Abstract
A Lyapunov-stability-guaranteed local model adaptive RBF neural network control algorithm is proposed for industrial robots. This algorithm eliminates the need for an exact plant mathematical model, enabling real-time learning and compensation of system nonlinearities and uncertainties. An adaptive control law adjusts neural network parameters online to achieve high-precision tracking control of robot manipulators. Particle Swarm Optimization (PSO) is employed to optimize the RBF basis width parameters. Validation was performed using the ABB IRB1600 industrial robot, modeled and simulated in MATLAB Simscape. Real-time trajectory tracking was demonstrated, with ADAMS co-simulation used for further verification. Results demonstrate the algorithm’s effectiveness in reducing tracking errors and enhancing robustness and adaptability, while maintaining stability within the Lyapunov framework.
Similar content being viewed by others
Data availability
The author confirms that all data generated or analyzed during this study are included in this published article or supplementary information files. Furthermore, primary and secondary sources and data supporting the findings of this study were all publicly available at the time of submission.
References
Khanesar, M. A. & Branson, D. Robust sliding mode fuzzy control of industrial robots using an extended Kalman filter inverse kinematic solver. Energies 15 https://doi.org/10.3390/en15051876 (2022).
Truong, T. N., Vo, A. T. & Kang, H. J. Neural network-based sliding mode controllers applied to robot manipulators: A review. Neurocomputing 562, 126896. https://doi.org/10.1016/j.neucom.2023.126896 (2023).
Yan, Y. et al. Trajectory tracking control of wearable upper limb rehabilitation robot based on Laguerre model predictive control. Robot. Auton. Syst. 179 https://doi.org/10.1016/j.robot.2024.104745 (2024).
Xu, Y. et al. A novel constraint tracking control with sliding mode control for industrial robots. Int. J. Adv. Rob. Syst. 18, 5682–5692. https://doi.org/10.1177/17298814211029778 (2021).
Wang, D. et al. Sliding mode observer-based model predictive tracking control for Mecanum-wheeled mobile robot. ISA Trans. 151, 51–61. https://doi.org/10.1016/j.isatra.2024.05.050 (2024).
Zhang, T. et al. Discrete nonsingular terminal sliding mode control for trajectory tracking of space manipulators with mismatched multiple disturbances and noisy measurements. Aerosp. Sci. Technol. 144 https://doi.org/10.1016/j.ast.2023.108766 (2024).
Cruz-Ortiz, D., Chairez, I. & Poznyak, A. Adaptive sliding-mode trajectory tracking control for state constraint master-slave manipulator systems. ISA Trans. 127, 273–282. https://doi.org/10.1016/j.isatra.2021.08.023 (2022).
Zahra, A. K. A. & Abdalla, T. Y. A PSO optimized RBFNN and STSMC scheme for path tracking of robot manipulator. Bull. Electr. Eng. Inf. 12, 2733–2744. https://doi.org/10.11591/eei.v12i5.5018 (2023).
Arents, J. & Greitans, M. Smart industrial robot control Trends, challenges and opportunities within manufacturing. Appl. Sci. 12 https://doi.org/10.3390/app12020937 (2022).
Liu, Z. et al. Robot learning towards smart robotic manufacturing: A review. Robot. Comput. Integr. Manuf. 77 https://doi.org/10.1016/j.rcim.2022.102360 (2022).
Khan, G. D. Adaptive neural network control framework for industrial robot manipulators. IEEE Access. 12 https://doi.org/10.1109/ACCESS.2024.3396782 (2024).
Yang, Z., Peng, J. & Liu, Y. Adaptive neural network force tracking impedance control for uncertain robotic manipulator based on nonlinear velocity observer. Neurocomputing 331, 263–280. https://doi.org/10.1016/j.neucom.2018.11.068 (2019).
Hu, J. et al. Neural network-based adaptive second-order sliding mode control for uncertain manipulator systems with input saturation. ISA Trans. 136, 126–138. https://doi.org/10.1016/j.isatra.2022.11.024 (2023).
Zhang, F., Yuan, Z. & Zhang, F. Research on coupling dynamics modeling and composite control of the multi-flexible space robot. Adv. Space Research: Official J. Comm. Space Research(COSPAR). 74 https://doi.org/10.1016/j.asr.2024.05.043 (2024).
Liu, Q. et al. Adaptive bias RBF neural network control for a robotic manipulator. Neurocomputing 447, 213–223. https://doi.org/10.1016/j.neucom.2021.03.033 (2021).
Yan, X. et al. Adaptive and intelligent control of a dual-arm space robot for target manipulation during the post-capture phase. Aerosp. Sci. Technol. 142 https://doi.org/10.1016/j.ast.2023.108688 (2023).
Zhu, N., Xie, W. F. & Shen, H. Position-based visual servoing of a 6-RSS parallel robot using adaptive sliding mode control. ISA Trans. 144, 398–408. https://doi.org/10.1016/j.isatra.2023.10.029 (2024).
Feng, H. et al. A new adaptive sliding mode controller based on the RBF neural network for an electro-hydraulic servo system. ISA Trans. 129, 472–484. https://doi.org/10.1016/j.isatra.2021.12.044 (2022).
Jiang, P. et al. Energy consumption prediction and optimization of industrial robots based on LSTM. J. Manuf. Syst. 70, 137–148. https://doi.org/10.1016/j.jmsy.2023.07.009 (2023).
Xu, Z. et al. Error compensation of collaborative robot dynamics based on deep recurrent neural network. Chin. J. Eng. 43, 995–1002. https://doi.org/10.13374/j.issn2095-9389.2020.04.30.003 (2021).
Liu, S., Wang, L. & Wang, V. Sensorless haptic control for human-robot collaborative assembly. CIRP J. Manufact. Sci. Technol. 32, 132–144. https://doi.org/10.1016/j.cirpj.2020.11.015 (2021).
Yu, X. et al. Human-Robot Co-Carrying using visual and force sensing. IEEE Trans. Industr. Electron. 68, 8657–8666. https://doi.org/10.1109/TIE.2020.3044792 (2020).
Hernandez-Sanchez, A. et al. Trajectory tracking controller of a robotized arm with joint constraints, a direct adaptive gain with state limitations approach. ISA Trans. 141, 276–287. https://doi.org/10.1016/j.isatra.2023.07.004 (2023).
Sai, H. et al. Adaptive local approximation neural network control based on extraordinariness particle swarm optimization for robotic manipulators. J. Mech. Sci. Technol. 36, 1469–1483. https://doi.org/10.1007/s12206-022-0234-3 (2022).
Funding
This research was Funded by the National Science Foundation of China, grant number 52205536; funded by the Young Talent project of Scientific Research Plan of Education Department of Hubei Province, grant number Q20232301; funded by Wuhan Donghu High-tech Zone “Unveiling the List and Leading the Way” Project, grant number 2024KJB325.
Author information
Authors and Affiliations
Contributions
Conceptualization, G.H., Y.P. and X.C.; methodology, G.H.; investigation, G.H.; formal analysis, G.H.; writing-preparation of the original draft, G.H.; writing-review and editing, Y.P., X.C., C.H., W.X. and Z.M.; visualization, C.H.; validation, W.X.; resources, Z.M.; funding acquisition, Y.P. and X.C.; project administration, Y.P. and X.C. All authors discussed the results and contributed to the final manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
Han, G., Huang, C., Xiao, W. et al. Tracking control of industrial manipulator based on adaptive RBF neural network with local model approximation. Sci Rep (2026). https://doi.org/10.1038/s41598-025-34816-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598-025-34816-4


