Abstract
This paper presents a nonlinear optimal feedback control approach for robot manipulators with dynamics nonlinearities. The task of tracking a preplanned trajectory of robot manipulator is formulated as an optimal control problem, in which the energy consumption and motion time are minimized. The optimal control problem is first solved as an open-loop optimal control problem by using a time-scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open-loop control and the optimal closed-loop control along the optimal trajectory, a practical method is presented to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results of two-link robot manipulator are presented to show that the proposed approach is highly effective.
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