Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-28T19:58:30.400Z Has data issue: false hasContentIssue false

Integrated sliding mode control with input restriction, output feedback and repetitive learning for space robot with flexible-base, flexible-link and flexible-joint

Published online by Cambridge University Press:  10 October 2022

Xiaodong Fu
School of Energy and Mechanical Engineering, Jiangxi University of Science and Technology, Nanchang, 330013 Jiangxi, China School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350108 Fujian, China
Haiping Ai*
School of Energy and Mechanical Engineering, Jiangxi University of Science and Technology, Nanchang, 330013 Jiangxi, China School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350108 Fujian, China
Li Chen
School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350108 Fujian, China
*Corresponding author. E-mail:


In the control of space robots, flexible vibrations exist in the base, links and joints. When building a motion control scheme, the following three aspects should be considered: (1) the complexity in dynamic modeling; (2) the low accuracy of motion control and (3) the simultaneous suppression of multiple flexible vibrations. In this paper, we propose a motion vibration integrated saturation control scheme. First, the dynamic model of space robot with flexible-base, flexible-link and flexible-joint is established according to the assumed modes method and Lagrange equation. Second, singular perturbation theory is used to decompose the model into two subsystems: a slow subsystem containing the rigid motions of base and joints as well as the vibration of links, and a fast subsystem containing vibrations of base and joints. Third, an integrated sliding mode control with input restriction, output feedback and repetitive learning (ISMC-IOR) is designed, which can track the desired trajectories of base and joints with −3 orders of magnitude accuracy, while suppressing the multiple flexible vibrations of base, links and joints 50%–80% and 37% performance improvement over ISMC-IOR-NV were achieved. Finally, the algorithm is verified by simulations.

Research Article
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Doyle, R., Kubota, T., Picard, M., Sommer, B., Ueno, H., Visentin, G. and Volpe, R., “Recent research and development activities on space robotics and AI,” Adv. Robot. 35(21), 12441264 (2021).CrossRefGoogle Scholar
Li, H. Q., Liu, X. F., Guo, S. J. and Cai, G. P., “Deployment dynamics of large-scale flexible solar arrays,” Proc. Inst. Mech. Eng. K J. Multi Body Dyn. 230(2), 147158 (2016).Google Scholar
Wie, B., Hu, A. and Singh, R., “Multibody interaction effects on space station attitude-control and momentum management,” J. Guid. Control Dyn. 13(6), 993999 (1990).CrossRefGoogle Scholar
Giordano, A. M., Calzolari, D., De Stefano, M., Mishra, H., Ott, C. and Albu-Schäffer, A., “Compliant floating-base control of space robots,” IEEE Robot. Autom. Lett. 6(4), 74857492 (2021).CrossRefGoogle Scholar
Ai, H. P., Zhu, A. and Chen, L., “Buffer compliance control of space robots capturing a non-cooperative spacecraft based on reinforcement learning,” Appl. Sci. (Switzerland) 11(5), 5783 (2021).Google Scholar
Singh, S. N. and Schy, A. A., “Robust Torque Control of an Elastic Robotic Arm Based on Invertibility and Feedback Stabilization,” In: Proceedings of the 24th IEEE Conference on Decision and Control (Cat. No.85CH2245-9), vol. 2 (1985) pp. 13171322.Google Scholar
Liu, L. X., Yao, W. and Guo, Y., “Prescribed performance tracking control of a free-flying flexible-joint space robot with disturbances under input saturation,” J. Franklin Inst. 358(9), 45714601 (2021).CrossRefGoogle Scholar
Yang, X. X., Ge, S. S. and Liu, J. K., “Dynamics and noncollocated model-free position control for a space robot with multi-link flexible manipulators,” Asian J. Control 21(2), 714724 (2019).CrossRefGoogle Scholar
Hu, Y., Dian, S. Y., Guo, R., Li, S. C. and Zhao, T., “Observer-based dynamic surface control for flexible-joint manipulator system with input saturation and unknown disturbance using type-2 fuzzy neural network,” Neurocomputing 436(2), 162173 (2021).CrossRefGoogle Scholar
Bégin, M. A., Poon, R. and Ian, H., “Streamlined tuning procedure for stable PID control of flexible-base manipulators,” IEEE Robot. Autom. Lett. 6(4), 74137420 (2021).CrossRefGoogle Scholar
Beck, F., Garofalo, G. and Ott, C., “Vibration Control for Manipulators on a Translationally Flexible Base,” In: Proceedings-IEEE International Conference on Robotics and Automation (2019) pp. 44514457.Google Scholar
Mori, R. and Murakami, T., “A Fusion Control of Impedance and Vibration Suppression for a Manipulator with Flexible Base,” In: Proceedings of the IEEE International Conference on Industrial Technology (2019) pp. 4247.Google Scholar
Yu, X. Y., “Hybrid-trajectory based terminal sliding mode control of a flexible space manipulator with an elastic base,” Robotica 38(3), 550563 (2020).CrossRefGoogle Scholar
Korayem, M. H., Dehkordi, S. F. and Mehrjooee, O., “Nonlinear analysis of open-chain flexible manipulator with time-dependent structure,” Adv. Space Res. 69(2), 10271049 (2022).CrossRefGoogle Scholar
Korayem, M. H., Dehkordi, S. F., Mojarradi, M. and Monfared, P., “Analytical and experimental investigation of the dynamic behavior of a revolute-prismatic manipulator with N flexible links and hubs,” Int. J. Adv. Manuf. Technol. 103(5-8), 22352256 (2019).CrossRefGoogle Scholar
Aghajari, M., Dehkordi, S. F. and Korayem, M. H., “Nonlinear dynamic analysis of the extended telescopic joints manipulator with flexible links,” Arab. J. Sci. Eng. 46(8), 79097928 (2021).CrossRefGoogle Scholar
Zhang, Q., Liu, X. F. and Cai, G. P., “Dynamics and control of a flexible‐link flexible‐joint space robot with joint friction,” Int. J. Aeronaut. Space Sci. 22(2), 415432 (2021).CrossRefGoogle Scholar
Xie, L. M., Yu, X. Y. and Chen, L., “Robust fuzzy sliding mode control and vibration suppression of free-floating flexible-link and flexible-joints space manipulator with external interference and uncertain parameter,” Robotica 40(4), 9971019 (2021).CrossRefGoogle Scholar
Sands, T., “Flattening the curve of flexible space robotics,” Appl. Sci. Basel 12(6), 136 (2022).Google Scholar
Sands, T., “Optimization provenance of whiplash compensation for flexible space robotics,” Aerospace 6(9), 118 (2019).CrossRefGoogle Scholar
Jia, S. Y. and Shan, J. J., “Finite-time trajectory tracking control of space manipulator under actuator saturation,” IEEE Trans. Ind. Electron. 67(3), 20862096 (2020).CrossRefGoogle Scholar
Q., L. I., Yuan, J. P. and Sun, C., “Robust fault-tolerant saturated control for spacecraft proximity operations with actuator saturation and faults,” Adv. Space Res. 63(5), 15411553 (2019).Google Scholar
Mizumoto, I., Fujii, S. and Mita, H., “Output feedback-based output tracking control with adaptive output predictive feedforward for multiple-input-multiple-output systems,” Ind. Eng. Chem. Res. 58(26), 1138211391 (2019).CrossRefGoogle Scholar
Yan, Q. Z., Cai, J. P., Li, Z. F. and Yang, Q. Y., “Multi-period repetitive control for nonparametric uncertain systems,” IEEE Access 7, 147849147856 (2019). doi: 10.1109/ACCESS.2019.2946103.CrossRefGoogle Scholar
Fedele, G., “A fractional-order repetitive controller for periodic disturbance rejection,” IEEE Trans. Autom. Control 63(5), 14261433 (2018).CrossRefGoogle Scholar
Liu, Y., Guo, F., He, X. Y. and Hui, Q., “Boundary control for an axially moving system with input restriction based on disturbance observers,” IEEE Trans. Syst. Man Cybern. Syst. 49(11), 22422253 (2019).CrossRefGoogle Scholar
Zhang, D. W. and Liu, G. P., “Coordinated control of quasilinear multiagent systems via output feedback predictive control,” ISA Trans. 128(Pt A), 5870 (2021).CrossRefGoogle ScholarPubMed
Califano, F., Bin, M., Macchelli, A. and Melchiorri, C., “Stability analysis of nonlinear repetitive control schemes,” IEEE Control Syst. Lett. 2(4), 773778 (2018).CrossRefGoogle Scholar
Spong, M., “Modeling and control of elastic joint robots,” J. Dyn. Syst. Meas. Control 109(4), 310319 (1987).CrossRefGoogle Scholar
Kelly, R., Santibanez, V. and Loria, A., Control of Robot Manipulators in Joint Space (Springer, London, 2005).Google Scholar
Khalil, H. K., Nonlinear Systems (Publishing House of Electronics Industry, Upper Saddle River, 2007).Google Scholar