On closed-form solutions to the 4D nearest rotation matrix problem

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2022 The Author...

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Autores: Sarabandi, Soheil|||0000-0002-2103-1610, Thomas, Federico|||0000-0001-9341-5528
Formato: artículo
Fecha de publicación:2024
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/408580
Acesso em linha:https://hdl.handle.net/2117/408580
https://dx.doi.org/10.1002/mma.8524
Access Level:acceso abierto
Palavra-chave:4D rotations
Double quaternions
Fourth-degree polynomials
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::11 Number theory::11E Forms and linear algebraic groups
Classificació AMS::20 Group theory and generalizations::20G Linear algebraic groups (classical groups)
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling On closed-form solutions to the 4D nearest rotation matrix problemSarabandi, Soheil|||0000-0002-2103-1610Thomas, Federico|||0000-0001-9341-55284D rotationsDouble quaternionsFourth-degree polynomialsClassificació AMS::15 Linear and multilinear algebramatrix theoryClassificació AMS::11 Number theory::11E Forms and linear algebraic groupsClassificació AMS::20 Group theory and generalizations::20G Linear algebraic groups (classical groups)Àrees temàtiques de la UPC::Matemàtiques i estadísticaThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2022 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.In this paper, we address the problem of restoring the orthogonality of a numerically noisy 4D rotation matrix by finding its nearest (in Frobenius norm) correct rotation matrix. This problem can be straightforwardly solved using the Singular Value Decomposition (SVD). Nevertheless, to avoid numerical methods, we present two new closed-form methods. One relies on the direct minimization of the mentioned Frobenius norm, and the other on the passage to double quaternion representation. A comparison of these two methods with respect to the SVD reveals that the method based on a double quaternion representation is superior in all aspects.Spanish Ministry of Economy andCompetitiveness, Grant/Award Number:PID2020-117509GB-I00/AEI/10.13039/50110001103Peer Reviewed20242024-02-0120242024-05-24journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/408580https://dx.doi.org/10.1002/mma.8524reponame: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:2117/4085802026-05-27T15:37:01Z
dc.title.none.fl_str_mv On closed-form solutions to the 4D nearest rotation matrix problem
title On closed-form solutions to the 4D nearest rotation matrix problem
spellingShingle On closed-form solutions to the 4D nearest rotation matrix problem
Sarabandi, Soheil|||0000-0002-2103-1610
4D rotations
Double quaternions
Fourth-degree polynomials
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::11 Number theory::11E Forms and linear algebraic groups
Classificació AMS::20 Group theory and generalizations::20G Linear algebraic groups (classical groups)
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short On closed-form solutions to the 4D nearest rotation matrix problem
title_full On closed-form solutions to the 4D nearest rotation matrix problem
title_fullStr On closed-form solutions to the 4D nearest rotation matrix problem
title_full_unstemmed On closed-form solutions to the 4D nearest rotation matrix problem
title_sort On closed-form solutions to the 4D nearest rotation matrix problem
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 4D rotations
Double quaternions
Fourth-degree polynomials
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::11 Number theory::11E Forms and linear algebraic groups
Classificació AMS::20 Group theory and generalizations::20G Linear algebraic groups (classical groups)
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic 4D rotations
Double quaternions
Fourth-degree polynomials
Classificació AMS::15 Linear and multilinear algebra
matrix theory
Classificació AMS::11 Number theory::11E Forms and linear algebraic groups
Classificació AMS::20 Group theory and generalizations::20G Linear algebraic groups (classical groups)
Àrees temàtiques de la UPC::Matemàtiques i estadística
description This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2022 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-02-01
2024
2024-05-24
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/2117/408580
https://dx.doi.org/10.1002/mma.8524
url https://hdl.handle.net/2117/408580
https://dx.doi.org/10.1002/mma.8524
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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