalex.org/W2515863864","https://openalex.org/W2950615493","https://openalex.org/W2952703938","https://openalex.org/W3101977391","https://openalex.org/W3103813575","https://openalex.org/W4205416474","https://openalex.org/W4292402580","https://openalex.org/W4302620424","https://openalex.org/W4365787134"],"related_works":["https://openalex.org/W2802540229","https://openalex.org/W2032198329","https://openalex.org/W1874066705","https://openalex.org/W1021426334","https://openalex.org/W2072344655","https://openalex.org/W2326481978","https://openalex.org/W2033907646","https://openalex.org/W2524844226","https://openalex.org/W2135584875","https://openalex.org/W2383775285"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,48,79,87,98],"study":[4],"the":[5,8,25,57,64,67,71,103,113,117,124],"complexity":[6],"of":[7,28,52,56,63,66,73,76,115,123],"motion":[9],"planning":[10],"problem":[11],"for":[12,92],"control-affine":[13],"systems.":[14,32],"Such":[15],"complexities":[16],"are":[17,99],"already":[18],"defined":[19],"and":[20,40,62,82],"rather":[21],"well":[22],"understood":[23],"in":[24],"particular":[26],"case":[27],"nonholonomic":[29],"(or":[30],"sub-Riemannian)":[31],"Our":[33],"aim":[34],"is":[35,60],"to":[36,42,70,101],"generalize":[37],"these":[38,77,93],"notions":[39],"results":[41],"systems":[43],"with":[44],"a":[45,96,120],"drift.":[46,125],"Accordingly,":[47],"present":[49],"various":[50],"definitions":[51],"complexity,":[53],"as":[54],"functions":[55],"curve":[58],"that":[59],"approximated,":[61],"precision":[65],"approximation.":[68],"Due":[69],"lack":[72],"time-rescaling":[74],"invariance":[75],"systems,":[78],"consider":[80],"geometric":[81],"parametrized":[83],"curves":[84],"separately.":[85],"Then,":[86],"give":[88],"some":[89],"asymptotic":[90],"estimates":[91,111],"quantities.":[94],"As":[95],"byproduct,":[97],"able":[100],"treat":[102],"long":[104],"time":[105],"local":[106],"controllability":[107],"problem,":[108],"giving":[109],"quantitative":[110],"on":[112],"cost":[114],"stabilizing":[116],"system":[118],"near":[119],"nonequilibrium":[121],"point":[122]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
