{"id":"https://openalex.org/W3111321218","doi":"https://doi.org/10.29007/mx3f","title":"A Robust Controlled Backward Reach Tube with (Almost) Analytic Solution for Two Dubins Cars","display_name":"A Robust Controlled Backward Reach Tube with (Almost) Analytic Solution for Two Dubins Cars","publication_year":2020,"publication_date":"2020-09-26","ids":{"openalex":"https://openalex.org/W3111321218","doi":"https://doi.org/10.29007/mx3f","mag":"3111321218"},"language":"en","primary_location":{"id":"doi:10.29007/mx3f","is_oa":true,"landing_page_url":"https://doi.org/10.29007/mx3f","pdf_url":"https://easychair.org/publications/open/Dd8G","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://easychair.org/publications/open/Dd8G","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064867908","display_name":"I. V. Mitchell","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Ian Mitchell","raw_affiliation_strings":["Department of Computer Science The University of British Columbia Vancouver, British Columbia, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science The University of British Columbia Vancouver, British Columbia, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064867908"],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":null,"apc_paid":null,"fwci":4.7144,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.96104969,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"74","issue":null,"first_page":"242","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T12158","display_name":"Guidance and Control Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.9739000201225281,"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/reachability","display_name":"Reachability","score":0.9244546294212341},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.7529758214950562},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5911413431167603},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5656136870384216},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5481364130973816},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5166407227516174},{"id":"https://openalex.org/keywords/pursuit-evasion","display_name":"Pursuit-evasion","score":0.4277426600456238},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33119451999664307},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2723444104194641}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9244546294212341},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.7529758214950562},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5911413431167603},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5656136870384216},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5481364130973816},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5166407227516174},{"id":"https://openalex.org/C2778388243","wikidata":"https://www.wikidata.org/wiki/Q7261573","display_name":"Pursuit-evasion","level":2,"score":0.4277426600456238},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33119451999664307},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2723444104194641},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.29007/mx3f","is_oa":true,"landing_page_url":"https://doi.org/10.29007/mx3f","pdf_url":"https://easychair.org/publications/open/Dd8G","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.29007/mx3f","is_oa":true,"landing_page_url":"https://doi.org/10.29007/mx3f","pdf_url":"https://easychair.org/publications/open/Dd8G","source":{"id":"https://openalex.org/S4220651395","display_name":"EPiC series in computing","issn_l":"2398-7340","issn":["2398-7340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"EPiC Series in Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8284766523","display_name":null,"funder_award_id":"(NSERC)","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3111321218.pdf","grobid_xml":"https://content.openalex.org/works/W3111321218.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W51127244","https://openalex.org/W584400962","https://openalex.org/W1541856741","https://openalex.org/W1581842928","https://openalex.org/W1582899597","https://openalex.org/W1879112630","https://openalex.org/W1964996923","https://openalex.org/W1971998222","https://openalex.org/W2116364955","https://openalex.org/W2132503805","https://openalex.org/W2313274380","https://openalex.org/W2936748422","https://openalex.org/W2963279226","https://openalex.org/W2963525569","https://openalex.org/W2963606896","https://openalex.org/W2967767199","https://openalex.org/W3098919244"],"related_works":["https://openalex.org/W2127267268","https://openalex.org/W2136512912","https://openalex.org/W2067910792","https://openalex.org/W2156446763","https://openalex.org/W2150194458","https://openalex.org/W2143461633","https://openalex.org/W4321471459","https://openalex.org/W2889071233","https://openalex.org/W2380814829","https://openalex.org/W2387511021"],"abstract_inverted_index":{"Benchmark":[0],"Proposal:":[1],"We":[2,89,130],"describe":[3,132],"how":[4],"a":[5,17,33,45,71,94],"well-known":[6],"backward":[7,36,105],"reachability":[8,99],"problem":[9,92,137],"with":[10,21,44,83],"nonlinear":[11],"dynamics":[12],"and":[13,76,118],"adversarial":[14],"inputs\u2014based":[15],"on":[16,60,70],"pursuit":[18],"evasion":[19],"game":[20,74],"two":[22],"identical":[23],"vehicles":[24],"that":[25,47],"have":[26,66],"Dubins":[27],"car":[28],"dynamics\u2014can":[29],"be":[30,81],"viewed":[31],"as":[32,93],"robust":[34,103,114],"controlled":[35,104],"reach":[37,106],"tube.":[38],"The":[39],"resulting":[40],"set":[41,65],"is":[42,48,144],"nonconvex":[43],"surface":[46,62],"nondifferentiable":[49],"in":[50],"places,":[51],"yet":[52],"(mostly":[53],"explicit)":[54],"closed":[55],"form":[56],"solutions":[57],"for":[58,111],"points":[59,79],"the":[61,113,136],"of":[63,116],"this":[64,91,119],"been":[67],"derived":[68],"based":[69],"classical":[72],"differential":[73],"analysis,":[75],"so":[77],"these":[78],"can":[80,101],"sampled":[82],"high":[84],"accuracy":[85],"at":[86],"arbitrary":[87],"density.":[88],"propose":[90],"benchmark":[95],"because":[96],"few":[97],"existing":[98],"algorithms":[100],"tackle":[102],"tubes":[107],"despite":[108],"their":[109],"potential":[110],"proving":[112],"safety":[115],"systems,":[117],"(almost)":[120],"analytic":[121],"solution":[122],"exists":[123],"against":[124],"which":[125],"to":[126,135,138],"compare":[127],"prospective":[128],"solutions.":[129],"then":[131],"some":[133],"extensions":[134],"provide":[139],"additional":[140],"future":[141],"challenges.":[142],"Code":[143],"provided.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}
