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Robust sliding mode impedance control of manipulators for complex force-controlled operations

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Abstract

The multi-source uncertainties in complex force control operation scenarios will seriously affect the force control accuracy and operation quality of industrial manipulators. The complex force control method of manipulators considering multi-source uncertainties (environmental position uncertainty, environmental stiffness uncertainty and other uncertainties, etc.) is investigated in this paper. Firstly, the parametric representation of environmental position uncertainty and the impedance model parameter uncertainty is introduced under the traditional impedance control framework. A new impedance control model is proposed by considering the environmental position uncertainty and the implicit dynamic adjustment terms of impedance model parameters as the lumped disturbance. Then, a finite-time disturbance observer is designed for real-time estimation of the lumped disturbance, and a new robust sliding-mode impedance control method is proposed to compensate for the lumped disturbance combined with the sliding-mode variable structure theory, so as to construct a novel composite control framework for uncertain and complex force control operation scenarios. Finally, based on the Lyapunov stability theory, the stability of the control method and the observer is guaranteed. Simulations and experiments are carried out to verify the proposed method, and a comprehensive comparison is made with existing state-of-the-art methods such as traditional impedance control, variable stiffness impedance control and indirect adaptive impedance control. The results show that the proposed sliding-mode impedance control method can realize the fast and stable adjustment of the contact force of the end-effector in different operation scenarios and can achieve the effect of the relative contact force error within 4.73%, which proves the effectiveness and feasibility of the proposed method.

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Data availability

The datasets generated during and analyzed during the current study are not publicly available due to the datasets to be used in subsequent studies, but are available from the corresponding author on reasonable request.

Abbreviations

\(^{0}T_6\) :

Pose of the linkage coordinate system \(\{6\}\) in the base coordinate system

\(^{0}R_6\) :

Orientation of the linkage coordinate system \(\{6\}\) in the base coordinate system

\(^{0}P_6\) :

Position of the origin of the linkage coordinate system \(\{6\}\) in the base coordinate system

V :

Robot end-effector Cartesian velocity vector

v :

Linear velocity vector

w :

Angular velocity vector

\(J(\theta )\) :

Robot’s Jacobian

\(\theta \) :

Joint position

\(x_c\) :

Commanded end-effector position

\(\dot{x}_c\) :

Commanded end-effector velocity

\(\ddot{x}_c\) :

Commanded end-effector acceleration

\(x_d\) :

Desired end-effector position

\(\dot{x}_d\) :

Desired end-effector velocity

\(\ddot{x}_d\) :

Desired end-effector acceleration

m :

Mass coefficient of the manipulator

b :

Damping coefficient of the manipulator

k :

Stiffness coefficient of the manipulator

\(f_e\) :

Actual contact force

\(f_d\) :

Desired contact force

\(x_e\) :

Environment position

\(x_m\) :

Measured end-effector position

\(\theta _c\) :

Commanded joint position

\(\theta _m\) :

Measured joint position

\(e_f\) :

Contact force error

e :

Position error

\(m_0\) :

Initial value of mass

\(b_0\) :

Initial value of damping

\(k_0\) :

Initial value of stiffness

\(\delta m\) :

Uncertain impedance mass

\(\delta b\) :

Uncertain impedance damping

\(\delta k\) :

Uncertain impedance stiffness

\(\delta x_e\) :

Uncertain environmental position

\(\delta \dot{x}_e\) :

Uncertain environmental velocity

\(\delta \ddot{x}_e\) :

Uncertain environmental acceleration

d :

Total disturbance

\({\hat{d}}\) :

Disturbance observation

\({\tilde{d}}\) :

Disturbance approximation error

References

  1. Tian, J., Yuan, L., Xiao, W., et al.: Constrained control methods for lower extremity rehabilitation exoskeleton robot considering unknown perturbations. Nonlinear Dyn. 108, 1395–1408 (2022)

    Article  Google Scholar 

  2. Li, L., Liu, J.: Consensus tracking control and vibration suppression for nonlinear mobile flexible manipulator multi-agent systems based on PDE model. Nonlinear Dyn. 111, 3345–3359 (2023)

    Article  Google Scholar 

  3. Jin, L., Zhang, Y., Li, S., et al.: Modified ZNN for time-varying quadratic programming with inherent tolerance to noises and its application to kinematic redundancy resolution of robot manipulators. IEEE Trans. Ind. Electron. 63(11), 6978–6988 (2016)

    Article  Google Scholar 

  4. Zhang, W., Cheng, H., Hao, L., et al.: An obstacle avoidance algorithm for robot manipulators based on decision-making force. Rob. Comput. Integr. Manuf. 71, 102114 (2021)

    Article  Google Scholar 

  5. Wang, Y., Gu, L., Xu, Y., et al.: Practical tracking control of robot manipulators with continuous fractional order nonsingular terminal sliding mode. IEEE Trans. Ind. Electron. 63(10), 6194–6204 (2016)

    Article  Google Scholar 

  6. Hogan N.: Impedance control: an approach to manipulation. In: 1984 American Control Conference, pp. 304–313 (1984)

  7. Raibert, M.H., Craig, J.J.: Hybrid position/force control of robot manipulators. J. Dyn. Syst. Meas. Control 103(2), 126–133 (1982)

    Article  Google Scholar 

  8. Zhou, F., Li, Y., Liu, G.: Robust decentralized force/position fault-tolerant control for constrained reconfigurable manipulators without torque sensing. Nonlinear Dyn. 89, 955–969 (2017)

    Article  Google Scholar 

  9. Liu, L., Hong, M., Gu, X., et al.: Fixed-time anti-saturation compensators based impedance control with finite-time convergence for a free-flying flexible-joint space robot. Nonlinear Dyn. 109, 1671–1691 (2022)

    Article  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. Liu, H., Lu, W., Zhu, X., et al.: Force tracking impedance control with moving target. In: 2017 IEEE International Conference on Robotics and Biomimetics, pp. 1369–1374 (2017)

  12. Seraji, H., Colbaugh, R.: Force tracking in impedance control. Int. J. Robot. Res. 16(1), 97–117 (1997)

    Article  Google Scholar 

  13. Roveda, L., Iannacci, N., Vicentini, F.: Optimal impedance force-tracking control design with impact formulation for interaction tasks. IEEE Robot. Autom. Lett. 1(1), 130–136 (2015)

    Article  Google Scholar 

  14. Zhang, X., Khamesee, M.B.: Adaptive force tracking control of a magnetically navigated microrobot in uncertain environment. IEEE/ASME Trans. Mechatron. 22(4), 1644–1651 (2017)

    Article  Google Scholar 

  15. Lu, W., Liu, H., Zhu, X., et al.: Variable stiffness force tracking impedance control using differential-less method. In: 2017 29th Chinese Control and Decision Conference, pp. 4906–4911 (2017)

  16. Lee, K., Buss, M.: Force tracking impedance control with variable target stiffness. IFAC Proc. Vol. 41(2), 6751–6756 (2008)

    Article  Google Scholar 

  17. Dinh, T.X., Thien, T.D., Anh, T.H.V., et al.: Disturbance observer based finite time trajectory tracking control for a 3 DOF hydraulic manipulator including actuator dynamics. IEEE Access 6, 36798–36809 (2018)

    Article  Google Scholar 

  18. Izadbakhsh, A., Khorashadizadeh, S.: Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator. Int. J. Robust. Nonlinear Control 30(7), 2719–2735 (2020)

    Article  MathSciNet  Google Scholar 

  19. Ferrara, A., Incremona, G.P., Sangiovanni, B.: Tracking control via switched integral sliding mode with application to robot manipulators. Control Eng. Pract. 90, 257–266 (2019)

    Article  Google Scholar 

  20. Song, Y., Yang, H., Lv, H.: Intelligent control for a robot belt grinding system. IEEE Trans. Control Syst. Technol. 21(3), 716–724 (2012)

    Google Scholar 

  21. Petković, D., Danesh, A.S., Dadkhah, M., et al.: Adaptive control algorithm of flexible robotic gripper by extreme learning machine. Rob. Comput. Integr. Manuf. 37, 170–178 (2016)

    Article  Google Scholar 

  22. Jin, L., Li, S., Hu, B., et al.: A noise-suppressing neural algorithm for solving the time-varying system of linear equations: a control-based approach. IEEE Trans. Ind. Inf. 15(1), 236–246 (2019)

    Article  Google Scholar 

  23. Lee, C.H., Wang, W.C.: Robust adaptive position and force controller design of robot manipulator using fuzzy neural networks. Nonlinear Dyn. 85(1), 343–354 (2016)

    Article  MathSciNet  Google Scholar 

  24. Zhang, L., Li, Z., Yang, C.: Adaptive neural network based variable stiffness control of uncertain robotic systems using disturbance observer. IEEE Trans. Ind. Electron. 64(3), 2236–2245 (2016)

    Article  Google Scholar 

  25. Wang, Y., Gao, Y., Karimi, H.R., et al.: Sliding mode control of fuzzy singularly perturbed systems with application to electric circuit. IEEE Trans. Syst. Man Cybern. Syst. 48(10), 1667–1675 (2016)

    Article  Google Scholar 

  26. Zhihong, M., Paplinski, A.P., Wu, H.R.: A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators. IEEE Trans. Autom. Control 39(12), 2464–2469 (1994)

    Article  MathSciNet  Google Scholar 

  27. Vafaei, A., Yazdanpanah, M.J.: Terminal sliding mode impedance control for bilateral teleoperation under unknown constant time delay and uncertainties. In: 2013 European Control Conference, pp. 3748–3753 (2013)

  28. Xu, Q.: Adaptive discrete-time sliding mode impedance control of a piezoelectric microgripper. IEEE Trans. Robot. 29(3), 663–673 (2013)

    Article  MathSciNet  Google Scholar 

  29. Sai, H., Xu, Z., Li, Y., et al.: Adaptive nonsingular fast terminal sliding mode impedance control for uncertainty robotic manipulators. Int. J. Precis. Eng. Manuf. 22(12), 1947–1961 (2021)

    Article  Google Scholar 

  30. Wu, J., Fan, S., Shi, S., et al.: Sliding mode hybrid impedance control of manipulators for complex interaction tasks. In: 2017 IEEE International Conference on Advanced Intelligent Mechatronics (AIM), pp. 1009–1014 (2017)

  31. Wang, T., Sun, Z., Song, A., et al.: Sliding mode impedance control for dual hand master single slave teleoperation systems. IEEE Trans. Intell. Transp. Syst. 23(12), 25500–25508 (2022)

    Article  Google Scholar 

  32. Pappalardo, C.M., Guida, D.: On the dynamics and control of underactuated nonholonomic mechanical systems and applications to mobile robots. Arch. Appl. Mech. 89(4), 669–698 (2019)

    Article  Google Scholar 

  33. Salehi, M., Vossoughi, G.: Impedance control of flexible base mobile manipulator using singular perturbation method and sliding mode control law. Int. J. Control Autom. Syst. 6(5), 677–688 (2008)

    Google Scholar 

  34. Jafari, A., Monfaredi, R., Rezaei, M., et al.: Sliding mode hybrid impedance control of robot manipulators interacting with unknown environments using VSMRC method. In: ASME International Mechanical Engineering Congress and Exposition, vol. 45202, pp. 1071–1081 (2012)

  35. Cruz-Zavala, E., Moreno, J.A., Fridman, L.M.: Uniform robust exact differentiator. IEEE Trans. Autom. Control 56(11), 2727–2733 (2011)

    Article  MathSciNet  Google Scholar 

  36. Yang, L., Yang, J.: Nonsingular fast terminal sliding mode control for nonlinear dynamical systems. Int. J. Robust Nonlinear Control 21(16), 1865–1879 (2011)

    Article  MathSciNet  Google Scholar 

  37. Zhihong, M., Yu, X.H.: Terminal sliding mode control of MIMO linear systems. IEEE Trans. Circuits Syst. Fundam. Theory Appl. 44(11), 1065–1070 (1997)

    Article  MathSciNet  Google Scholar 

  38. Goldenberg, A.A.: Implementation of force and impedance control in robot manipulators. In: 1988 IEEE International Conference on Robotics and Automation, vol. 3, pp. 1626–1632 (1988)

  39. Liu, X., Ge, S.S., Zhao, F., et al.: Optimized interaction control for robot manipulator interacting with flexible environment. IEEE/ASME Trans. Mechatron. 26(6), 2888–2898 (2020)

    Article  Google Scholar 

  40. Agarwal, D., Thakur, A.D., Thakur, A.: A feedback-based manoeuvre planner for nonprehensile magnetic micromanipulation of large microscopic biological objects. Robot. Auton. Syst. 148, 103941 (2022)

    Article  Google Scholar 

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Funding

This work was supported by National Natural Science Foundation of China (62073075) and Jiangsu Science and Technology Achievements Transformation Fund Project (BA2017075).

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Authors and Affiliations

  1. School of Automation, Southeast University, Nanjing, 210096, Jinagsu, China

    Bo Zhou, Yirong Liu, Fang Fang & Yahui Gan

  2. School of Software, Southeast University, Suzhou, 215123, Jiangsu, China

    Fuyang Song

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  1. Bo Zhou
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Correspondence to Bo Zhou.

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Zhou, B., Song, F., Liu, Y. et al. Robust sliding mode impedance control of manipulators for complex force-controlled operations. Nonlinear Dyn 111, 22267–22281 (2023). https://doi.org/10.1007/s11071-023-09008-2

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