Planning Rigid Body Motions and Optimal Control Problem on Lie Group So(2, 1)
Loading...
Files
Date
2010
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Open Access Color
OpenAIRE Downloads
OpenAIRE Views
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 minimizes the integral of the Lorentz inner product 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.
Description
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, Elastic energy, Frenet frame, Hamiltonian systems, Hamiltonian vector fields, Inner product, Integrable Hamiltonian system, Minkowski space, Motion planning problems, Optimal control problem, Rigid body systems, Smooth trajectories, Control, Curve fitting, Maximum principle, Motion planning, Optimization, Rigid structures, Vectors, Lie groups, Optimal control systems, Hamiltonians
Fields of Science
Citation
WoS Q
N/A
Scopus Q
N/A
Source
World Academy of Science, Engineering and Technology
Volume
64
Issue
Start Page
448
End Page
452
Page Views
2
checked on Feb 13, 2026
