{"id":"https://openalex.org/W4389164267","doi":"https://doi.org/10.1109/lra.2023.3337701","title":"SO(2)-Equivariant Downwash Models for Close Proximity Flight","display_name":"SO(2)-Equivariant Downwash Models for Close Proximity Flight","publication_year":2023,"publication_date":"2023-11-30","ids":{"openalex":"https://openalex.org/W4389164267","doi":"https://doi.org/10.1109/lra.2023.3337701"},"language":"en","primary_location":{"id":"doi:10.1109/lra.2023.3337701","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2023.3337701","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/A5101911473","display_name":"Henry Smith","orcid":"https://orcid.org/0009-0000-3088-9419"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":true,"raw_author_name":"Henry Smith","raw_affiliation_strings":["Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210096386"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101862960","display_name":"Ajay Shankar","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":false,"raw_author_name":"Ajay Shankar","raw_affiliation_strings":["Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210096386"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023654000","display_name":"Jennifer Gielis","orcid":"https://orcid.org/0000-0002-1711-4851"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":false,"raw_author_name":"Jennifer Gielis","raw_affiliation_strings":["Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210096386"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081322765","display_name":"Jan Blumenkamp","orcid":"https://orcid.org/0000-0002-1243-7707"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":false,"raw_author_name":"Jan Blumenkamp","raw_affiliation_strings":["Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210096386"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066624177","display_name":"Amanda Prorok","orcid":"https://orcid.org/0000-0001-7313-5983"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210096386","display_name":"Bridge University","ror":"https://ror.org/00cbm0437","country_code":"SS","type":"education","lineage":["https://openalex.org/I4210096386"]}],"countries":["GB","SS"],"is_corresponding":false,"raw_author_name":"Amanda Prorok","raw_affiliation_strings":["Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science &amp; Technology, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210096386"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101911473"],"corresponding_institution_ids":["https://openalex.org/I241749","https://openalex.org/I4210096386"],"apc_list":null,"apc_paid":null,"fwci":1.2211,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82054632,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"2","first_page":"1174","last_page":"1181"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10586","display_name":"Robotic Path Planning Algorithms","score":0.9980000257492065,"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":0.9980000257492065,"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/T10653","display_name":"Robot Manipulation and Learning","score":0.9957000017166138,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9950000047683716,"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/downwash","display_name":"Downwash","score":0.9772545099258423},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5595208406448364},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5389286875724792},{"id":"https://openalex.org/keywords/aerodynamics","display_name":"Aerodynamics","score":0.5201599597930908},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.49446797370910645},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.4904782474040985},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.46080756187438965},{"id":"https://openalex.org/keywords/wake","display_name":"Wake","score":0.44188469648361206},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.410503089427948},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.35202860832214355},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.33723682165145874},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.2991947829723358},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19925564527511597},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.16866201162338257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1667868196964264},{"id":"https://openalex.org/keywords/astronomy","display_name":"Astronomy","score":0.08124792575836182},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.07632166147232056}],"concepts":[{"id":"https://openalex.org/C202685678","wikidata":"https://www.wikidata.org/wiki/Q336311","display_name":"Downwash","level":3,"score":0.9772545099258423},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5595208406448364},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5389286875724792},{"id":"https://openalex.org/C13393347","wikidata":"https://www.wikidata.org/wiki/Q8424","display_name":"Aerodynamics","level":2,"score":0.5201599597930908},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.49446797370910645},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.4904782474040985},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46080756187438965},{"id":"https://openalex.org/C48939323","wikidata":"https://www.wikidata.org/wiki/Q294879","display_name":"Wake","level":2,"score":0.44188469648361206},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.410503089427948},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.35202860832214355},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.33723682165145874},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.2991947829723358},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19925564527511597},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.16866201162338257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1667868196964264},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.08124792575836182},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.07632166147232056},{"id":"https://openalex.org/C19417346","wikidata":"https://www.wikidata.org/wiki/Q7922","display_name":"Pedagogy","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lra.2023.3337701","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lra.2023.3337701","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":[{"id":"https://openalex.org/G8727507575","display_name":null,"funder_award_id":"949940","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"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":39,"referenced_works":["https://openalex.org/W607505555","https://openalex.org/W2026606537","https://openalex.org/W2091083460","https://openalex.org/W2322303423","https://openalex.org/W2600080636","https://openalex.org/W2724334548","https://openalex.org/W2884236119","https://openalex.org/W2886401384","https://openalex.org/W2890491818","https://openalex.org/W2901402208","https://openalex.org/W2910655755","https://openalex.org/W2963148914","https://openalex.org/W2963755523","https://openalex.org/W3015694949","https://openalex.org/W3091076647","https://openalex.org/W3116723949","https://openalex.org/W3120474262","https://openalex.org/W3144345581","https://openalex.org/W3157286395","https://openalex.org/W3192144420","https://openalex.org/W3199197426","https://openalex.org/W3206822272","https://openalex.org/W3207644545","https://openalex.org/W3207996406","https://openalex.org/W3216136749","https://openalex.org/W4221161303","https://openalex.org/W4236362309","https://openalex.org/W4283219642","https://openalex.org/W4287554311","https://openalex.org/W4309394346","https://openalex.org/W4366388458","https://openalex.org/W4382935954","https://openalex.org/W4391020231","https://openalex.org/W6752307458","https://openalex.org/W6775703289","https://openalex.org/W6794315554","https://openalex.org/W6803403409","https://openalex.org/W6839015768","https://openalex.org/W6846841888"],"related_works":["https://openalex.org/W17155033","https://openalex.org/W2810260967","https://openalex.org/W2757285599","https://openalex.org/W2984696102","https://openalex.org/W3207760230","https://openalex.org/W1496222301","https://openalex.org/W1590307681","https://openalex.org/W4312814274","https://openalex.org/W4285370786","https://openalex.org/W56544090"],"abstract_inverted_index":{"Multirotors":[0],"flying":[1],"in":[2,74],"close":[3],"proximity":[4],"induce":[5],"aerodynamic":[6],"wake":[7],"effects":[8],"on":[9,132],"each":[10],"other":[11],"through":[12],"propeller":[13],"downwash.":[14],"Conventional":[15],"methods":[16],"have":[17],"fallen":[18],"short":[19],"of":[20,89,109],"providing":[21],"adequate":[22],"3D":[23,123],"force-based":[24],"models":[25,99],"that":[26,66,79],"can":[27],"be":[28],"incorporated":[29],"into":[30],"robust":[31],"control":[32],"paradigms":[33],"for":[34,44,61],"deploying":[35,118],"dense":[36,112],"formations.":[37],"Thus,":[38],"<italic":[39],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[40,85,105,129,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">learning</i>":[41],"a":[42,57],"model":[43,95,120],"these":[45],"downwash":[46,64],"patterns":[47],"presents":[48],"an":[49],"attractive":[50],"solution.":[51],"In":[52,111],"this":[53],"paper,":[54],"we":[55],"present":[56,73],"novel":[58],"learning-based":[59],"approach":[60],"modelling":[62],"the":[63,68,75],"forces":[65],"exploits":[67],"latent":[69],"geometries":[70],"(i.e.":[71],"symmetries)":[72],"problem.":[76],"We":[77],"demonstrate":[78],"when":[80],"trained":[81,100],"with":[82,101,115],"only":[83],"<inline-formula":[84,104,128,138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[86,106,130,140],"notation=\"LaTeX\">$5$</tex-math></inline-formula>":[87],"minutes":[88,108],"real-world":[90,113],"flight":[91],"data,":[92],"our":[93,119],"geometry-aware":[94],"outperforms":[96],"state-of-the-art":[97],"baseline":[98],"more":[102],"than":[103],"notation=\"LaTeX\">$15$</tex-math></inline-formula>":[107],"data.":[110],"flights":[114],"two":[116],"vehicles,":[117],"online":[121],"improves":[122],"trajectory":[124],"tracking":[125,136],"by":[126,137],"nearly":[127],"notation=\"LaTeX\">$36\\%$</tex-math></inline-formula>":[131],"average":[133],"(and":[134],"vertical":[135],"notation=\"LaTeX\">$56\\%$</tex-math></inline-formula>":[141],").":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}
