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Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory

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  • Yusheng Zhou

    (Nanjing University of Aeronautics and Astronautics)

  • Zaihua Wang

    (Nanjing University of Aeronautics and Astronautics)

Abstract

This paper investigates the control of Back-and-Forth motion to fetch object and Lower-Raise-Head motion to avoid obstacle of the wheeled inverted pendulum system with an input delay. In controlling the Back-and-Forth motion, the linear optimal control theory is used because the tilt angle of the pendulum is forced to be small enough by minimizing a quadratic performance criterion with large weight of tilt angle error, and the controller is represented by using predictor-based feedback. In controlling the Lower-Raise-Head motion, linearized models do not work due to the strong nonlinearity caused by big tilt angle for avoiding obstacle. Without considering yaw movement, the wheeled inverted pendulum system is decoupled, the subsystem governing the state of the tilt angle is transformed into a simple linear system by using feedback linearization. With a properly chosen trajectory tracking target, the control of Lower-Raise-Head motion is solved on the basis of optimal trajectory tracking control for linear subsystems with an input delay. Numerical simulations illustrate the effectiveness of the proposed approaches.

Suggested Citation

  • Yusheng Zhou & Zaihua Wang, 2016. "Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 625-645, February.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0759-z
    DOI: 10.1007/s10957-015-0759-z
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    References listed on IDEAS

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    1. S. F. P. Saramago & V. Steffen, 2001. "Trajectory Modeling of Robot Manipulators in the Presence of Obstacles," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 17-34, July.
    2. M. S. Mahmoud & M. Zribi, 1999. "H∞-Controllers for Time-Delay Systems Using Linear Matrix Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 100(1), pages 89-122, January.
    3. J. D. Chen, 2005. "LMI-Based Robust H∞ Control of Uncertain Neutral Systems with State and Input Delays," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 553-570, September.
    4. Yusheng Zhou & Zaihua Wang, 2014. "Optimal Feedback Control for Linear Systems with Input Delays Revisited," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 989-1017, December.
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    Cited by:

    1. Yusheng Zhou & Zaihua Wang & Kwok-wai Chung, 2019. "Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 634-652, May.

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