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Adaptive neural impedance control for electrically driven robotic systems based on a neuro-adaptive observer

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Abstract

This paper proposes an adaptive neural impedance control (ANIC) strategy for electrically driven robotic systems, considering system uncertainties and external disturbances. For the considered robotic system, the joint velocities and armature currents are assumed to be unknown and unmeasured, and an adaptive observer is then designed to estimate its unknown states using a neural network. Based on the observed joint velocities and armature currents, an ANIC scheme is proposed and the performances of the joint positions and force tracking can be improved. We also prove that the control system is stable and all the signals in closed-loop system are bounded. Simulation examples on a two-link electrically driven robotic manipulator are presented to show the effectiveness of the proposed observer-based intelligent impedance control method.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (61773351, 61703372), the Program for Science & Technology Innovation Talents in Universities of Henan Province (20HASTIT031), the Training Plan for University’s Young Backbone Teachers of Henan Province (2017GGJS004), Outstanding Foreign Scientists Support Project in Henan Province of China (GZS201908) and the China Scholarship Council (201907045008).

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Authors and Affiliations

  1. School of Electrical Engineering, Zhengzhou University, Zhengzhou, 450001, China

    Jinzhu Peng, Shuai Ding, Zeqi Yang & Jianbin Xin

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  1. Jinzhu Peng
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  2. Shuai Ding
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  3. Zeqi Yang
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  4. Jianbin Xin
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Correspondence to Jianbin Xin.

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Appendix A

Appendix A

The proof of Lemma 1.

Taking the derivative of \(M^*\) with respect to time, we can obtain,

$$\begin{aligned} {{\dot{M}}}^*= {J^{\mathrm {-T}}}{\dot{M}_0}(q)J^{-1}-2{J^{\mathrm {-T}}}M_0(q)J^{-1}{\dot{J}}J^{-1}. \end{aligned}$$
(89)

Considering \({C}^*={J^{\mathrm {-T}}}\Big (C_0(q,\dot{q})-M_0(q)J^{-1}\dot{J} \Big )J^{-1}\) and substituting Eq. (89) and \({C}^*\) into Eq. (12), yields

$$\begin{aligned}&\zeta ^{{\mathrm {T}}}({{\dot{M}}}^*-2{C}^*)\zeta \nonumber \\&\quad = \zeta ^{{\mathrm {T}}}\left[ {J^{\mathrm {-T}}}{\dot{M}_0}(q)J^{-1} \right. \nonumber \\&\left. \qquad -2{J^{\mathrm {-T}}}M_0(q)J^{-1}{\dot{J}}J^{-1}-2{C}^*\right] \zeta \nonumber \\&\quad = \zeta ^{{\mathrm {T}}}\left[ {J^{\mathrm {-T}}}{\dot{M}_0}(q)J^{-1}-2{J^{\mathrm {-T}}}M_0(q)J^{-1}{\dot{J}}J^{-1}\right. \nonumber \\&\qquad \left. -2{J^{{\mathrm {T}}}}^{-1}\left( C_0(q,\dot{q})-M_0(q)J^{-1}\dot{J} \right) J^{-1} \right] \zeta \nonumber \\&\quad = \zeta ^{{\mathrm {T}}}\left[ {J^{\mathrm {-T}}}{\dot{M}_0}(q)J^{-1}-2{J^{\mathrm {-T}}}C_0(q,\dot{q})J^{-1} \right] \zeta \nonumber \\&\quad = \zeta ^{{\mathrm {T}}}\left[ {J^{\mathrm {-T}}}\left( {\dot{M}_0}(q)-2C_0(q,\dot{q}) \right) J^{-1} \right] \zeta \nonumber \\&\quad = 0. \end{aligned}$$
(90)

It means that the matrix \({{\dot{M}}}^*-2{C}^*\) is skew symmetric.

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Peng, J., Ding, S., Yang, Z. et al. Adaptive neural impedance control for electrically driven robotic systems based on a neuro-adaptive observer. Nonlinear Dyn 100, 1359–1378 (2020). https://doi.org/10.1007/s11071-020-05569-8

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