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Journal of Applied MathematicsVolume 2013 2013, Article ID 958597, 6 pages

Research ArticleResearch Institute of Robotics, Henan University of Technology, Zhengzhou 450001, China

Received 7 July 2013; Revised 8 September 2013; Accepted 9 September 2013

Academic Editor: Weihai Zhang

Copyright © 2013 Shijie Zhang and Yi Ning. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The mathematic description of the trajectory of robot manipulators with the optimal trajectory tracking problem is formulated as an optimal control problem, and a parametric approach is proposed for the optimal trajectory tracking control problem. 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 2-link robot manipulator are presented to show the effectiveness of the proposed method.

Autor: Shijie Zhang and Yi Ning



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