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    A Distance Metric for Finite Sets of Rigid-Body Displacements via the Polar Decomposition

    Source: Journal of Mechanical Design:;2007:;volume( 129 ):;issue: 008::page 883
    Author:
    Pierre M. Larochelle
    ,
    Andrew P. Murray
    ,
    Jorge Angeles
    DOI: 10.1115/1.2735640
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: An open research question is how to define a useful metric on the special Euclidean group SE(n) with respect to: (1) the choice of coordinate frames and (2) the units used to measure linear and angular distances that is useful for the synthesis and analysis of mechanical systems. We discuss a technique for approximating elements of SE(n) with elements of the special orthogonal group SO(n+1). This technique is based on using the singular value decomposition (SVD) and the polar decompositions (PD) of the homogeneous transform representation of the elements of SE(n). The embedding of the elements of SE(n) into SO(n+1) yields hyperdimensional rotations that approximate the rigid-body displacements. The bi-invariant metric on SO(n+1) is then used to measure the distance between any two displacements. The result is a left invariant PD based metric on SE(n).
    keyword(s): Theorems (Mathematics) , Structural frames , Motion AND Displacement ,
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      A Distance Metric for Finite Sets of Rigid-Body Displacements via the Polar Decomposition

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    http://yetl.yabesh.ir/yetl1/handle/yetl/136443
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    contributor authorPierre M. Larochelle
    contributor authorAndrew P. Murray
    contributor authorJorge Angeles
    date accessioned2017-05-09T00:25:02Z
    date available2017-05-09T00:25:02Z
    date copyrightAugust, 2007
    date issued2007
    identifier issn1050-0472
    identifier otherJMDEDB-27854#883_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/136443
    description abstractAn open research question is how to define a useful metric on the special Euclidean group SE(n) with respect to: (1) the choice of coordinate frames and (2) the units used to measure linear and angular distances that is useful for the synthesis and analysis of mechanical systems. We discuss a technique for approximating elements of SE(n) with elements of the special orthogonal group SO(n+1). This technique is based on using the singular value decomposition (SVD) and the polar decompositions (PD) of the homogeneous transform representation of the elements of SE(n). The embedding of the elements of SE(n) into SO(n+1) yields hyperdimensional rotations that approximate the rigid-body displacements. The bi-invariant metric on SO(n+1) is then used to measure the distance between any two displacements. The result is a left invariant PD based metric on SE(n).
    publisherThe American Society of Mechanical Engineers (ASME)
    titleA Distance Metric for Finite Sets of Rigid-Body Displacements via the Polar Decomposition
    typeJournal Paper
    journal volume129
    journal issue8
    journal titleJournal of Mechanical Design
    identifier doi10.1115/1.2735640
    journal fristpage883
    journal lastpage886
    identifier eissn1528-9001
    keywordsTheorems (Mathematics)
    keywordsStructural frames
    keywordsMotion AND Displacement
    treeJournal of Mechanical Design:;2007:;volume( 129 ):;issue: 008
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
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