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    Motion Control for Nonholonomic Systems on Matrix Lie Groups

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    PhD_98-1.pdf (573.1Kb)
    No. of downloads: 2224

    Date
    1998
    Author
    Struemper, Herbert Karl
    Advisor
    Krishnaprasad, P.S.
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    Abstract
    In this dissertation we study the control of nonholonomic systems defined by invariant vector fields on matrix Lie groups. We make use of canonical constructions of coordinates and other mathematical tools provided by the Lie group setting. An approximate tracking control law is derived for so-called chained form systems which arise as local representations of systems on a certain nilpotent matrix group. After studying the technique of nilpotentization in the setting of systems on matrix Lie groups we show how motion control laws derived for nilpotent systems can be extended to nilpotentizable systems using feedback and state transformations. The proposed control laws exhibit highly oscillatory components both for tracking and feedback stabilization of local representations of nonholonomic systems on Lie groups. Applications to the control and analysis of the kinematics of mechanical systems are discussed and numerical simulations are presented.
    URI
    http://hdl.handle.net/1903/6002
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    • Institute for Systems Research Technical Reports

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