Browsing by Author "Sager I."

Now showing 1 - 4 of 4

An Optimal Control Problem for Rigid Body Motions on Lie Group So(2, 1) [pp. 1054-1059]
(2010) Abazari N.; Sager I.
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.
An Optimal Control Problem for Rigid Body Motions on Lie Group So(2, 1) [pp. 1068-1073]
(2010) Abazari N.; Sager I.
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.
Optimization Problem of the Rigid Body Motion With the Geodesic Frame
(2010) Sager I.; Abazari N.
This study tries to solve the motion of a rigid body, its optimal control problem on the Lie group SE(3) with respect to geodesic frame of curves on the surface in Euclidian 3-space. In this case, optimal control problem is solved on the Lie group SE(3). The motion planning problem is formulated as an optimal control problem in which the cost function to be minimized is equivalent to integrate the conjugated square norm of Darboux vector with respect to the geodesic frame of the curve. The coordinate free Maximum Principle is applied to the theory of integrable Hamiltonian systems to solve this problem.
Planning Rigid Body Motions and Optimal Control Problem on Lie Group So(2, 1)
(2010) Abazari N.; Sager I.
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.