An Optimal Control Problem for Rigid Body Motions on Lie Group So(2, 1) [pp. 1068-1073]
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Date
2010
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Abstract
In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.
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Keywords
Darboux vector, Hamiltonian vector field, Lie group, Lorentz metric, Maximum principle, Optimal control, Rigid body motion, Darboux vector, Hamiltonian vector field, Lie group, Lorentz, Optimal controls, Rigid-body motion, Control, Curve fitting, Maximum principle, Motion planning, Optimization, Rigid structures, Vectors, Hamiltonians
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World Academy of Science, Engineering and Technology
Volume
66
Issue
Start Page
1068
End Page
1073
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3
checked on Mar 25, 2026
