Parametric Approach to Trajectory Tracking Control of Robot Manipulators
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 op...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/958597 |
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| _version_ | 1849406379835523072 |
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| author | Shijie Zhang Yi Ning |
| author_facet | Shijie Zhang Yi Ning |
| author_sort | Shijie Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-53c0294c84a444d59de3ee2ec5db216e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-53c0294c84a444d59de3ee2ec5db216e2025-08-20T03:36:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/958597958597Parametric Approach to Trajectory Tracking Control of Robot ManipulatorsShijie Zhang0Yi Ning1Research Institute of Robotics, Henan University of Technology, Zhengzhou 450001, ChinaResearch Institute of Robotics, Henan University of Technology, Zhengzhou 450001, ChinaThe 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.http://dx.doi.org/10.1155/2013/958597 |
| spellingShingle | Shijie Zhang Yi Ning Parametric Approach to Trajectory Tracking Control of Robot Manipulators Journal of Applied Mathematics |
| title | Parametric Approach to Trajectory Tracking Control of Robot Manipulators |
| title_full | Parametric Approach to Trajectory Tracking Control of Robot Manipulators |
| title_fullStr | Parametric Approach to Trajectory Tracking Control of Robot Manipulators |
| title_full_unstemmed | Parametric Approach to Trajectory Tracking Control of Robot Manipulators |
| title_short | Parametric Approach to Trajectory Tracking Control of Robot Manipulators |
| title_sort | parametric approach to trajectory tracking control of robot manipulators |
| url | http://dx.doi.org/10.1155/2013/958597 |
| work_keys_str_mv | AT shijiezhang parametricapproachtotrajectorytrackingcontrolofrobotmanipulators AT yining parametricapproachtotrajectorytrackingcontrolofrobotmanipulators |