Robust-Adaptive Finite-Time Sliding Mode Control for Flexible Joint Manipulators Facing Unknown Unbounded Disturbances

Subject Areas : International Journal of Smart Electrical Engineering

Mehdi Siahi ¹ , Saedeh Tavoosi ² , Mohammadreza Soltanpour ³ , Ali Moarefian Pour ⁴

1 -
2 -
3 - Department of Electrical Engineering, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran
4 -

Received: 2024-10-31 Accepted : 2025-01-24 Published : 2025-07-12

Keywords: Robot Manipulator, Joint Flexibility, Adaptive Sliding Mode Control, Finite-Time Control, Modeling Uncertainties, External Disturbance, Disturbance Upper Bound ,

Abstract :

This paper addresses the stabilization of flexible joint manipulators (FJMs) under the influence of unknown and unbounded faults, model uncertainties, and external disturbances. To achieve this, the upper bound of model uncertainties and external disturbances is treated as a nonlinear function of the system states with unknown parameters. A novel robust-adaptive finite-time sliding mode controller (RAFSMC) is designed, where the unknown coefficients of the functional upper bound of disturbances are estimated using stable adaptive laws. The RAFSMC enhances the convergence speed of the flexible joints to their desired values, offering a more practical solution for the finite-time control of FJMs, even in scenarios where disturbances may have unbounded amplitudes. Initially, the equations governing the FJM model are segmented into two subsystems, after which the innovative robust-adaptive sliding mode controller is formulated, featuring a third-order finite-time sliding mode surface, a continuous control approach, and stable adaptive laws. The finite-time convergence of the FJM system states to the sliding surface is established, and a new approximation for the sign function is introduced to further reduce chattering. Stability proofs are provided using finite-time Lyapunov theory, and the simulation results, along with comparative analyses presented at the conclusion of the paper, demonstrate the effectiveness of the proposed methodology.

References:

[1] A Azizi, M Naderi Soorki, T Vedadi Moghaddam, A Soleimanizadeh, A New Fractional-Order Adaptive Sliding-Mode Approach for Fast Finite-Time Control of Human Knee Joint Orthosis with Unknown Dynamic, Mathematics 11 (21), 4511, 2023.
[2] Cong, V.D. Visual servoing control of 4-DOF palletizing robotic arm for vision based sorting robot system.Int. J. Interact. Des. Manuf. (IJIDeM)2023, 17, 717–728.
[3] Yi, J.B.; Nasrat, S.; Jo, M.S.; Yi, S.J. A Software Platform for Quadruped Robots with Advanced Manipulation Capabilities. Sensors 2023, 23, 8247.
[4] Su, Y.X.; Zheng, C.H. PID control for global finite-time regulation of robot manipulators.Int. J. Syst. Sci. 2017, 48, 547–558.
[5] H. Li, B. Yang, S. Jiang and J. Luo, "Robot Manipulator Trajectory Tracking with Uncertainties Based on Adaptive Sliding Control," 2023 IEEE International Conference on Unmanned Systems (ICUS), Hefei, China, 2023, pp. 1434-1439, 2023.
[6] M. Zhang, Z. Zhang and M. Sun, "Adaptive Tracking Control of Uncertain Robotic Manipulators," in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 71, no. 5, pp. 2734-2738, May 2024.
[7] H. Wang, W. Peng, X. Tan, J. Sun, X. Tang and I. -M. Chen, "Robust Output Feedback Tracking Control for Flexible-Joint Robots Based on CTSMC Technique," in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 6, pp. 1982-1986, June 2021.
[8] J. Kim and E. A. Croft, ``Full-state tracking control for flexible joint robots with singular perturbation techniques,'' IEEE Trans. Control Syst. Technol., vol. 27, no. 1, pp. 63_73, Jan. 2019.
[9] H. Wang, Y. Zhang, Z. Zhao, X. Tang, J. Yang, I.-M. Chen, Finite-time disturbance observer-based trajectory tracking control for flexible-joint robots, Nonlinear Dynamics 106 (1) (2021) 459–471.
[10] L. Le-Tien and A. Albu-Schäffer, ``Robust adaptive tracking control based on state feedback controller with integrator terms for elastic joint robots with uncertain parameters,'' IEEE Trans. Control Syst. Technol., vol. 26, no. 6, pp. 2259_2267, Nov. 2018.
[11] B. Zhan, M. Jin, J.Liu, “Extended-state-observer-based adaptive control of flexible-joint space manipulators with system uncertainties,” Advances in Space Research, Vol. 69, no. 8, pp. 3088-3102, 2022.
[12] W. Chang, Y. Li and S. Tong, "Adaptive Fuzzy Backstepping Tracking Control for Flexible Robotic Manipulator," in IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 12, pp. 1923-1930, December 2021.
[13] W. Sun, S.-F. Su, J. Xia, V.-T. Nguyen, Adaptive fuzzy tracking control of flexible-joint robots with full-state constraints, IEEE transactions on Systems, Man, and Cybernetics: Systems 49 (11) (2018) 2201–2209.
[14] H. Gao, W. He, C. Zhou, C. Sun, Neural network control of a two-link flexible robotic manipulator using assumed mode method, IEEE Transactions on Industrial Informatics 15 (2) (2018) 755–765.
[15] Y. Pan, X. Li, H. Yu, Efficient pid tracking control of robotic manipulators driven by compliant actuators, IEEE Transactions on Control Systems Technology 27 (2) (2019) 915–922.
[16] Ak, A. Sliding Mode Controller Design Using Fuzzy Sliding Surface for Flexible Joint Manipulator. IETE Journal of Research, 68(1), 760–767. 2021.
[17] Gao Y, Lu H. Sliding Mode Control of Flexible Articulated Manipulator Based on Robust Observer. Jan 4, 2440770. Retraction in: Computer Intelligent Neuroscience. 2022.
[18] Azeez, M.I., Abdelhaleem, A.M.M., Elnaggar, S. et al. Optimized sliding mode controller for trajectory tracking of flexible joints three-link manipulator with noise in input and output. Sci Rep 13, 12518, 2023.
[19] Majidi B., Ikbel B. CH. A., Zie H., sliding mode controller design: stability analysis and tracking control for flexible joint manipulator. rrst-ee. 2021;66(3):161-167. Accessed August 17, 2024.
[20] Shixuan Zhang, Wan-Cheng Wang, Adaptive sliding mode robust control of manipulator driven by tendon-sheath based on HJI theory, Measurement and Control, 55, 684 – 702, 2022.
[21] Kamal Rsetam, Mohammad Al-Rawi, Zhenwei Cao, Zhihong Man, Sliding mode control based on high-order extended state observer for flexible joint robot under time-varying disturbance, AIP Conf. Proc. 2651, 05001, 2023.
[22] Cheng, X.; Liu, H.; Lu, W. Chattering-Suppressed Sliding Mode Control for Flexible-Joint Robot Manipulators. Actuators 2021, 10, 288, 2021.
[23] S. zaare, M. R. Soltanpour, M. Moattari,” Voltage based sliding mode control of flexible joint robot manipulators in presence of uncertainties,” Robotics and Autonomous Systems, vol. 118, pp. 204-219, 2019.
[24] K. Rsetam, Z. Cao, Z. Man, M. Mitrevska, Optimal second order integral sliding mode control for a flex-ible joint robot manipulator, in: IECON 2017-43rd Annual Conference of the IEEE Industrial Electronics Society, IEEE, 2017, pp. 3069–3074, 2017.
[25] H. Du, G. Wen, Y. Cheng, W. Lu, T. Huang, Designing discrete-time sliding mode controller with mis-matched disturbances compensation, IEEE Transactions on Industrial Informatics 16 (6), 4109–4118, 2019.
[26] A.-C. Huang, Y.-C. Chen, Adaptive sliding control for single-link flexible-joint robot with mismatched un-certainties, IEEE Transactions on Control Systems Technology 12 (5), 770–775, 2004.
[27] K. A. Rsetam, Z. Cao, Z. Man, Cascaded extended state observer based sliding mode control for underactu-ated flexible joint robot, IEEE Transactions on Industrial Electronics, 2019.
[28] S. Chávez-Vázquez, J. E. Lavín-Delgado, J. F. Gómez-Aguilar, J. R. Razo-Hernández, S. Etemad, S. Rezapour, “Trajectory tracking of Stanford robot manipulator by fractional-order sliding mode control,” Applied Mathematical Modelling, Vol. 120, pp. 436-462, 2023
[29] Z. Yan, X. Lai, Q. Meng, J. She, M. Wu, “Time-varying disturbance-observer-based tracking control of uncertain flexible-joint manipulator,” Control Engineering Practice, Vol. 139, pp. 105624, 2023.
[30] L. Liu, W. Yao, Y. Guo, “Prescribed performance tracking control of a free-flying flexible-joint space robot with disturbances under input saturation,” Journal of the Franklin Institute, Vol. 358, no. 9, pp. 4571-4601, 2021.
[31] M. Ramírez-Neria, G. Ochoa-Ortega, N. Lozada-Castillo, M. A. Trujano-Cabrera, J. P. Campos-López, and A. Luviano-Juárez, ``On the robust trajectory tracking task for flexible-joint robotic arm with unmodeled dynamics,'' IEEE Access, vol. 4, pp. 7816_7827, 2016.
[32] D. Shang, X. Li, M. Yin, F. Li,”Dynamic modeling and fuzzy adaptive control strategy for space flexible robotic arm considering joint flexibility based on improved sliding mode controller,” Advances in Space Research, Vol. 70, no. 11, pp. 3520-3539, 2022.
[33] S. Zhang, Y. Wu, X. He and J. Wang, "Neural Network-Based Cooperative Trajectory Tracking Control for a Mobile Dual Flexible Manipulator," in IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 9, pp. 6545-6556, Sept. 2023.
[34] K. Rsetam, Z. Cao and Z. Man, Design of Robust Terminal Sliding Mode Control for Underactuated Flexible Joint Robot," in IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 7, pp. 4272-4285, July 2022,
[35] M. Hong, X. Gu, L. Liu, Y. Guo, “Finite time extended state observer based nonsingular fast terminal sliding mode control of flexible-joint manipulators with unknown disturbance,” Journal of the Franklin Institute, vol. 360, no. 1, pp.18-37, 2023.
[36] Jing C, Zhang H, Liu Y, Zhang J. Adaptive Super-Twisting Sliding Mode Control for Robot Manipulators with Input Saturation. Sensors. 2024; 24(9), 2783, 2024.
[37] Khooban, M.H., Niknam, T., Blaabjerg, F., Dehghani,M.: Free chattering hybrid sliding mode control for a class of non-linear systems: electric vehicles as a case study. IET Sci. Meas. Technol. Vol. 10, no. 7, pp. 776–785, 2016.
[38] Shokoohinia, M.R., Fateh, M.M.: Robust dynamic sliding mode control of robot manipulators using the Fourier series expansion. Trans. Inst. Meas. Control 1–8, 2018.
[39] S. Zaare, S., Soltanpour, M. R., Moattari, Adaptive sliding mode control of n flexible-joint robot manipulators in the presence of structured and unstructured uncertainties,” Multibody System Dynamics 47, pp. 397-434, 2019.