{"id":"https://openalex.org/W2912849082","doi":"https://doi.org/10.1109/tcyb.2019.2895305","title":"Solving Trajectory Optimization Problems in the Presence of Probabilistic Constraints","display_name":"Solving Trajectory Optimization Problems in the Presence of Probabilistic Constraints","publication_year":2019,"publication_date":"2019-02-07","ids":{"openalex":"https://openalex.org/W2912849082","doi":"https://doi.org/10.1109/tcyb.2019.2895305","mag":"2912849082","pmid":"https://pubmed.ncbi.nlm.nih.gov/30763253"},"language":"en","primary_location":{"id":"doi:10.1109/tcyb.2019.2895305","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2895305","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Transactions on Cybernetics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.lib.cranfield.ac.uk/handle/1826/15266","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024866488","display_name":"Runqi Chai","orcid":"https://orcid.org/0000-0003-4083-8863"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Runqi Chai","raw_affiliation_strings":["School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K"],"raw_orcid":"https://orcid.org/0000-0003-4083-8863","affiliations":[{"raw_affiliation_string":"School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102861951","display_name":"Al Savvaris","orcid":"https://orcid.org/0000-0003-3210-5838"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Al Savvaris","raw_affiliation_strings":["School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085012064","display_name":"Antonios Tsourdos","orcid":"https://orcid.org/0000-0002-3966-7633"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Antonios Tsourdos","raw_affiliation_strings":["School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070349528","display_name":"Senchun Chai","orcid":"https://orcid.org/0000-0003-1910-1795"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Senchun Chai","raw_affiliation_strings":["School of Automation, Beijing Institute of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1910-1795","affiliations":[{"raw_affiliation_string":"School of Automation, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064231378","display_name":"Yuanqing Xia","orcid":"https://orcid.org/0000-0002-5977-4911"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanqing Xia","raw_affiliation_strings":["School of Automation, Beijing Institute of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-5977-4911","affiliations":[{"raw_affiliation_string":"School of Automation, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100639215","display_name":"Shuo Wang","orcid":"https://orcid.org/0000-0002-1390-9219"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuo Wang","raw_affiliation_strings":["State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-1390-9219","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0696,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.92299646,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"50","issue":"10","first_page":"4332","last_page":"4345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9987000226974487,"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9986000061035156,"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/T11701","display_name":"Space Satellite Systems and Control","score":0.9890999794006348,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.75228351354599},{"id":"https://openalex.org/keywords/trajectory-optimization","display_name":"Trajectory optimization","score":0.7041064500808716},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6910659074783325},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6468820571899414},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5795161724090576},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5541048049926758},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5006704330444336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48136836290359497},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.46534430980682373},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4612722396850586},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.4508386552333832},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.42576074600219727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41992321610450745},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3207992911338806},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08183357119560242}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.75228351354599},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.7041064500808716},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6910659074783325},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6468820571899414},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5795161724090576},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5541048049926758},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5006704330444336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48136836290359497},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.46534430980682373},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4612722396850586},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.4508386552333832},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.42576074600219727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41992321610450745},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3207992911338806},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08183357119560242},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tcyb.2019.2895305","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcyb.2019.2895305","pdf_url":null,"source":{"id":"https://openalex.org/S4210191041","display_name":"IEEE Transactions on Cybernetics","issn_l":"2168-2267","issn":["2168-2267","2168-2275"],"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 Transactions on Cybernetics","raw_type":"journal-article"},{"id":"pmid:30763253","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30763253","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on cybernetics","raw_type":null},{"id":"pmh:oai:dspace.lib.cranfield.ac.uk:1826/15266","is_oa":true,"landing_page_url":"https://dspace.lib.cranfield.ac.uk/handle/1826/15266","pdf_url":null,"source":{"id":"https://openalex.org/S4306401778","display_name":"CERES (Cranfield University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I82284825","host_organization_name":"Cranfield University","host_organization_lineage":["https://openalex.org/I82284825"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:dspace.lib.cranfield.ac.uk:1826/15266","is_oa":true,"landing_page_url":"https://dspace.lib.cranfield.ac.uk/handle/1826/15266","pdf_url":null,"source":{"id":"https://openalex.org/S4306401778","display_name":"CERES (Cranfield University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I82284825","host_organization_name":"Cranfield University","host_organization_lineage":["https://openalex.org/I82284825"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1963788580","https://openalex.org/W1969839206","https://openalex.org/W1971092617","https://openalex.org/W1979775288","https://openalex.org/W1982100856","https://openalex.org/W1982661895","https://openalex.org/W1987361260","https://openalex.org/W2000587848","https://openalex.org/W2004743525","https://openalex.org/W2031244688","https://openalex.org/W2035670438","https://openalex.org/W2041177669","https://openalex.org/W2073278424","https://openalex.org/W2085232378","https://openalex.org/W2087083349","https://openalex.org/W2091425556","https://openalex.org/W2099506495","https://openalex.org/W2101929046","https://openalex.org/W2107345353","https://openalex.org/W2126998183","https://openalex.org/W2157384372","https://openalex.org/W2164313740","https://openalex.org/W2168953036","https://openalex.org/W2191512642","https://openalex.org/W2299168252","https://openalex.org/W2339802450","https://openalex.org/W2341115255","https://openalex.org/W2342918308","https://openalex.org/W2343290328","https://openalex.org/W2345847332","https://openalex.org/W2560859876","https://openalex.org/W2594215104","https://openalex.org/W2608587872","https://openalex.org/W2609100750","https://openalex.org/W2609367643","https://openalex.org/W2610176484","https://openalex.org/W2619105776","https://openalex.org/W2734753379","https://openalex.org/W2743593866","https://openalex.org/W2748977773","https://openalex.org/W2750408863","https://openalex.org/W2766428590","https://openalex.org/W2766963179","https://openalex.org/W2767157617","https://openalex.org/W2774276467","https://openalex.org/W2964111918","https://openalex.org/W3102002161","https://openalex.org/W3104291870"],"related_works":["https://openalex.org/W2347515520","https://openalex.org/W1600119608","https://openalex.org/W1977418846","https://openalex.org/W2351297735","https://openalex.org/W2490746371","https://openalex.org/W4286778616","https://openalex.org/W3091489580","https://openalex.org/W3001359952","https://openalex.org/W4308269003","https://openalex.org/W2912849082"],"abstract_inverted_index":{"The":[0,25],"objective":[1],"of":[2,15,22,73,81,93,122],"this":[3,150],"paper":[4],"is":[5,58,85],"to":[6,34,71,87,89,132],"present":[7],"an":[8],"approximation-based":[9],"strategy":[10],"for":[11],"solving":[12],"the":[13,20,39,44,61,65,74,78,82,90,94,118,123,134],"problem":[14],"nonlinear":[16,52],"trajectory":[17,46,106,114],"optimization":[18,47,107,146],"with":[19],"consideration":[21],"probabilistic":[23,36],"constraints.":[24],"proposed":[26,124,135],"method":[27],"defines":[28],"a":[29,50,101,110],"smooth":[30],"and":[31,64,109,120,141],"differentiable":[32],"function":[33,63],"replace":[35],"constraints":[37],"by":[38],"deterministic":[40],"ones,":[41],"thereby":[42],"converting":[43],"chance-constrained":[45,103,145],"model":[48,84,108],"into":[49],"parametric":[51],"programming":[53],"model.":[54],"In":[55],"addition,":[56],"it":[57],"proved":[59],"that":[60,72],"approximation":[62,67],"corresponding":[66],"set":[68],"will":[69],"converge":[70,88],"original":[75,95],"problem.":[76,96],"Furthermore,":[77],"optimal":[79,91],"solution":[80,92],"approximated":[83],"ensured":[86],"Numerical":[97],"results,":[98],"obtained":[99],"from":[100],"new":[102],"space":[104],"vehicle":[105,113],"3-D":[111],"unmanned":[112],"smoothing":[115],"problem,":[116],"verify":[117],"feasibility":[119],"effectiveness":[121],"approach.":[125],"Comparative":[126],"studies":[127],"were":[128],"also":[129],"carried":[130],"out":[131],"show":[133],"design":[136],"can":[137],"yield":[138],"good":[139],"performance":[140],"outperform":[142],"other":[143],"typical":[144],"techniques":[147],"investigated":[148],"in":[149],"paper.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
