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Recursive terminal sliding mode based control of robot manipulators with a novel sliding mode disturbance observer

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Abstract

This paper investigates the high-precision sliding mode based tracking control of robot manipulators with uncertain dynamics and external disturbances. Different from most currently used fast nonsingular terminal sliding mode surfaces (FNTSMs) which use linear sliding mode (LSM) to avoid singularity, a new recursive terminal sliding mode surface (RTSM) is firstly constructed with a recursive structure to avoid the singularity problem in this paper. The RTSM can improve convergence precision and speed near the equilibrium point compared with FNTSMs. Then a sliding mode based controller has been designed to stabilize the closed-loop system. To cope with model uncertainties, frictions and external disturbances, a novel adaptive sliding mode disturbance observer (ASMDO) has been constructed, which can estimate lumped uncertainties and feed them to the controller to achieve disturbance-rejection control. Compared with traditional disturbance observer with asymptotic stability, the observation error of ASMDO can be driven into a sufficiently small set centered on zero within a predefined fixed time, which means fast observation speed and high observation accuracy. The upper bounds of uncertainties and their derivatives are not needed in observer design. Abundant simulations and experiments also verified the effectiveness and superior properties of the proposed scheme.

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References

  1. Baek, S., Baek, J.C., Kwon, W.Y., Han, S.: An adaptive model uncertainty estimator using delayed state-based model-free control and its application to robot manipulators. IEEE ASME Trans. Mechatron. 27(6), 4573–4584 (2022)

  2. Spong, M.W., Ortega, R.: On adaptive inverse dynamics control of rigid robots. IEEE Trans. Autom. Control 35(1), 92–95 (1990)

    Article  MathSciNet  Google Scholar 

  3. Giusti, A., Malzahn, J., Tsagarakis, N.G., Althoff, M.: On the combined inverse-dynamics/passivity-based control of elastic-joint robots. IEEE Trans. Robot. 34(6), 1461–1471 (2018)

    Article  Google Scholar 

  4. Jin, M., Lee, J., Chang, P.H., Choi, C.: Practical nonsingular terminal sliding-mode control of robot manipulators for high-accuracy tracking control. IEEE Trans. Ind. Electron. 56(9), 3593–3601 (2009)

    Article  Google Scholar 

  5. Khan, R.F.A., Rsetam, K., Cao, Z.W., Man, Z.H.: Singular perturbation-based adaptive integral sliding mode control for flexible joint robots. IEEE Trans. Ind. Electron. 70(10), 10516–10525 (2023)

    Article  Google Scholar 

  6. Van, M., Mavrovouniotis, M., Ge, S.S.: An adaptive backstepping nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators. IEEE Trans. Syst. Man Cybern. Syst. 49(7), 1448–1458 (2019)

  7. Jie, W., Yudong, Z., Yulong, B., Kim, H.H., Lee, M.C.: Trajectory tracking control using fractional-order terminal sliding mode control with sliding perturbation observer for a 7-DOF robot manipulator. IEEE ASME Trans. Mechatron. 25(4), 1886–1893 (2020)

    Article  Google Scholar 

  8. Wang, Y.C., Leibold, M., Lee, J., Ye, W.Y., Xie, J., Buss, M.: Incremental model predictive control exploiting time-delay estimation for a robot manipulator. IEEE Trans. Control Syst. Technol. 30(6), 2285–2300 (2022)

    Article  Google Scholar 

  9. Dai, L., Yu, Y.T., Zhai, D.H., Huang, T., Xia, Y.Q.: Robust model predictive tracking control for robot manipulators with disturbances. IEEE Trans. Ind. Electron. 68(5), 4288–4297 (2021)

    Article  Google Scholar 

  10. Arteaga-Peréz, M.A., Pliego-Jiménez, J., Romero, J.G.: Experimental results on the robust and adaptive control of robot manipulators without velocity measurements. IEEE Trans. Control Syst. Technol. 28(6), 2770–2773 (2020)

  11. Tomei, P.: Robust adaptive friction compensation for tracking control of robot manipulators. IEEE Trans. Autom. Control 45(11), 2164–2169 (2000)

    Article  MathSciNet  Google Scholar 

  12. Zhang, F., Dawson, D.M., de Queiroz, M.S., Dixon, W.E.: Global adaptive output feedback tracking control of robot manipulators. IEEE Trans. Autom. Control 45(6), 1203–1208 (2000)

    Article  MathSciNet  Google Scholar 

  13. Vadim, I.U.: Variable structure systems with sliding modes. IEEE Trans. Autom. Control 22(2), 212–222 (1977)

    Article  MathSciNet  Google Scholar 

  14. Incremona, G.P., Rubagotti, M., Ferrara, A.: Sliding mode control of constrained nonlinear systems. IEEE Trans. Autom. Control 62(6), 2965–2972 (2017)

  15. Lu, P., Sandy, T., Buchli, J.: Adaptive unscented Kalman filter-based disturbance rejection with application to high precision hydraulic robotic control. In: 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4365–4372 (2019)

  16. Gandikota, G., Das, D.K.: Disturbance observer-based adaptive boundary layer sliding mode controller for a type of nonlinear multiple-input multiple-output system. Int. J. Robust Nonlinear Control 29(4), 5886–5912 (2019)

    Article  MathSciNet  Google Scholar 

  17. Boiko, I., Fridman, L.: Analysis of chattering in continuous sliding-mode controllers. IEEE Trans. Autom. Control 50(9), 1442–1446 (2005)

    Article  MathSciNet  Google Scholar 

  18. Van, M., Ge, S.S.: Adaptive fuzzy integral sliding-mode control for robust fault-tolerant control of robot manipulators with disturbance observer. IEEE Trans. Fuzzy Syst. 29(5), 1284–1296 (2021)

    Article  Google Scholar 

  19. Hung, J.Y., Gao, W., Hung, J.C.: Variable structure control: a survey. IEEE Trans. Ind. Electron. 40(1), 2–22 (1993)

    Article  Google Scholar 

  20. Chang, Y.T.: Adaptive sliding mode control of multi-input nonlinear systems with perturbations to achieve asymptotical stability. IEEE Trans. Autom. Control 54(12), 2863–2869 (2009)

    Article  MathSciNet  Google Scholar 

  21. Baek, J., Jin, M.L., Han, S.: A new adaptive sliding-mode control scheme for application to robot manipulators. IEEE Trans. Ind. Electron. 63(6), 3628–3637 (2016)

    Article  Google Scholar 

  22. Lavin-Delgado, J.E., Chavez-Vazquez, S., Gomez-Aguilar, J.F., Alassafi, M.O., Alsaadi, F.E., Ahmad, A.M.: Intelligent neural integral sliding-mode controller for a space robotic manipulator mounted on a free-floating satellite. Adv. Space Res. 71(9), 3734–3747 (2022)

    Article  Google Scholar 

  23. Chavez-Vazquez, S., Lavin-Delgado, J.E., Gomez-Aguilar, J.F., Razo-Hernandez, J.R., Etemad, S., Rezapour, S.: Trajectory tracking of Stanford robot manipulator by fractional-order sliding mode control. Appl. Math. Model. 120, 436–462 (2023)

    Article  MathSciNet  Google Scholar 

  24. Hou, Q.K., Ding, S.H., Yu, X.H.: Composite super-twisting sliding mode control design for pmsm speed regulation problem based on a novel disturbance observer. IEEE Trans. Energy Convers. 36(4), 2591–2599 (2021)

    Article  Google Scholar 

  25. Pupadubsin, R., Chayopitak, N., Taylor, D.G., Nulek, N., Kachapornkul, S., Jitkreeyarn, P., Somsiri, P., Tungpimolrut, K.: Adaptive integral sliding-mode position control of a coupled-phase linear variable reluctance motor for high-precision applications. IEEE Trans. Ind. Appl. 48(4), 1353–1363 (2012)

    Article  Google Scholar 

  26. Wang, T.Q., Wang, B., Yu, Y., Xu, D.G.: Discrete sliding-mode-based MRAS for speed-sensorless induction motor drives in the high-speed range. IEEE Trans. Power Electron. 38(5), 5777–5790 (2023)

    Article  Google Scholar 

  27. Mi, Y., Song, Y.Y., Fu, Y., Wang, C.S.: The adaptive sliding mode reactive power control strategy for wind-diesel power system based on sliding mode observer. IEEE Trans. Sustain. Energy 11(4), 2241–2251 (2020)

  28. Lv, Y.L., Zhang, Y.C., Liu, Q., Wang, S., Shi, D.L.: Sliding mode control of two-parameter fourth-order chaos model of power system. IEEE Trans. Circuits Syst. II Express Briefs 69(12), 4849–4853 (2022)

  29. Fuhui, G., Pingli, L.: Fast self-adapting high-order sliding mode control for a class of uncertain nonlinear systems. J. Syst. Eng. Electron. 32(3), 690–699 (2021)

    Article  Google Scholar 

  30. Yong, F., Yu, X., Man, Z.: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38(12), 2159–2167 (2002)

    Article  MathSciNet  Google Scholar 

  31. Ding, S.H., Liu, L., Park, J.H.: A novel adaptive nonsingular terminal sliding mode controller design and its application to active front steering system. Int. J. Robust Nonlinear Control 29(12), 4250–4269 (2019)

    Article  MathSciNet  Google Scholar 

  32. Wang, Y.Y., Li, S.Z., Wang, D., Ju, F., Chen, B., Wu, H.T.: Adaptive time-delay control for cable-driven manipulators with enhanced nonsingular fast terminal sliding mode. IEEE Trans. Ind. Electron. 68(3), 2356–2367 (2021)

    Article  Google Scholar 

  33. Liu, Z., Zhang, O.Y., Gao, Y.B., Zhao, Y., Sun, Y.Z., Liu, J.X.: Adaptive neural network-based fixed-time control for trajectory tracking of robotic systems. IEEE Trans. Circuits Syst. II Express Briefs 70(1), 241–245 (2023)

    Google Scholar 

  34. Zhang, Y., Tang, S., Guo, J.: Adaptive terminal angle constraint interception against maneuvering targets with fast fixed-time convergence. Int. J. Robust Nonlinear Control 28, 2996–3014 (2018)

    Article  MathSciNet  Google Scholar 

  35. Yaoyao, W., Kangwu, Z., Bai, C., Maolin, J.: Model-free continuous nonsingular fast terminal sliding mode control for cable-driven manipulators. ISA Trans. 98, 483–495 (2020)

    Article  Google Scholar 

  36. Zou, A.M., Kumar, K.D., Hou, Z.G., Liu, X.: Finite-time attitude tracking control for spacecraft using terminal sliding mode and chebyshev neural network. IEEE Trans. Syst. Man Cybern. Part B Cybern. 41(4), 950–963 (2011)

    Article  Google Scholar 

  37. Na, J., Jing, B.R., Huang, Y.B., Gao, G.B., Zhang, C.: Unknown system dynamics estimator for motion control of nonlinear robotic systems. IEEE Trans. Ind. Electron. 67(5), 3850–3859 (2020)

    Article  Google Scholar 

  38. Ren, B.B., Zhong, Q.C., Chen, J.H.: Robust control for a class of nonaffine nonlinear systems based on the uncertainty and disturbance estimator. IEEE Trans. Ind. Electron. 62(9), 5881–5888 (2015)

    Article  Google Scholar 

  39. Xiao, B., Yang, X.B., Huo, X.: A novel disturbance estimation scheme for formation control of ocean surface vessels. IEEE Trans. Ind. Electron. 64(6), 4994–5003 (2017)

    Article  Google Scholar 

  40. Li, B., Gong, W.Q., Yang, Y.S., Xiao, B., Ran, D.C.: Appointed fixed time observer-based sliding mode control for a quadrotor UAV under external disturbances. IEEE Trans. Aerosp. Electron. Syst. 58(1), 290–303 (2022)

    Article  Google Scholar 

  41. Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57(8), 2106–2110 (2012)

  42. Parsegov, S., Polyakov, A., Shcherbakov, P.: Nonlinear fixed-time control protocol for uniform allocation of agents on a segment. In: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp. 7732–7737 (2012)

  43. Shen, Y., Huang, Y.: Uniformly observable and globally Lipschitzian nonlinear systems admit global finite-time observers. IEEE Trans. Autom. Control 54(11), 2621–2625 (2009)

  44. Zuo, Z.: Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica 54, 305–309 (2015)

    Article  MathSciNet  Google Scholar 

  45. Sun, L., Liu, Y.J.: Extended state observer augmented finite-time trajectory tracking control of uncertain mechanical systems. Mech. Syst. Signal Proc. 139, 106374 (2019)

    Article  Google Scholar 

  46. Grimm, W.M.: Robot non-linearity bounds evaluation techniques for robust control. Int. J. Adapt. Control Signal Process. 4(6), 501–522 (1990)

  47. Hu, Y.S., Yan, H.C., Zhang, H., Wang, M., Zeng, L.: Robust adaptive fixed-time sliding-mode control for uncertain robotic systems with input saturation. IEEE Trans. Cybern. 53(4), 2636–2646 (2023)

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Funding

This work was supported by The Liaoning Province Basic Research Program under Grant 2022JH2/101300202; The Natural Science Foundation of China under Grant 62273081.

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Authors and Affiliations

  1. Faculty of Robot Science and Engineering, Northeastern University, Shenyang, China

    Tangzhong Song, Lijin Fang & Hesong Shen

  2. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China

    Yue Zhang

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  1. Tangzhong Song
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  2. Lijin Fang
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Correspondence to Lijin Fang.

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Song, T., Fang, L., Zhang, Y. et al. Recursive terminal sliding mode based control of robot manipulators with a novel sliding mode disturbance observer. Nonlinear Dyn 112, 1105–1121 (2024). https://doi.org/10.1007/s11071-023-09136-9

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  • DOI: https://doi.org/10.1007/s11071-023-09136-9

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