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This article is cited in 7 scientific papers (total in 7 papers)
The Serret–Andoyer Formalism in Rigid-Body Dynamics: II. Geometry, Stabilization, and Control
A. Blocha, P. Gurfilb, K. Lumc a University of Michigan, Ann Arbor, MI 48109 USA
b Technion–Israel Institute of Technology, Haifa, 32000 Israel
c Temasek Laboratories, National University of Singapore, 117508 Singapore
Abstract:
This paper continues the review of the Serret–Andoyer (SA) canonical formalism in rigid-body dynamics, commenced by [1], and presents some new results. 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.
Keywords:
nonlinear stabilization, Hamiltonian control systems, Lyapunov control.
Received: 24.07.2006 Accepted: 25.03.2007
Citation:
A. Bloch, P. Gurfil, K. Lum, “The Serret–Andoyer Formalism in Rigid-Body Dynamics: II. Geometry, Stabilization, and Control”, Regul. Chaotic Dyn., 12:4 (2007), 426–447
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https://www.mathnet.ru/eng/rcd631 https://www.mathnet.ru/eng/rcd/v12/i4/p426
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