The Serret-Andoyer formalism in rigid-body dynamics: II. Geometry,stabilization, and control |
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Authors: | A Bloch P Gurfil K -Y Lum |
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Institution: | (1) University of Michigan, Ann Arbor, MI 48109, USA;(2) Technion-Israel Institute of Technology, Haifa, 32000, Israel;(3) Temasek Laboratories, National University of Singapore, 117508, Singapore |
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Abstract: | This paper continues the review of the Serret-Andoyer (SA) canonical formalism in rigid-body dynamics, commenced by 1], and
presents some new result. We discuss the applications of the SA formalism to control theory. Considerable attention is devoted
to the geometry of the Andoyer variables and to the modeling of control torques. We develop a new approach to Stabilization
of rigid-body dynamics, an approach wherein the state-space model is formulated through sets of canonical elements that partially
or completely reduce the unperturbed Euler-Poinsot problem. The controllability of the system model is examined using the
notion of accessibility, and is shown to be accessible. Based on the accessibility proof, a Hamiltonian controller is derived
by using the Hamiltonian as a natural Lyapunov function for the closed-loop dynamics. It is shown that the Hamiltonian controller
is both passive and inverse optimal with respect to a meaningful performance-index. Finally, we point out the possibility
to apply methods of structure-preserving control using the canonical Andoyer variables, and we illustrate this approach on
rigid bodies containing internal rotors.
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Keywords: | nonlinear stabilization Hamiltonian control systems Lyapunov control |
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