{"id":"https://openalex.org/W4210935092","doi":"https://doi.org/10.1109/lra.2022.3148468","title":"Time-Optimization of Trajectories Using Zero-Clamped Cubic Splines and Their Analytical Gradients","display_name":"Time-Optimization of Trajectories Using Zero-Clamped Cubic Splines and Their Analytical Gradients","publication_year":2022,"publication_date":"2022-02-07","ids":{"openalex":"https://openalex.org/W4210935092","doi":"https://doi.org/10.1109/lra.2022.3148468"},"language":"en","primary_location":{"id":"doi:10.1109/lra.2022.3148468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2022.3148468","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766"],"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 Robotics and Automation Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://mediatum.ub.tum.de/1650027","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072138942","display_name":"Jonas Wittmann","orcid":"https://orcid.org/0000-0001-5116-3625"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jonas Wittmann","raw_affiliation_strings":["Chair of Applied Mechanics, School of Engineering and Design, Munich Institute of Robotics and Machine Intelligence, Technical University of Munich, M&#x00FC;nchen, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5116-3625","affiliations":[{"raw_affiliation_string":"Chair of Applied Mechanics, School of Engineering and Design, Munich Institute of Robotics and Machine Intelligence, Technical University of Munich, M&#x00FC;nchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041955731","display_name":"Daniel J. Rixen","orcid":"https://orcid.org/0000-0002-2303-4292"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel J. Rixen","raw_affiliation_strings":["Chair of Applied Mechanics, School of Engineering and Design, Munich Institute of Robotics and Machine Intelligence, Technical University of Munich, M&#x00FC;nchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Applied Mechanics, School of Engineering and Design, Munich Institute of Robotics and Machine Intelligence, Technical University of Munich, M&#x00FC;nchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072138942"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":0.9721,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.73105472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"7","issue":"2","first_page":"4528","last_page":"4534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":1.0,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":1.0,"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/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9997000098228455,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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","display_name":"Trajectory","score":0.6719172596931458},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6292291879653931},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5854469537734985},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5067325234413147},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.49091988801956177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4821288585662842},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.450672447681427},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4437611997127533},{"id":"https://openalex.org/keywords/trajectory-optimization","display_name":"Trajectory optimization","score":0.4297955632209778},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3714233636856079},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34659379720687866},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33765706419944763},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.30084550380706787},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25224965810775757},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.1976182758808136},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1631758213043213}],"concepts":[{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6719172596931458},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6292291879653931},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5854469537734985},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5067325234413147},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.49091988801956177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4821288585662842},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.450672447681427},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4437611997127533},{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.4297955632209778},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3714233636856079},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34659379720687866},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33765706419944763},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.30084550380706787},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25224965810775757},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.1976182758808136},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1631758213043213},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"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/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lra.2022.3148468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2022.3148468","pdf_url":null,"source":{"id":"https://openalex.org/S4210169774","display_name":"IEEE Robotics and Automation Letters","issn_l":"2377-3766","issn":["2377-3766"],"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 Robotics and Automation Letters","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1650027","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1650027","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"article"}],"best_oa_location":{"id":"pmh:oai:mediatum.ub.tum.de:node/1650027","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1650027","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"article"},"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W146346647","https://openalex.org/W169402212","https://openalex.org/W1630678085","https://openalex.org/W1970412155","https://openalex.org/W1977174110","https://openalex.org/W1982926243","https://openalex.org/W1999982311","https://openalex.org/W2137055801","https://openalex.org/W2148110735","https://openalex.org/W2171074980","https://openalex.org/W2895857504","https://openalex.org/W4237688380","https://openalex.org/W6636808768","https://openalex.org/W6923407621"],"related_works":["https://openalex.org/W2972304041","https://openalex.org/W4285056964","https://openalex.org/W2099531806","https://openalex.org/W2903025760","https://openalex.org/W4289147272","https://openalex.org/W2084214244","https://openalex.org/W4206218156","https://openalex.org/W3131131110","https://openalex.org/W2982309288","https://openalex.org/W3129100938"],"abstract_inverted_index":{"Modern":[0],"flexible":[1],"production":[2],"systems":[3,8],"benefit":[4],"from":[5],"collaborative":[6],"robot":[7,13,43],"that":[9,26,77],"support":[10],"to":[11,17,65,93,115],"teach":[12],"configurations":[14],"by":[15],"hand":[16],"quickly":[18],"implement":[19],"collision-free":[20],"motions.":[21],"However,":[22],"appropriate":[23],"interpolation":[24],"schemes":[25],"allow":[27],"a":[28,51,71],"fast":[29],"and":[30,86,110,131,134],"smooth":[31],"motion":[32],"through":[33],"this":[34],"sequence":[35],"of":[36,42,53,69,104],"waypoints":[37],"is":[38],"often":[39],"not":[40],"part":[41],"control":[44],"systems.":[45],"Instead,":[46],"only":[47],"point-to-point":[48],"motions":[49,58],"or":[50],"set":[52],"predefined":[54],"curves":[55],"like":[56],"circular":[57],"are":[59,113],"supported.":[60],"We":[61,125],"propose":[62,116],"an":[63,117],"approach":[64,120],"improve":[66],"the":[67,94,101,105,138],"efficiency":[68],"finding":[70],"time":[72],"parameterization":[73],"with":[74,137],"cubic":[75],"splines":[76],"computes":[78],"minimum":[79],"trajectory":[80,140],"durations":[81],"while":[82],"respecting":[83],"actuator":[84],"limits":[85],"<inline-formula":[87],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[88,146],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[89],"notation=\"LaTeX\">$C^2$</tex-math></inline-formula>":[90],"-continuity.":[91],"Compared":[92],"existing":[95],"method,":[96],"our":[97,127],"contribution":[98],"consists":[99],"in":[100,129,132,144],"analytical":[102],"gradients":[103],"underlying":[106],"nonlinear":[107],"optimization":[108,123],"problem":[109],"thus":[111],"we":[112],"able":[114],"efficient":[118],"solution":[119],"using":[121],"state-of-the-art":[122],"solvers.":[124],"validate":[126],"implementation":[128],"simulation":[130],"experiments,":[133],"benchmark":[135],"it":[136],"three":[139],"generation":[141],"methods":[142],"implemented":[143],"<italic":[145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">MoveIt!</i>":[147],".":[148]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}