Solution methods to the nearest rotation matrix problem in R3: a comparative survey

Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and prese...

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Autores: Sarabandi, Soheil|||0000-0002-2103-1610, Thomas, Federico|||0000-0001-9341-5528
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/443361
Acceso en línea:https://hdl.handle.net/2117/443361
https://dx.doi.org/10.1002/nla.2492
Access Level:acceso abierto
Palabra clave:Numerical analysis
Rotation matrices
Quaternions
Singular value decomposition
Àlgebra lineal numèrica
Classificació AMS::65 Numerical analysis::65F Numerical linear algebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
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spelling Solution methods to the nearest rotation matrix problem in R3: a comparative surveySarabandi, Soheil|||0000-0002-2103-1610Thomas, Federico|||0000-0001-9341-5528Numerical analysisRotation matricesQuaternionsSingular value decompositionÀlgebra lineal numèricaClassificació AMS::65 Numerical analysis::65F Numerical linear algebraÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèricaNowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed-form methods are as robust as the SVD, but significantly faster and more accurate.Peer Reviewed20232023-10-0120252025-10-08journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/443361https://dx.doi.org/10.1002/nla.2492reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-117509GB-I00 SINTESIS DE MOVIMIENTOS ROBOTICOS OPTIMAMENTE AGILES Y GRACILESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4433612026-05-27T15:37:01Z
dc.title.none.fl_str_mv Solution methods to the nearest rotation matrix problem in R3: a comparative survey
title Solution methods to the nearest rotation matrix problem in R3: a comparative survey
spellingShingle Solution methods to the nearest rotation matrix problem in R3: a comparative survey
Sarabandi, Soheil|||0000-0002-2103-1610
Numerical analysis
Rotation matrices
Quaternions
Singular value decomposition
Àlgebra lineal numèrica
Classificació AMS::65 Numerical analysis::65F Numerical linear algebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
title_short Solution methods to the nearest rotation matrix problem in R3: a comparative survey
title_full Solution methods to the nearest rotation matrix problem in R3: a comparative survey
title_fullStr Solution methods to the nearest rotation matrix problem in R3: a comparative survey
title_full_unstemmed Solution methods to the nearest rotation matrix problem in R3: a comparative survey
title_sort Solution methods to the nearest rotation matrix problem in R3: a comparative survey
dc.creator.none.fl_str_mv Sarabandi, Soheil|||0000-0002-2103-1610
Thomas, Federico|||0000-0001-9341-5528
author Sarabandi, Soheil|||0000-0002-2103-1610
author_facet Sarabandi, Soheil|||0000-0002-2103-1610
Thomas, Federico|||0000-0001-9341-5528
author_role author
author2 Thomas, Federico|||0000-0001-9341-5528
author2_role author
dc.subject.none.fl_str_mv Numerical analysis
Rotation matrices
Quaternions
Singular value decomposition
Àlgebra lineal numèrica
Classificació AMS::65 Numerical analysis::65F Numerical linear algebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
topic Numerical analysis
Rotation matrices
Quaternions
Singular value decomposition
Àlgebra lineal numèrica
Classificació AMS::65 Numerical analysis::65F Numerical linear algebra
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
description Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed-form methods are as robust as the SVD, but significantly faster and more accurate.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-10-01
2025
2025-10-08
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/443361
https://dx.doi.org/10.1002/nla.2492
url https://hdl.handle.net/2117/443361
https://dx.doi.org/10.1002/nla.2492
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-117509GB-I00 SINTESIS DE MOVIMIENTOS ROBOTICOS OPTIMAMENTE AGILES Y GRACILES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
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