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Nonlinear Optimal Control for Robot Manipulator Trajectory Tracking

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Foundations and Applications of Intelligent Systems

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 213))

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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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Acknowledgments

This work was supported by the National Natural Science Foundation of China (61075083), and Henan Province Innovation and Technology Fund for Outstanding Scholarship(0421000500), and the Key Scientific Research Projects of Henan University of technology(09XZD008), and the Science Foundation of Henan University of Technology(150166).

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Authors and Affiliations

  1. Research Institute of Robotics, Henan University of Technology, Zhengzhou, China

    Shijie Zhang, Ning Yi & Fengzhi Huang

Authors
  1. Shijie Zhang
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  2. Ning Yi
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  3. Fengzhi Huang
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Corresponding author

Correspondence to Shijie Zhang .

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Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, People's Republic of China

    Fuchun Sun

  2. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, People's Republic of China

    Tianrui Li

  3. Department of Computer Science and Techn, Tsinghua University, Beijing, People's Republic of China

    Hongbo Li

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Zhang, S., Yi, N., Huang, F. (2014). Nonlinear Optimal Control for Robot Manipulator Trajectory Tracking. In: Sun, F., Li, T., Li, H. (eds) Foundations and Applications of Intelligent Systems. Advances in Intelligent Systems and Computing, vol 213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37829-4_57

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  • DOI: https://doi.org/10.1007/978-3-642-37829-4_57

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37828-7

  • Online ISBN: 978-3-642-37829-4

  • eBook Packages: EngineeringEngineering (R0)

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