This paper introduces methods to determine the exponential coordinates of first kind and of second kind for an arbitrary spatial displacement given in terms of the left adjoint representation. Due to the algebraic properties of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(6 \times 6)$$\end{document}-matrix group, the obtained formulae are structure-preserving generalizations of their purely-rotative counterparts in coherence with the principle of transference. While the exponential coordinates of first kind represent the line-geometric parameters of a displacement (rotation and translation along a unit spear), the exponential coordinates of second kind coincide with dual Euler angles and with the parameters according to the kinematic convention by Sheth and Uicker. In either case, a spatial displacement is specified via six independent scalars, in form of a dual angle and a dual unit vector (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2+4=6$$\end{document}) for the first kind and in form of three dual angles (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\cdot 2 =6$$\end{document}) along three sequentially orthogonal axes for the second kind. From a practical viewpoint, the parametrization method enables an automated parametrization of the kinematics of an arbitrary mechanism. From a theoretical viewpoint, the reported methods are relevant due to their structural simplicity and coherence.


    Zugriff

    Zugriff prüfen

    Verfügbarkeit in meiner Bibliothek prüfen

    Bestellung bei Subito €


    Exportieren, teilen und zitieren



    Titel :

    Exponential Displacement Coordinates by Means of the Adjoint Representation


    Weitere Titelangaben:

    Springer Proceedings in Advanced Robotics


    Beteiligte:
    Lenarčič, Jadran (Herausgeber:in) / Siciliano, Bruno (Herausgeber:in) / Bongardt, Bertold (Autor:in) / Uicker, John J. (Autor:in)

    Kongress:

    International Symposium on Advances in Robot Kinematics ; 2020 ; Ljubljana, Slovenia December 06, 2020 - December 10, 2020



    Erscheinungsdatum :

    2020-07-18


    Format / Umfang :

    9 pages





    Medientyp :

    Aufsatz/Kapitel (Buch)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch




    Decentralized Consensus Control of Rigid Bodies Using Exponential Coordinates

    Maadani, Mohammad / Butcher, Eric A. / Nazari, Morad et al. | AIAA | 2019


    Fractional Control of Rigid Body Attitude Dynamics Using Exponential Coordinates

    Nazari, Morad / Butcher, Eric A. / Sanyal, Amit K. | AIAA | 2018



    Adaptive Control of a Rigid Body Vehicle on Exponential Coordinates with Guaranteed Performance

    Arabi, Ehsan / Sarsilmaz, Selahattin Burak / Yucelen, Tansel et al. | AIAA | 2018