Document Type : Research Articles
Authors
1 Department of Electrical and Computer Engineering, Babol Noshirvani University of Technology, Babol, Iran
2 Department of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood, Iran.
Abstract
This paper presents an innovative adaptive sliding mode controller with disturbance rejection for robotic manipulators. The proposed approach employs orthogonal functions-based estimation to handle system uncertainties, while an adaptive mechanism is introduced to estimate the unknown upper bounds of external disturbances. Moreover, the dynamics of the robot actuators, namely the motors, are explicitly considered in the control law design. Three adaptive laws are proposed in this work. The first addresses the estimation of the parameters of orthogonal functions, the second deals with the approximation error, and the third concerns the estimation of the upper bound of external disturbances. Furthermore, a robust control term is proposed to compensate for the approximation error. Stability of the closed-loop system is ensured using Lyapunov theory. The performance of the proposed controller is evaluated through simulations on a SCARA robotic manipulator and compared with conventional and dynamic sliding mode control schemes in terms of tracking accuracy, control effort, and disturbance rejection.
Keywords
- Uncertainty Estimation
- Orthogonal Functions
- Adaptive Sliding Mode Control
- Trajectory Tracking
- Robot Manipulators
Main Subjects
[1] K. Shao, J. Zheng, and M. Fu, "Review on the developments of sliding function and adaptive gain in sliding mode control," Journal of Automation and Intelligence, 2025/06/18/ 2025, doi: 10.1016/j.jai.2025.06.001.
[2] D. Yao, H. Li, and Y. Shi, "Adaptive Event-Triggered Sliding-Mode Control for Consensus Tracking of Nonlinear Multiagent Systems With Unknown Perturbations," IEEE Transactions on Cybernetics, vol. 53, pp. 2672-2684, 2023, doi: 10.1109/TCYB.2022.3172127.
[3] Y. Yin, Z. Xu, Y. Wei, W. Jiang, D. Yao, and Z. Dong, "Model-free sliding mode control for path following in autonomous vehicle," Journal of the Franklin Institute, vol. 362, p. 107806, 2025/08/01/ 2025, doi: 10.1016/j.jfranklin.2025.107806.
[4] Q. Zhang, J. Hu, and J. Cao, "Fixed-time synchronization of nonlinear coupling MNNs with time delay via aperiodically intermittent sliding mode control," Communications in Nonlinear Science and Numerical Simulation, vol. 150, p. 108995, 2025/11/01/ 2025, doi: 10.1016/j.cnsns.2025.108995.
[5] N. Zhu and W.-F. Xie, "Distributed adaptive sliding mode control with deep recurrent neural network for cooperative robotic system in automated fiber placement," ISA Transactions, 2025/05/17/ 2025, doi: 10.1016/j.isatra.2025.05.021.
[6] R. Gholipour, A. Khosravi, and H. Mojallali, "Multiobjective optimal backstepping controller design for chaos control in a rod-type plasma torch system using Bees algorithm," Applied Mathematical Modelling, vol. 39, pp. 4432-4444, 2015/08/01/ 2015, doi: 10.1016/j.apm.2014.12.049.
[7] A. taheri and N. Asgari, "Sliding Mode Control of LLC Resonant DC-DC Converter for Wide output voltage Range in Battery Charging Applications," International Journal of Industrial Electronics Control and Optimization, vol. 2, pp. 127-136, 2019, 10.22111/ieco.2018.27333.1096.
[8] A. Rezaie, "Sliding Mode Control for Chaotic Systems with Unknown Uncertainties," International Journal of Industrial Electronics Control and Optimization, vol. 7, pp. 53-60, 2024, 10.22111/ieco.2024.47439.1518.
[9] L. Wu, J. Liu, S. Vazquez, and S. K. Mazumder, "Sliding Mode Control in Power Converters and Drives: A Review," IEEE/CAA Journal of Automatica Sinica, vol. 9, pp. 392- 406, 2022, doi: 10.1109/JAS.2021.1004380.
[10] M. Van and S. S. Ge, "Adaptive Fuzzy Integral SlidingMode Control for Robust Fault-Tolerant Control of Robot Manipulators With Disturbance Observer," IEEE Transactions on Fuzzy Systems, vol. 29, pp. 1284-1296, 2021, doi: 10.1109/TFUZZ.2020.2973955.
[11] Z. Yan, M. Wang, and J. Xu, "Robust adaptive sliding mode control of underactuated autonomous underwater vehicles with uncertain dynamics," Ocean Engineering, vol. 173, pp. 802-809, 2019/02/01/ 2019, doi: 10.1016/j.oceaneng.2019.01.008.
[12] J. Guerrero, A. Chemori, V. Creuze, and J. Torres, "Improved Adaptive High-Order Sliding Mode-Based Control for Trajectory Tracking of Autonomous Underwater Vehicles," IEEE Journal of Oceanic Engineering, vol. 49, pp. 1337-1349, 2024, doi: 10.1109/JOE.2024.3381391.
[13] C. Yang, Y. Liu, and H. Gao, "Reliability-Constrained Uncertain Spacecraft Sliding Mode Attitude Tracking Control With Interval Parameters," IEEE Transactions on Aerospace and Electronic Systems, vol. 61, pp. 6589-6600, 2025, doi: 10.1109/TAES.2025.3529798.
[14] M. Ä°nci̇ and N. S. Özbek, "A novel predictive current sliding mode control for improving the performance efficiency of fuel cell vehicle-to-load (V2L) system with boost converter," International Journal of Hydrogen Energy, vol. 138, pp. 973-984, 2025/06/16/ 2025, doi: 10.1016/j.ijhydene.2025.05.203.
[15] X. Shen, G. Liu, J. Liu, Y. Gao, J. I. Leon, L. Wu, et al., "Fixed-Time Sliding Mode Control for NPC Converters With Improved Disturbance Rejection Performance," IEEE Transactions on Industrial Informatics, vol. 21, pp. 4476-4487, 2025, doi: 10.1109/TII.2025.3540481.
[16] H. Rabiee, M. Ataei, and M. Ekramian, "Continuous nonsingular terminal sliding mode control based on adaptive sliding mode disturbance observer for uncertain nonlinear systems," Automatica, vol. 109, p. 108515, 2019/11/01/ 2019, doi: 10.1016/j.automatica.2019.108515.
[17] S. Vaidyanathan and C.-H. Lien, Applications of sliding mode control in science and engineering: Springer, 2017, doi: 10.1007/978-3-319-55598-0.
[18] T. Jin and X. Han, "Robotic arms in precision agriculture: A comprehensive review of the technologies, applications, challenges, and future prospects," Computers and Electronics in Agriculture, vol. 221, p. 108938, 2024/06/01/ 2024, doi:10.1016/j.compag.2024.108938.
[19] Y. Zheng, Y. Wang, and J. Liu, "Research on structure optimization and motion characteristics of wearable medical robotics based on Improved Particle Swarm Optimization Algorithm," Future Generation Computer Systems, vol. 129, pp. 187-198, 2022/04/01/ 2022, doi: 10.1016/j.future.2021.11.021.
[20] J. Liu, "Application of entertainment and fitness robots based on game interaction in sports training data analysis," Entertainment Computing, vol. 52, p. 100837, 2025/01/01/2025, doi: 10.1016/j.entcom.2024.100837.
[21] C. Xiaochun, "Research on entertainment robots based on artificial intelligence interaction for human posture recognition and sports activity monitoring," Entertainment Computing, vol. 52, p. 100761, 2025/01/01/ 2025, doi: 10.1016/j.entcom.2024.100761.
[22] L. Zhang, M. Lv, H. Fan, X. Zhao, T. Yang, and K. Li, "Underwater reconfigurable robot based on modular piezoelectric jet unit," Sensors and Actuators A: Physical, vol. 388, p. 116526, 2025/07/01/ 2025, doi: 10.1016/j.sna.2025.116526.
[23] S. Xu, T. Chen, H. Wen, and D. Jin, "Predefined-Time Tracking Control of a Free-Flying Space Robot on SE(3)," IEEE Transactions on Aerospace and Electronic Systems, vol. 60, pp. 5906-5919, 2024, doi: 10.1109/TAES.2024.3398600.
[24] L. Shi, H. Yao, M. Shan, Q. Gao, and X. Jin, "Robust control of a space robot based on an optimized adaptive variable structure control method," Aerospace Science and Technology, vol. 120, p. 107267, 2022/01/01/ 2022, doi: 10.1016/j.ast.2021.107267.
[25] R. Gholipour and M. M. Fateh, "Designing a Robust Control Scheme for Robotic Systems with an Adaptive Observer," International Journal of Engineering, vol. 32, pp. 270-276, 2019, doi: 10.5829/ije.2019.32.02b.12.
[26] R. Gholipour and M. M. Fateh, "Adaptive task-space control of robot manipulators using the Fourier series expansion without task-space velocity measurements," Measurement, vol. 123, pp. 285-292, 2018/07/01/ 2018, doi: 10.1016/j.measurement.2018.04.003.
[27] J. Keighobadi, M. M. Fateh, and H. Chenarani, "Adaptive Fuzzy Passivation Control Based on Backstepping Method for Electrically Driven Robotic Manipulators," in 2018 6th RSI International Conference on Robotics and Mechatronics (IcRoM), 2018, pp. 292-297.
[28] S. Khorashadizadeh, M. M. Zirkohi, H. Eliasi, and R. Gholipour, "Adaptive control of robot manipulators driven by permanent magnet synchronous motors using orthogonal functions theorem," Journal of Vibration and Control, vol. 29, pp. 2789-2801, 2023/06/01 2022,10.1177/10775463221085784.
[29] J. Barnett, M. Duke, C. K. Au, and S. H. Lim, "Work distribution of multiple Cartesian robot arms for kiwifruit harvesting," Computers and Electronics in Agriculture, vol. 169, p. 105202, 2020/02/01/ 2020, doi: 10.1016/j.compag.2019.105202.
[30] R. Gholipour and M. M. Fateh, "Observer-based robust task-space control of robot manipulators using Legendre polynomial," in 2017 Iranian Conference on Electrical Engineering (ICEE), 2017, pp. 766-771.
[31] F. Amiri and S. Khorashadizadeh, "Adaptive control of a class of uncertain nonlinear systems using brain emotional learning and Legendre polynomials," Transactions of the Institute of Measurement and Control, vol. 46, pp. 1667-1679, 2024/06/01 2023, doi: 10.1177/01423312231203270.
[32] M. R. Shokoohinia and M. M. Fateh, "Model-Free Tracking Control via Adaptive Dynamic Sliding Mode Control With Application to Robotic Systems," International Journal of Industrial Electronics Control and Optimization, vol. 3, pp. 431-438, 2020, doi: 10.22111/ieco.2020.31596.1207.
[33] R. Gholipour and M. M. Fateh, "Robust Control of Robotic Manipulators in the Task-Space Using an Adaptive Observer Based on Chebyshev Polynomials," Journal of Systems Science and Complexity, vol. 33, pp. 1360-1382, 2020/10/01 2020, doi: 10.1007/s11424-020-8186-0.
[34] M. Spong, S. Hutchinson, and M. Vidyasagar, "Robot Modeling and Control," ed: John Wiley & Sons Inc, 2020.
[35] J. keighobadi and M. m. Fateh, "Adaptive Robust Tracking Control Based on Backstepping Method for Uncertain Robotic Manipulators Including Motor Dynamics," International Journal of Industrial Electronics Control and Optimization, vol. 4, pp. 13-22, 2021, 10.22111/ieco.2020.31792.1213.
[36] S. Khorashadizadeh and M. M. Fateh, "Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation," Nonlinear Dynamics, vol. 79, pp. 1151-1161, 2015/01/01 2015, 10.1007/s11071-014-1730-5.
[37] J.-J. E. Slotine and W. Li, Applied nonlinear control vol. 199: Prentice hall Englewood Cliffs, NJ, 1991,
[38] J. Keighobadi, M. M. Fateh, B. Xu, and G. Nazmara, "Composite fuzzy voltage-based command-filtered learning control of electrically-driven robots with input delay using disturbance observer," Journal of the Franklin Institute, vol. 360, pp. 813-840, 2023/01/01/ 2023,doi:10.1016/j.jfranklin.2022.11.027.
[39] J. Keighobadi, M. M. Fateh, and B. Xu, "Adaptive fuzzy voltage-based backstepping tracking control for uncertain robotic manipulators subject to partial state constraints and input delay," Nonlinear Dynamics, vol. 100, pp. 2609-2634, 2020/05/01 2020, 10.1007/s11071-020-05674-8.
[40] J. Keighobadi, A. Mehrjouyan, and A. Alfi, "Efficient learning control of uncertain nonlinear systems with input constraints: a disturbance observer-based neural network approach," International Journal of Dynamics and Control, vol. 12, pp. 3392-3406, 2024/09/01 2024, 10.1007/s40435-024-01416-5.
[41] M. R. Shokoohinia, M. M. Fateh, and R. Gholipour, "Design of an adaptive dynamic sliding mode control approach for robotic systems via uncertainty estimators with exponential convergence rate," SN Applied Sciences, vol. 2, p. 180, 2020/01/10 2020, 10.1007/s42452-020-1947-5.
[42] M. W. Spong, S. Hutchinson, and M. Vidyasagar, "Robot modeling and control," John Wiley &, 2020,
[43] A. Aboud, N. Rokbani, S. Mirjalili, A. Hussain, and A. M. Alimi, "A novel Quantum Beta distributed multi-objective Particle Swarm Optimization algorithm for fake accounts detection," Engineering Applications of Artificial Intelligence, vol. 167, p. 113724, 2026/03/01/ 2026, doi:10.1016/j.engappai.2026.113724.
[44] S. A. Saadat, M. M. Fateh, and J. Keighobadi, "Grey wolf optimization algorithm-based robust neural learning control of passive torque simulators with predetermined performance," Turkish Journal of Electrical Engineering and Computer Sciences, vol. 32, pp. 126-143, 2024, 10.55730/1300-0632.4059.
[45] R. Gholipour, J. Addeh, H. Mojallali, and A. Khosravi, "Multi-objective evolutionary optimization of PID controller by chaotic particle swarm optimization," International Journal of Computer and Electrical Engineering, vol. 4, pp. 833-838, 2012,
[46] R. Gholipour, A. Khosravi, and H. Mojallali, "Suppression of chaotic behavior in duffing-holmes system using backstepping controller optimized by unified particle swarm optimization algorithm," International Journal of Engineering, Transactions B: Applications, vol. 26, pp. 1299-1306, 2013, doi: 10.5829/idosi.ije.2013.26.11b.05.
[47] R. Gholipour, A. Khosravi, and H. Mojallali, "Parameter estimation of loranz chaotic dynamic system using bees algorithm," International Journal of Engineering, Transactions C: Aspects, vol. 26, pp. 257-262, 2013, doi: 10 .58 2 9/i d o s i . ij e . 2 0 1 3 .26.03c.05.
[48] E. Salahshour, M. Malekzadeh, R. Gholipour, and S. Khorashadizadeh, "Designing multi-layer quantum neural network controller for chaos control of rod-type plasma torch system using improved particle swarm optimization," Evolving Systems, vol. 10, pp. 317-331, 2019/09/01 2019, 10.1007/s12530-018-9222-3.
[49] D. Izci, E. Eker, S. Ekinci, M. Bajaj, V. Blazek, and L. Prokop, "Neighborhood centroid opposition-based flood algorithm for optimizing fractional-order PID control in nonlinear heat exchanger dynamics," Chaos, Solitons & Fractals, vol. 204, p. 117729, 2026/03/01/ 2026, doi: 10.1016/j.chaos.2025.117729.
[50] A. Ghanbarpour, S. Zaremotlagh, and F. Dabaghi-Zarandi, "Addressing Dependent Data in Constrained Optimization Problems: A WOA-based Algorithm," International Journal of Industrial Electronics Control and Optimization, vol. 7, pp. 119-127, 2024, 10.22111/ieco.2024.47541.1523.
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