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dc.contributor.authorSarabandi, Soheil
dc.contributor.authorThomas, Federico
dc.contributor.otherUniversitat Politècnica de Catalunya. Doctorat en Enginyeria Mecànica, Fluids i Aeronàutica
dc.contributor.otherInstitut de Robòtica i Informàtica Industrial
dc.date.accessioned2020-02-21T16:41:32Z
dc.date.available2020-02-21T16:41:32Z
dc.date.issued2019-04-01
dc.identifier.citationSarabandi, S.; Thomas, F. A survey on the computation of quaternions from rotation matrices. "Journal of mechanisms and robotics", 1 Abril 2019, vol. 11, núm. 2, p. 1-9.
dc.identifier.issn1942-4302
dc.identifier.urihttp://hdl.handle.net/2117/178326
dc.description.abstractThe parameterization of rotations is a central topic in many theoretical and applied fields such as rigid body mechanics, multibody dynamics, robotics, spacecraft attitude dynamics, navigation, 3D image processing, computer graphics, etc. Nowadays, the main alternative to the use of rotation matrices, to represent rotations in R3, is the use of Euler parameters arranged in quaternion form. Whereas the passage from a set of Euler parameters to the corresponding rotation matrix is unique and straightforward, the passage from a rotation matrix to its corresponding Euler parameters has been revealed to be somewhat tricky if numerical aspects are considered. Since the map from quaternions to 3x3 rotation matrices is a 2-to-1 covering map, this map cannot be smoothly inverted. As a consequence, it is erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception is herein clarified. This paper reviews the most representative methods available in the literature, including a comparative analysis of their computational costs and error performances. The presented analysis leads to the conclusion that Cayley's factorization, a little-known method used to compute the double quaternion representation of rotations in four dimensions from 4x4 rotation matrices, is the most robust method when particularized to three dimensions
dc.format.extent9 p.
dc.language.isoeng
dc.publisherASME PRESS
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Informàtica::Automàtica i control
dc.subject.otherAutomation
dc.subject.otherEuler parameters
dc.subject.otherQuaternions
dc.subject.otherRotation matrices
dc.subject.otherNumerical accuracy
dc.subject.otherRotation
dc.subject.otherComputation
dc.subject.otherErrors
dc.subject.otherAlgebra
dc.titleA survey on the computation of quaternions from rotation matrices
dc.typeArticle
dc.contributor.groupUniversitat Politècnica de Catalunya. KRD - Cinemàtica i Disseny de Robots
dc.identifier.doi10.1115/1.4041889
dc.subject.inspecClassificació INSPEC::Automation
dc.relation.publisherversionhttp://mechanismsrobotics.asmedigitalcollection.asme.org/article.aspx?articleid=2712878
dc.rights.accessOpen Access
local.identifier.drac24243700
dc.description.versionPreprint
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/2PE/MDM-2016-0656
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO//DPI2014-57220-C2-2-P/ES/ESTRATEGIAS DE CONTROL PARA UN ROBOT ACTUADO POR CABLES PARA SIMULACION DE BAJA GRAVEDAD/
local.citation.authorSarabandi, S.; Thomas, F.
local.citation.publicationNameJournal of mechanisms and robotics
local.citation.volume11
local.citation.number2
local.citation.startingPage1
local.citation.endingPage9


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