{"id":"https://openalex.org/W3208129034","doi":"https://doi.org/10.1109/lra.2022.3219019","title":"Learning Stable Vector Fields on Lie Groups","display_name":"Learning Stable Vector Fields on Lie Groups","publication_year":2022,"publication_date":"2022-10-01","ids":{"openalex":"https://openalex.org/W3208129034","doi":"https://doi.org/10.1109/lra.2022.3219019","mag":"3208129034"},"language":"en","primary_location":{"id":"doi:10.1109/lra.2022.3219019","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2022.3219019","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067156748","display_name":"Julen Urain","orcid":"https://orcid.org/0000-0003-1135-6654"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Julen Urain","raw_affiliation_strings":["Computer Science Department, Institute for Intelligent Autonomous Systems, Technische Universit&#x00E4;t Darmstadt, Darmstadt, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1135-6654","affiliations":[{"raw_affiliation_string":"Computer Science Department, Institute for Intelligent Autonomous Systems, Technische Universit&#x00E4;t Darmstadt, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001304610","display_name":"Davide Tateo","orcid":"https://orcid.org/0000-0002-7193-923X"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Davide Tateo","raw_affiliation_strings":["Computer Science Department, Institute for Intelligent Autonomous Systems, Technische Universit&#x00E4;t Darmstadt, Darmstadt, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7193-923X","affiliations":[{"raw_affiliation_string":"Computer Science Department, Institute for Intelligent Autonomous Systems, Technische Universit&#x00E4;t Darmstadt, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071367253","display_name":"Jan Peters","orcid":"https://orcid.org/0000-0002-5266-8091"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]},{"id":"https://openalex.org/I4210125013","display_name":"Hessian Agency for Nature Conservation, Environment and Geology","ror":"https://ror.org/02y05ge92","country_code":"DE","type":"government","lineage":["https://openalex.org/I4210125013"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jan Peters","raw_affiliation_strings":["Computer Science Department, Institute for Intelligent Autonomous Systems, Technische Universit&#x00E4;t Darmstadt, Darmstadt, Germany","Centre for Cognitive Science, Germany","Hessian Center for AI, Hessian.AI, Germany"],"raw_orcid":"https://orcid.org/0000-0002-5266-8091","affiliations":[{"raw_affiliation_string":"Computer Science Department, Institute for Intelligent Autonomous Systems, Technische Universit&#x00E4;t Darmstadt, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]},{"raw_affiliation_string":"Centre for Cognitive Science, Germany","institution_ids":[]},{"raw_affiliation_string":"Hessian Center for AI, Hessian.AI, Germany","institution_ids":["https://openalex.org/I4210125013"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4272,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.88278002,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"4","first_page":"12569","last_page":"12576"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10653","display_name":"Robot Manipulation and Learning","score":0.9998999834060669,"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/T10653","display_name":"Robot Manipulation and Learning","score":0.9998999834060669,"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.998199999332428,"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/T10879","display_name":"Robotic Locomotion and Control","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/vector-field","display_name":"Vector field","score":0.8298225998878479},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6358681321144104},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.628348171710968},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5436469912528992},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5418229699134827},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5370842814445496},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5234089493751526},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.498507022857666},{"id":"https://openalex.org/keywords/fundamental-vector-field","display_name":"Fundamental vector field","score":0.48777657747268677},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4789441227912903},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.47790440917015076},{"id":"https://openalex.org/keywords/lie-bracket-of-vector-fields","display_name":"Lie bracket of vector fields","score":0.4512927532196045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4474697411060333},{"id":"https://openalex.org/keywords/robotics","display_name":"Robotics","score":0.4109956622123718},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.4054381847381592},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40046244859695435},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1832796037197113},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15088945627212524},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.10544842481613159},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09400114417076111},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09169188141822815}],"concepts":[{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.8298225998878479},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6358681321144104},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.628348171710968},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5436469912528992},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5418229699134827},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5370842814445496},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5234089493751526},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.498507022857666},{"id":"https://openalex.org/C99775784","wikidata":"https://www.wikidata.org/wiki/Q5508976","display_name":"Fundamental vector field","level":5,"score":0.48777657747268677},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4789441227912903},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.47790440917015076},{"id":"https://openalex.org/C14344131","wikidata":"https://www.wikidata.org/wiki/Q5478310","display_name":"Lie bracket of vector fields","level":5,"score":0.4512927532196045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4474697411060333},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.4109956622123718},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.4054381847381592},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40046244859695435},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1832796037197113},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15088945627212524},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.10544842481613159},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09400114417076111},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09169188141822815},{"id":"https://openalex.org/C203946495","wikidata":"https://www.wikidata.org/wiki/Q1017106","display_name":"Adjoint representation of a Lie algebra","level":4,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lra.2022.3219019","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2022.3219019","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W130216483","https://openalex.org/W1557324374","https://openalex.org/W1866230956","https://openalex.org/W1965421192","https://openalex.org/W1999874108","https://openalex.org/W2008491851","https://openalex.org/W2024145790","https://openalex.org/W2056114668","https://openalex.org/W2100993276","https://openalex.org/W2112474089","https://openalex.org/W2129202194","https://openalex.org/W2140801763","https://openalex.org/W2141664020","https://openalex.org/W2148112459","https://openalex.org/W2156174987","https://openalex.org/W2160609165","https://openalex.org/W2478063815","https://openalex.org/W2555641442","https://openalex.org/W2580438233","https://openalex.org/W2740824349","https://openalex.org/W2783192199","https://openalex.org/W2902093375","https://openalex.org/W2952860575","https://openalex.org/W2962695743","https://openalex.org/W2963047245","https://openalex.org/W2963090522","https://openalex.org/W2963641970","https://openalex.org/W2963755523","https://openalex.org/W2964319110","https://openalex.org/W2970898247","https://openalex.org/W2979652999","https://openalex.org/W3004753434","https://openalex.org/W3029926839","https://openalex.org/W3030328006","https://openalex.org/W3034932593","https://openalex.org/W3036264357","https://openalex.org/W3036362011","https://openalex.org/W3040183635","https://openalex.org/W3049389301","https://openalex.org/W3106892592","https://openalex.org/W3132689247","https://openalex.org/W3174273518","https://openalex.org/W4286891162","https://openalex.org/W4288418907","https://openalex.org/W4289145348","https://openalex.org/W4293203252","https://openalex.org/W4294411035","https://openalex.org/W4297798428","https://openalex.org/W4312558117","https://openalex.org/W4313011305","https://openalex.org/W6610566761","https://openalex.org/W6680971464","https://openalex.org/W6714644935","https://openalex.org/W6729826568","https://openalex.org/W6741853627","https://openalex.org/W6748202546","https://openalex.org/W6752307458","https://openalex.org/W6755056417","https://openalex.org/W6756279856","https://openalex.org/W6760904531","https://openalex.org/W6773165445","https://openalex.org/W6778073884","https://openalex.org/W6778324997","https://openalex.org/W6779435032","https://openalex.org/W6780315847","https://openalex.org/W6803241323","https://openalex.org/W6810161201"],"related_works":["https://openalex.org/W1865549704","https://openalex.org/W91468474","https://openalex.org/W4239012421","https://openalex.org/W4381890375","https://openalex.org/W2009957374","https://openalex.org/W2105684760","https://openalex.org/W4205489324","https://openalex.org/W43129718","https://openalex.org/W4390142895","https://openalex.org/W4385963966"],"abstract_inverted_index":{"Learning":[0],"robot":[1,15,122],"motions":[2],"from":[3],"demonstration":[4],"requires":[5,61],"models":[6],"able":[7],"to":[8,115],"specify":[9],"vector":[10,40,48,57,79,112,118],"fields":[11,41,49,58,119],"for":[12,59,120],"the":[13,18,63,87,98,102,107],"full":[14,121],"pose":[16],"when":[17],"task":[19],"is":[20,42],"defined":[21],"in":[22,27,65,128],"operational":[23],"space.":[24,100],"Recent":[25],"advances":[26],"reactive":[28],"motion":[29],"generation":[30],"have":[31],"shown":[32],"that":[33,82],"learning":[34],"adaptive,":[35],"reactive,":[36],"smooth,":[37],"and":[38,95,126,131],"stable":[39,117],"possible.":[43],"However,":[44],"these":[45],"approaches":[46,91],"define":[47],"on":[50],"a":[51,77],"flat":[52],"Euclidean":[53,99],"manifold,":[54],"while":[55],"representing":[56],"orientations":[60],"modeling":[62],"dynamics":[64],"non-Euclidean":[66],"manifolds,":[67],"such":[68],"as":[69,124],"Lie":[70],"Groups.":[71],"In":[72,101],"this":[73],"paper,":[74],"we":[75,105],"present":[76],"novel":[78],"field":[80,113],"model":[81,114],"can":[83],"guarantee":[84],"most":[85],"of":[86,89,109],"properties":[88],"previous":[90],"i.e.,":[92],"stability,":[93],"smoothness,":[94],"reactivity":[96],"beyond":[97],"experimental":[103],"evaluation,":[104],"show":[106],"performance":[108],"our":[110],"proposed":[111],"learn":[116],"poses":[123],"SE(2)":[125],"SE(3)":[127],"both":[129],"simulated":[130],"real":[132],"robotics":[133],"tasks.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
