{"id":"https://openalex.org/W3212084571","doi":"https://doi.org/10.1109/taes.2021.3128869","title":"Robust Low-Thrust Trajectory Optimization Using Convex Programming and a Homotopic Approach","display_name":"Robust Low-Thrust Trajectory Optimization Using Convex Programming and a Homotopic Approach","publication_year":2021,"publication_date":"2021-11-17","ids":{"openalex":"https://openalex.org/W3212084571","doi":"https://doi.org/10.1109/taes.2021.3128869","mag":"3212084571"},"language":"en","primary_location":{"id":"doi:10.1109/taes.2021.3128869","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2021.3128869","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11311/1196084","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062235726","display_name":"Andrea C. Morelli","orcid":"https://orcid.org/0000-0002-2779-5996"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Carlo Morelli","raw_affiliation_strings":["Politecnico di Milano, Milan, Italy"],"raw_orcid":"https://orcid.org/0000-0002-2779-5996","affiliations":[{"raw_affiliation_string":"Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065593942","display_name":"Christian Hofmann","orcid":"https://orcid.org/0000-0002-7270-8898"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Christian Hofmann","raw_affiliation_strings":["Politecnico di Milano, Milan, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7270-8898","affiliations":[{"raw_affiliation_string":"Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036488441","display_name":"Francesco Topputo","orcid":"https://orcid.org/0000-0002-5369-6887"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Topputo","raw_affiliation_strings":["Politecnico di Milano, Milan, Italy"],"raw_orcid":"https://orcid.org/0000-0002-5369-6887","affiliations":[{"raw_affiliation_string":"Politecnico di Milano, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":34.1217,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.99470499,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"58","issue":"3","first_page":"2103","last_page":"2116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","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/T11082","display_name":"Spacecraft Dynamics and Control","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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9904000163078308,"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":0.9781000018119812,"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/trajectory-optimization","display_name":"Trajectory optimization","score":0.853309154510498},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.6241284608840942},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6210602521896362},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6096110939979553},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5060939192771912},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.495096355676651},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.4825141131877899},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.47372737526893616},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.47236090898513794},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4684080481529236},{"id":"https://openalex.org/keywords/thrust","display_name":"Thrust","score":0.4681948125362396},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.41715043783187866},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41123440861701965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4012068212032318},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.313620924949646},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.29334717988967896},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.19997555017471313},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08934539556503296},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.0802558958530426}],"concepts":[{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.853309154510498},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.6241284608840942},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6210602521896362},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6096110939979553},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5060939192771912},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.495096355676651},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.4825141131877899},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.47372737526893616},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.47236090898513794},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4684080481529236},{"id":"https://openalex.org/C79420006","wikidata":"https://www.wikidata.org/wiki/Q533668","display_name":"Thrust","level":2,"score":0.4681948125362396},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.41715043783187866},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41123440861701965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4012068212032318},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.313620924949646},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.29334717988967896},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.19997555017471313},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08934539556503296},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0802558958530426},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/taes.2021.3128869","is_oa":false,"landing_page_url":"https://doi.org/10.1109/taes.2021.3128869","pdf_url":null,"source":{"id":"https://openalex.org/S193624734","display_name":"IEEE Transactions on Aerospace and Electronic Systems","issn_l":"0018-9251","issn":["0018-9251","1557-9603","2371-9877"],"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 Aerospace and Electronic Systems","raw_type":"journal-article"},{"id":"pmh:oai:re.public.polimi.it:11311/1196084","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1196084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:re.public.polimi.it:11311/1196084","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1196084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4625212892","display_name":null,"funder_award_id":"864697","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G7319883546","display_name":null,"funder_award_id":"864697","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1490395035","https://openalex.org/W1992983007","https://openalex.org/W2002679258","https://openalex.org/W2008645856","https://openalex.org/W2019459464","https://openalex.org/W2021762091","https://openalex.org/W2031218830","https://openalex.org/W2035670438","https://openalex.org/W2078457570","https://openalex.org/W2086333075","https://openalex.org/W2097280161","https://openalex.org/W2129516068","https://openalex.org/W2154522750","https://openalex.org/W2159583056","https://openalex.org/W2162218551","https://openalex.org/W2473800515","https://openalex.org/W2513178932","https://openalex.org/W2521801528","https://openalex.org/W2554071958","https://openalex.org/W2744091781","https://openalex.org/W2773080460","https://openalex.org/W2774276467","https://openalex.org/W2781572223","https://openalex.org/W2781624996","https://openalex.org/W2790624030","https://openalex.org/W2796944097","https://openalex.org/W2891386315","https://openalex.org/W2902496574","https://openalex.org/W2910557787","https://openalex.org/W2910843116","https://openalex.org/W2967267347","https://openalex.org/W2984995564","https://openalex.org/W3010423153","https://openalex.org/W3039923911","https://openalex.org/W3098154867","https://openalex.org/W3102244603","https://openalex.org/W3134170990","https://openalex.org/W3147389577","https://openalex.org/W3162910338","https://openalex.org/W3184430965","https://openalex.org/W4255604297","https://openalex.org/W6683009563","https://openalex.org/W6750531648","https://openalex.org/W6792856973","https://openalex.org/W7042729144","https://openalex.org/W7056732646"],"related_works":["https://openalex.org/W4206704743","https://openalex.org/W2019128690","https://openalex.org/W436931041","https://openalex.org/W1495847109","https://openalex.org/W2390817143","https://openalex.org/W2106813160","https://openalex.org/W2355743697","https://openalex.org/W2894731288","https://openalex.org/W2384138382","https://openalex.org/W2381309080"],"abstract_inverted_index":{"A":[0,44],"robust":[1],"algorithm":[2],"to":[3,61,91],"solve":[4],"the":[5,49,97],"low-thrust":[6],"fuel-optimal":[7,71],"trajectory":[8],"optimization":[9,32],"problem":[10,24,33],"for":[11],"interplanetary":[12],"spacecraft":[13],"is":[14,25,53,67],"developed":[15],"in":[16,69,83,96],"this":[17],"article.":[18],"The":[19,64,77],"original":[20],"nonlinear":[21,41],"optimal":[22],"control":[23,42],"convexified":[26],"and":[27,87],"transformed":[28],"into":[29],"a":[30,80],"parameter":[31],"using":[34],"an":[35,56],"arbitrary-order":[36],"Gauss\u2013Lobatto":[37],"discretization":[38],"scheme":[39],"with":[40,55,73],"interpolation.":[43],"homotopic":[45],"approach":[46],"that":[47],"considers":[48],"energy-to-fuel":[50],"smoothing":[51],"path":[52],"combined":[54],"adaptive":[57],"second-order":[58],"trust-region":[59],"mechanism":[60],"increase":[62],"performance.":[63],"overall":[65],"robustness":[66],"assessed":[68],"several":[70],"transfers":[72],"poor":[74],"initial":[75],"guesses.":[76],"results":[78],"show":[79],"superior":[81],"performance":[82],"terms":[84],"of":[85],"convergence":[86],"computational":[88],"time":[89],"compared":[90],"standard":[92],"convex":[93],"programming":[94],"approaches":[95],"literature.":[98]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":7}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}