Adaptive Task-Space Control of Five-Bar Parallel Robot Dynamic Model with Fully Unknown Using Radial Basis Function Neural Networks for High-Precision Applications

Authors

  • Thanh Hai Tran Industrial University of Ho Chi Minh City
  • Thanh Quyen Ngo Industrial University of Ho Chi Minh City
  • Hoang Thi Tu Uyen Industrial University of Ho Chi Minh City
  • Van Tho Nguyen Industrial University of Ho Chi Minh City
  • Tien Đoan Duong Industrial University of Ho Chi Minh City

DOI:

https://doi.org/10.18196/jrc.v6i4.26537

Keywords:

Nonlinear Uncertain Systems, MIMO Systems, Lyapunov Stability, Radial Basis Function Neural Network (RBFNN), Adaptive Parameter Tuning

Abstract

Designing a stable and accurate controller for nonlinear systems remains a significant challenge, mainly when the system contains uncertain factors or is affected by external disturbances. This study proposes an adaptive control method based on a Radial Basis Function Neural Network (RBFNN) to effectively estimate the uncertain components in nonlinear systems. The gradient descent algorithm updates the RBFNN parameters, and the control system's stability is rigorously proven based on the Lyapunov theory. The designed controller ensures accuracy under changing conditions and can adapt to nonlinear disturbances and system fluctuations flexibly. Through 45 consecutive test cycles, the system significantly improves precision and outperforms other control methods in comparative tests. This study opens up the potential for broad application in highly uncertain nonlinear MIMO systems, thanks to the effective combination of adaptive learning ability, stability, and simple implementation structure of the proposed controller.

References

C. C. Cheah, S. P. Hou, Y. Zhao, and J. -J. E. Slotine, “Adaptive Vision and Force Tracking Control for Robots With Constraint Uncertainty,” IEEE/ASME Transactions on Mechatronics, vol. 15, no. 3, pp. 389-399, 2010.

Z. Li, S. S. Ge, M. Adams, and W. S. Wijesoma, “Robust adaptive control of uncertain force/motion constrained nonholonomic mobile manipulators,” Automatica, vol. 44, no. 3, pp. 776-784, 2008.

L. Huang, S. S. Ge, and T. Lee, “Position/force control of uncertain constrained flexible joint robots,” Mechatronics, vol. 16, no. 2, pp. 111-120, 2006.

Z. Li, J. Li, and Y. Kang, “Adaptive robust coordinated control of multiple mobile manipulators interacting with rigid environments,” Automatica, vol. 46, no. 12, pp. 2028-2034, 2010.

Z. Li, S.S. Ge, and Z. Wang, “Robust adaptive control of coordinated multiple mobile manipulators,” Mechatronics vol. 18, no. 5-6, pp. 239-250, 2008.

K. P. Tee, R. Yan, and H. Li, “Adaptive admittance control of a robot manipulator under task space constraint,” 2010 IEEE International Conference on Robotics and Automation, pp. 5181-5186, 2010.

H. N. Rahimi, I. Howard, and L. Cui, “Neural impedance adaption for assistive human–robot interaction,” Neurocomputing, vol. 290, pp. 50-59, 2018.

O. Cerman and P. Hušek, “Adaptive fuzzy sliding mode control for electro-hydraulic servo mechanism,” Expert Systems with Applications, vol. 39, no. 11, pp. 10269-10277, 2012.

Q. K. Li, J. Zhao, and G. M. Dimirovski, “Robust tracking control for switched linear systems with time-varying delays,” IET Control Theory & Applications, vol. 2, no. 6, pp. 449-457, 2008.

M. Roopaei, M. Zolghadri, and S. Meshksar, “Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 9, pp. 3670-3681, 2009.

F. Liu, M. Chen, and T. Li, “Fixed-time anti-disturbance control for nonlinear turbofan engine with impulsive prescribed performance,” Journal of the Franklin Institute, vol. 361, no. 17, p. 107193, 2024.

Y. Zhang, J. Sun, H. Liang, and H. Li, “Event-Triggered Adaptive Tracking Control for Multiagent Systems With Unknown Disturbances,” IEEE Transactions on Cybernetics, vol. 50, no. 3, pp. 890-901, 2020.

C. K. Verginis, Y. Kantaros, and D. V. Dimarogonas, “Planning and control of multi-robot-object systems under temporal logic tasks and uncertain dynamics,” Robotics and Autonomous Systems, vol. 174, p. 104646, 2024.

S. J. Yoo and B. S. Park, “Distributed quantized state feedback strategy for ensuring predesignated formation tracking performance of networked uncertain nonholonomic multi-robot systems with quantized communication,” Expert Systems with Applications, vol. 201, p. 116987, 2022.

X. Liu and H. Sheng, “Active fault tolerant control of uncertain robotic system based on observer and sliding mode,” IFAC-PapersOnLine, vol. 55, no. 1, pp. 598-603, 2022.

A. Zhai, J. Wang, H. Zhang, G. Lu, and H. Li, “Adaptive robust synchronized control for cooperative robotic manipulators with uncertain base coordinate system,” ISA Transactions, vol. 126, pp. 134–143, 2022.

F. Ye, J. Perrett, L. Zhang, Y. Laili, and Y. Wang, “A self-evolving system for robotic disassembly sequence planning under uncertain interference conditions,” Robotics and Computer-Integrated Manufacturing, vol. 78, p. 102392, 2022.

M. Souzanchi-K and M. R. Akbarzadeh-T, “Brain emotional learning impedance control of uncertain nonlinear systems with time delay: Experiments on a hybrid elastic joint robot in telesurgery,” Computers in Biology and Medicine, vol. 138, p. 104786, 2021.

Z. Li and S. Li, “Saturated PI Control for Nonlinear System With Provable Convergence: An Optimization Perspective,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 2, pp. 742-746, 2021,

T. Q. Ngo, T. N. A. Nguyen, N. T. P. Le, D. C. Pham, and N. D. Ngo, “Adaptive Tracking Control Based on Recurrent Wavelet Fuzzy CMAC for Uncertain Nonlinear Systems,” International Journal of Control and Automation, vol. 11, no. 1, pp. 75-90, 2018.

A. -V. Nguyen, V. -T. Ngo, W. -J. Wang, V. -P. Vu, T. -Q. Ngo, and A. –. Nguyen, “Fuzzy Logic Based LQG Controller Design for Inverted Pendulum On Cart,” 2021 International Conference on System Science and Engineering (ICSSE), pp. 387-392, 2021.

M. A. Llama, R. Kelly, and V. Santibanez, “Stable computed-torque control of robot manipulators via fuzzy self-tuning,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 30, no. 1, pp. 143-150, 2000.

T. Sun, L. Cheng, W. Wang, and Y. Pan, “Semiglobal exponential control of Euler–Lagrange systems using a sliding-mode disturbance observer,” Automatica, vol. 112, p. 108677, 2020.

M. Chen, G. Tao, and B. Jiang, “Dynamic Surface Control Using Neural Networks for a Class of Uncertain Nonlinear Systems With Input Saturation,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 9, pp. 2086-2097, 2015.

T. Yang, N. Sun, and Y. Fang, “Adaptive Fuzzy Control for Uncertain Mechatronic Systems With State Estimation and Input Nonlinearities,” IEEE Transactions on Industrial Informatics, vol. 18, no. 3, pp. 1770-1780, 2022.

S. Roy, S. Baldi, and L. Fridman, “On adaptive sliding mode control without a priori bounded uncertainty,” Automatica, vol. 111, p. 108650, 2020.

Q. Deng, Y. Peng, T. Han, and D. Qu, “Event-Triggered Bipartite Consensus in Networked Euler–Lagrange Systems With External Disturbance,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 8, pp. 2870-2874, 2021.

J. Han, “From PID to Active Disturbance Rejection Control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900-906, 2009.

W. -H. Chen, J. Yang, L. Guo, and S. Li, “Disturbance-Observer-Based Control and Related Methods-An Overview,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1083-1095, 2016.

W. He, Y. Sun, Z. Yan, C. Yang, Z. Li, and O. Kaynak, “Disturbance Observer-Based Neural Network Control of Cooperative Multiple Manipulators With Input Saturation,” IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 5, pp. 1735-1746, 2020.

M. Basin and P. Ramirez, “Sliding mode controller design for linear systems with unmeasured states,” Journal of the Franklin Institute, vol. 349, no. 4, pp. 1337-1349, 2012.

H. Wu and P. Shi, “Adaptive variable structure state estimation for uncertain systems with persistently bounded disturbances,” International Journal of Robust and Nonlinear Control, vol. 20, no. 17, pp. 2003-2015, 2010.

L. Wu, P. Shi, and H. Gao, “State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1213-1219, 2010.

Y. Xia, H. Yang, M. Fu, and P. Shi, “Sliding mode control for linear systems with time-varying input and state delays,” Circuits, Systems, and Signal Processing, vol. 30, no. 3, pp. 629-641, 2011.

İ. Eker, “Second-order sliding mode control with experimental application,” ISA Transactions, vol. 49, no. 3, pp. 394-405, 2010.

H. F. Ho, Y. K. Wong, and A. B. Rad, “Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems,” Simulation Modelling Practice and Theory, vol. 17, pp. 1199-1210, 2009.

J. Hu, Z. Wang, H. Gao, and L. K. Stergioulas, “Robust H∞ sliding mode control for discrete time-delay systems with stochastic nonlinearities,” Journal of the Franklin Institute, vol. 349, pp. 1459-1479, 2012.

T. Sun, H. Pei, Y. Pan, H. Zhou, and C. Zhang, “Neural network-based sliding mode adaptive control for robot manipulators,” Neurocomputing, vol. 74, no. 14, pp. 2377–2384, 2011.

M. Shahriari Kahkeshi, F. Sheikholeslam, and M. Zekri, “Design of adaptive fuzzy wavelet neural sliding mode controller for uncertain nonlinear systems,” ISA Transactions, vol. 52, no. 3, pp. 342–350, 2013.

B. Ren, Q. -C. Zhong, and J. Chen, “Robust Control for a Class of Nonaffine Nonlinear Systems Based on the Uncertainty and Disturbance Estimator,” IEEE Transactions on Industrial Electronics, vol. 62, no. 9, pp. 5881-5888, 2015.

B. Ren, Q. -C. Zhong, and J. Dai, “Asymptotic Reference Tracking and Disturbance Rejection of UDE-Based Robust Control,” IEEE Transactions on Industrial Electronics, vol. 64, no. 4, pp. 3166-3176, 2017.

P. Shendge and B. Patre, “Robust model following load frequency sliding mode controller based on UDE and error improvement with higher order filter,” IAENG International Journal of Applied Mathematics, vol. 37, no. 1, pp. 27-32, 2007.

Q. Zhong and D. Rees, “Control of uncertain LTI systems based on an uncertainty and disturbance estimator,” Journal of Dynamic Systems, Measurement, and Control, Transactions of the ASME, vol. 126, no. 4, pp. 905-910, 2004.

B. Cong, X. Liu, and Z. Chen, “Backstepping based adaptive sliding mode control for spacecraft attitude maneuvers,” Aerospace Science and Technology, vol. 30, no. 1, pp. 1-7, 2013.

M. Rafiq, S. Rehman, F. Rehman, Q. Butt, and I. Awan, “A second order sliding mode control design of a switched reluctance motor using super twisting algorithm,” Simulation Modelling Practice and Theory, vol. 25, pp. 106-117, 2012.

G. R. Chen, J. Zhou, and S. Celikovsky, “On LaSalle’s invariance principle and its application to robust synchronization of general vector Liénard equations,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 869–874, 2005.

V. Lakshmikantham, S. Leela, and A. A. P. Martynyuk, Practical Stability of Nonlinear Systems. World Scientific, 1990.

Y. J. Huang, T. C. Kuo, and S. H. Chang, “Adaptive sliding-mode control for nonlinear systems with uncertain parameters,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 38, pp. 534–539, 2008.

M. Zeinali and L. Notash, “Adaptive sliding mode control with uncertainty estimator for robot manipulators,” Mechanism and Machine Theory, vol. 45, no. 1, pp. 80-90, 2010.

J. H. Liu, C. L. Wang, and X. Cai, “Adaptive neural network finite-time tracking control for a class of high-order nonlinear multi-agent systems with powers of positive odd rational numbers and prescribed performance,” Neurocomputing, vol. 419, pp. 157-167, 2021.

Z. Wang, Y. Z. Zhu, H. Xue, and H. J. Liang, “Neural networks-based adaptive event-triggered consensus control for a class of multi-agent systems with communication faults,” Neurocomputing, vol. 470, pp. 99-108, 2022.

X. Zhao, P. Shi, X. Zheng, and J. Zhang, “Intelligent tracking control for a class of uncertain high-order nonlinear systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 21, no. 9, pp. 1976-1982, 2019.

W. He, Y. Dong, and C. Sun, “Adaptive neural impedance control of a robotic manipulator with input saturation,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 46, no. 3, pp. 334-344, 2016.

R. Yang, C. Yang, M. Chen, and A. S. Annamalai, “Discrete-time optimal adaptive RBFNN control for robot manipulators with uncertain dynamics,” Neurocomputing, vol. 234, pp. 107-114, 2017.

Z. Wang, J. Yuan, Y. Pan, and J. Wei, “Neural network-based adaptive fault tolerant consensus control for a class of high order multi-agent systems with input quantization and time-varying parameters,” Neurocomputing, vol. 266, pp. 315–324, 2017.

H. R. Nohooji, I. Howard, and L. Cui, “Neural adaptive assist-as-needed control for rehabilitation robots,” Proceedings of the Australasian Conference on Robotics and Automation (ACRA), 2016.

M. Daachi, T. Madani, B. Daachi, and K. Djouani, “A radial basis function neural network adaptive controller to drive a powered lower limb knee joint orthosis,” Applied Soft Computing, vol. 34, pp. 324–336, 2015.

H. R. Nohooji, “Constrained neural adaptive PID control for robot manipulators,” Journal of the Franklin Institute, vol. 357, no. 7, pp. 3907–3923, 2020.

C. Lauretti, F. Cordella, A. L. Ciancio, E. Trigili, J. M. Catalan, F. J. Badesa, S. Crea, S. M. Pagliara, S. Sterzi, and N. Vitiello, “Learning by demonstration for motion planning of upper-limb exoskeletons,” Frontiers in Neurorobotics, vol. 12, p. 5, 2018.

S. Seshagiri and H. K. Khalil, “Output feedback control of nonlinear systems using RBF neural networks,” IEEE Transactions on Neural Networks, vol. 11, no. 1, pp. 69–79, 2000.

R. J. Schalkoff, Artificial Neural Networks. McGraw-Hill, 1997.

M. R. Berthold and J. Diamond, “Boosting the performance of RBF networks with dynamic decay adjustment,” Advances in Neural Information Processing Systems, 1994.

S. Zhao and J. Yuh, “Experimental study on advanced underwater robot control,” IEEE Transactions on Robotics, vol. 21, no. 4, pp. 695–703, 2005.

Y. Lu, J. K. Liu, and F. C. Sun, “Actuator Nonlinearities Compensation Using RBF Neural Networks in Robot Control System,” The Proceedings of the Multiconference on “Computational Engineering in Systems Applications”, pp. 231-238, 2006.

W. Hao, “A gradient descent method for solving a system of nonlinear equations,” Applied Mathematics Letters, vol. 112, p. 106739, 2021.

T. Q. Ngo, T. H. Tran, V. T. Nguyen, and T. T. H. Le, “Adaptive single input tracking controller for parallel robot system based on hybrid brain emotion and cerebellar model articulation control network using wavelet function,” Journal of Electrical Engineering and Technology, 2025.

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Published

2025-06-21

How to Cite

[1]
T. H. Tran, T. Q. Ngo, H. T. T. Uyen, V. T. Nguyen, and T. Đoan Duong, “Adaptive Task-Space Control of Five-Bar Parallel Robot Dynamic Model with Fully Unknown Using Radial Basis Function Neural Networks for High-Precision Applications”, J Robot Control (JRC), vol. 6, no. 4, pp. 1624–1635, Jun. 2025.

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