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Finite-time disturbance observer-based trajectory tracking control for flexible-joint robots

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Abstract

This paper proposes a robust finite-time control scheme for the high-precision tracking problem of (FJRs) with various types of unpredictable disturbances. Specifically, based on a flatness dynamic model, a finite-time disturbance observer (FTDO) with only link-side position measurements is firstly developed to estimate the lumped unknown time-varying disturbance and unmeasurable states. Then, through the information of the states and disturbances provided by the FTDO, a robust output feedback controller is constructed, which can accomplish the tasks of disturbance suppression and trajectory tracking in finite time. Moreover, a rigorous stability analysis of the closed-loop system based on a finite-time bounded (FTB) function is conducted. Finally, the simulation results validate the feasibility and superiority of the proposed control scheme against other existing control results.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Author information

Authors and Affiliations

  1. Key Laboratory of Industrial Internet of Things and Networked Control, Ministry of Education, Innovation Research Group of Universities in Chongqing, and Chongqing Key Laboratory of Complex Systems and Bionic Control, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Huiming Wang

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798, Singapore, Singapore

    Huiming Wang & I-Ming Chen

  3. School of Automation, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Yang Zhang & Xianlun Tang

  4. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Zhenhua Zhao

  5. Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough, LE11 3TU, UK

    Jun Yang

Authors
  1. Huiming Wang
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  2. Yang Zhang
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  3. Zhenhua Zhao
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  4. Xianlun Tang
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  5. Jun Yang
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Correspondence to Huiming Wang.

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This work was supported in part by National Natural Science Foundation of China (61803059, 61903192), in part by National Robotics Program, RDS, SERC, Singapore (1922200001), and in part by Foundation of Chongqing University of Posts and Telecommunications (A2017-74, A2017-15).

Appendix

Appendix

\(\varvec{\tau }\) is the following

$$\begin{aligned} \begin{aligned} \varvec{\tau }&=\varvec{J}{{{\dot{\varvec{x}}}}_{4}}+\varvec{B}{\varvec{{x}}_{4}}+\varvec{K}\left( {\varvec{x}_{3}}-{\varvec{x}_{1}} \right) -{\varvec{w}_{2}} \\&=\frac{\varvec{J}}{\varvec{K}}\left( \varvec{M}\left( \varvec{z} \right) {\varvec{z}^{\left( 4 \right) }}+ 2\dot{\varvec{M}}\left( \varvec{z} \right) {\varvec{{z}}^{\left( 3 \right) }}+\right. \ddot{\varvec{M}}\left( \varvec{z} \right) \ddot{\varvec{z}} +\varvec{C}\left( \varvec{z},\dot{\varvec{z}} \right) {\varvec{z}^{\left( 3 \right) }}\\&\quad +2\dot{\varvec{C}}\left( \varvec{z},\dot{\varvec{z}} \right) \ddot{\varvec{z}} +\ddot{\varvec{C}}\left( \varvec{ z},\dot{\varvec{z}} \right) \dot{\varvec{z}}+ \varvec{K}{\ddot{\varvec{z}}} +\ddot{\varvec{G}}\left( \varvec{z} \right) -{{{\ddot{\varvec{{w}}}}}_{1}} \Big ) +\frac{\varvec{B}}{\varvec{K}} \\&\quad \Big ( \varvec{M}\left( \varvec{z} \right) {\varvec{z}^{\left( 3 \right) }}+\dot{\varvec{M}}\left( \varvec{z} \right) \ddot{\varvec{z}} + \varvec{C}\left( \varvec{z},\dot{\varvec{z}} \right) \ddot{\varvec{z}} +\dot{\varvec{C}}\left( \varvec{z},\dot{\varvec{z}} \right) \dot{\varvec{z}} +\varvec{K}\dot{\varvec{z}} \\&\quad +\dot{\varvec{G}}\left( \varvec{z} \right) -{{{\dot{\varvec{\omega }}}}_{1}} \Big ) +\varvec{M}\left( \varvec{z} \right) \ddot{\varvec{z}} + \varvec{C}(z,\dot{z})\dot{\varvec{z}}+\varvec{G}\left( \varvec{z} \right) -{\varvec{w}_{1}} -{\varvec{w}_{2}} \\&=\frac{\varvec{JM}\left( \varvec{z} \right) }{\varvec{K}}{\varvec{z}^{\left( 4 \right) }}+ \frac{2\varvec{J}\dot{\varvec{M}}( \varvec{z} ) + \varvec{BM}(\varvec{z})+\varvec{JC}( \varvec{z},\dot{\varvec{z}})}{\varvec{K}} {\varvec{z}^{\left( 3 \right) }} \\&\quad + \Bigg (\frac{\varvec{J}\ddot{\varvec{M}}( \varvec{z} )+2\varvec{J}\dot{\varvec{C}} ( \varvec{z},\dot{\varvec{z}} )}{\varvec{K}}+\frac{\varvec{B}\dot{\varvec{M}}\left( \varvec{z} \right) +\varvec{BC}( \varvec{z},\dot{\varvec{z}} )}{\varvec{K}} + \varvec{M}( \varvec{z} ) \\&\quad +\varvec{J} \Bigg )\ddot{\varvec{z}} + \left( \frac{\varvec{J}\ddot{\varvec{C}}\left( \varvec{z},\dot{\varvec{z}} \right) }{\varvec{K}}+\frac{\varvec{B}\dot{\varvec{C}}\left( \varvec{z},\dot{\varvec{z}} \right) }{\varvec{K}} +\varvec{C}\left( \varvec{z},\dot{\varvec{z}} \right) +\varvec{B} \right) \dot{\varvec{z}}\\&\quad +\frac{\varvec{J}}{\varvec{K}}\Big ( \ddot{\varvec{G}}\left( \varvec{z} \right) -{{{\ddot{\varvec{\omega }}}}_{1}} \Big ) +\frac{\varvec{B}}{\varvec{K}}\left( \dot{\varvec{G}}\left( \varvec{z} \right) -{{{\dot{\varvec{\omega }}}}_{1}} \right) + \varvec{G}\left( \varvec{z} \right) -{\varvec{\omega }_{1}} \\&\quad -{\varvec{\omega }_{2}}. \\ \end{aligned} \end{aligned}$$

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Wang, H., Zhang, Y., Zhao, Z. et al. Finite-time disturbance observer-based trajectory tracking control for flexible-joint robots. Nonlinear Dyn 106, 459–471 (2021). https://doi.org/10.1007/s11071-021-06868-4

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