Design of a Robust Component-wise Sliding Mode Controller for a Two-Link Manipulator
DOI:
https://doi.org/10.18196/jrc.v6i2.25632Keywords:
Two-Link Manipulator, Sliding Mode Control, Style, Component-Wise SMC, Model UncertaintiesAbstract
Compared to conventional Multiple-Input Multiple-Output (MIMO) Sliding Mode Control (SMC) techniques, the component-wise SMC approach offers several advantages, including improved decoupling of system dynamics, enhanced robustness, and greater flexibility in controller design. This paper proposes a novel trajectory tracking controller for a two-link manipulator based on the component-wise sliding mode control approach. The design methodology involves determining controller gains by solving a set of inequalities. This analysis results in conditions on the system parameter uncertainties that guarantee the existence of a feasible solution to the set of inequalities. Furthermore, an algorithm is presented to determine the maximum allowable uncertainties that ensure the feasibility of the controller gains. To evaluate the performance and robustness of the proposed tracking controller, the manipulator is subjected to a series of challenging trajectories, including circular and figure-8 ones, under both nominal and maximum allowable uncertainty conditions. The proposed controller demonstrates superior performance across both circular and figure-8 trajectories, exhibiting excellent transient response and minimal steady-state error even under the maximum permissible uncertainties, which extend up to 27% in link masses. This performance is validated through a quantitative analysis that incorporates a comparative evaluation against two conventional MIMO SMC techniques. The comparison is conducted using the Integral Norm of Error (INE) to assess tracking accuracy and the Integral Norm of Control Action (INU) to evaluate the energy efficiency of the controllers. These metrics provide a comprehensive basis for analyzing both the precision and the energy consumption of the proposed control strategy in relation to established methods.
References
B. Zhang, Y. Xie, J. Zhou, K. Wang, and Z. Zhang, “State-of-the-art robotic grippers, grasping and control strategies, as well as their applications in agricultural robots: A review,” Computers and Electronics in Agriculture, vol. 177, p. 105694, Oct. 2020, doi: 10.1016/j.compag.2020.105694.
Y. H. Alnema, M. Almaged, and M. N. Noaman, “Driverless Model Cars: a Review and Analysis of Autonomous Vehicle Literature on Technology and Application,” International Review of Automatic Control (IREACO), vol. 13, no. 2, p. 84, Mar. 2020, doi: 10.15866/ireaco.v13i2.18659.
A. Sathish Kumar et al., “An intelligent fuzzy-particle swarm optimization supervisory-based control of robot manipulator for industrial welding applications,” Scientific Reports, vol. 13, no. 1, May 2023, doi: 10.1038/s41598-023-35189-2.
L. Zongxing, L. Wanxin, and Z. Liping, “Research development of soft manipulator: A review,” Advances in Mechanical Engineering, vol. 12, no. 8, Aug. 2014, doi: 10.1177/1687814020950094.
Z. Liu, K. Peng, L. Han, and S. Guan, “Modeling and Control of Robotic Manipulators Based on Artificial Neural Networks: A Review,” Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, vol. 47, no. 4, pp. 1307–1347, Jan. 2023, doi: 10.1007/s40997-023-00596-3.
N. Tan, C. Li, P. Yu, and F. Ni, “Two model-free schemes for solving kinematic tracking control of redundant manipulators using CMAC networks,” Applied Soft Computing, vol. 126, p. 109267, Sep. 2022, doi: 10.1016/j.asoc.2022.109267.
J. Perez and M. S. L. de la Fuente, “Trajectory Tracking Error Using Fractional Order PID Control Law for Two‐Link Robot Manipulator via Fractional Adaptive Neural Networks,” Robotics - Legal, Ethical and Socioeconomic Impacts, Dec. 2017, doi: 10.5772/intechopen.70020.
Q. V. Doan, A. T. Vo, T. D. Le, H.-J. Kang, and N. H. A. Nguyen, “A Novel Fast Terminal Sliding Mode Tracking Control Methodology for Robot Manipulators,” Applied Sciences, vol. 10, no. 9, p. 3010, Apr. 2020, doi: 10.3390/app10093010.
S. Jia and J. Shan, “Finite-Time Trajectory Tracking Control of Space Manipulator Under Actuator Saturation,” IEEE Transactions on Industrial Electronics, vol. 67, no. 3, pp. 2086–2096, Mar. 2020, doi: 10.1109/tie.2019.2902789.
S. Tian and T. Zhao, “Self-organizing interval type-2 function-link fuzzy neural network control for uncertain manipulators under saturation: A predefined-time sliding-mode approach,” Applied Soft Computing, vol. 165, p. 112064, Nov. 2024, doi: 10.1016/j.asoc.2024.112064.
S. I. Abdelmaksoud, M. H. Al-Mola, G. E. M. Abro, and V. S. Asirvadam, “In-Depth Review of Advanced Control Strategies and Cutting-Edge Trends in Robot Manipulators: Analyzing the Latest Developments and Techniques,” IEEE Access, vol. 12, pp. 47672–47701, 2024, doi: 10.1109/access.2024.3383782.
A. Billard and D. Kragic, “Trends and challenges in robot manipulation,” Science, vol. 364, no. 6446, Jun. 2019, doi: 10.1126/science.aat8414.
T. Q. Ngo, T. H. Tran, T. T. H. Le, and B. M. Lam, “An Application of Modified T2FHC Algorithm in Two-Link Robot Controller,” Journal of Robotics and Control (JRC), vol. 4, no. 4, pp. 509–520, Aug. 2023, doi: 10.18196/jrc.v4i4.18943.
F. Wang et al., “Sliding Mode Robust Active Disturbance Rejection Control for Single-Link Flexible Arm with Large Payload Variations,” Electronics, vol. 10, no. 23, p. 2995, Dec. 2021, doi: 10.3390/electronics10232995.
A. Ollero, M. Tognon, A. Suarez, D. Lee, and A. Franchi, “Past, Present, and Future of Aerial Robotic Manipulators,” IEEE Transactions on Robotics, vol. 38, no. 1, pp. 626–645, Feb. 2022, doi: 10.1109/tro.2021.3084395.
J. Liu, L. Wu, C. Wu, W. Luo, and L. G. Franquelo, “Event-triggering dissipative control of switched stochastic systems via sliding mode,” Automatica, vol. 103, pp. 261–273, May 2019, doi: 10.1016/j.automatica.2019.01.029.
J. Kumar, V. Kumar, and K. P. S. Rana, “Fractional-order self-tuned fuzzy PID controller for three-link robotic manipulator system,” Neural Computing and Applications, vol. 32, no. 11, pp. 7235–7257, May 2019, doi: 10.1007/s00521-019-04215-8.
E. Kelekci and S. Kizir, “Trajectory and vibration control of a flexible joint manipulator using interval type-2 fuzzy logic,” ISA Transactions, vol. 94, pp. 218–233, Nov. 2019, doi: 10.1016/j.isatra.2019.04.001.
X. Guo, H. Zhang, J. Sun, and Y. Zhou, “Fixed-Time Fuzzy Adaptive Control of Manipulator Systems Under Multiple Constraints: A Modified Dynamic Surface Control Approach,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 53, no. 4, pp. 2522–2532, Apr. 2023, doi: 10.1109/tsmc.2022.3212988.
I. K. Mohammed and M. N. Noaman, “Optimal Control Approach for Robot System Using LQG Technique,” Journal Européen des Systèmes Automatisés, vol. 55, no. 5, pp. 671–677, Nov. 2022, doi: 10.18280/jesa.550513.
M. N. Alghanim, M. Qasim, K. P. Valavanis, M. J. Rutherford, and M. Stefanovic, “Passivity-Based Adaptive Controller for Dynamic Self-Leveling of a Custom-Built Landing Platform on Top of a UGV,” 2020 28th Mediterranean Conference on Control and Automation (MED), pp. 458–464, Sep. 2020, doi: 10.1109/med48518.2020.9182807.
B. Rahmani and M. Belkheiri, “Adaptive neural network output feedback control for flexible multi-link robotic manipulators,” International Journal of Control, vol. 92, no. 10, pp. 2324–2338, Feb. 2018, doi: 10.1080/00207179.2018.1436774.
O. Tutsoy and D. E. Barkana, “Model free adaptive control of the under-actuated robot manipulator with the chaotic dynamics,” ISA Transactions, vol. 118, pp. 106–115, Dec. 2021, doi: 10.1016/j.isatra.2021.02.006.
M. N. Alghanim, M. Qasim, K. P. Valavanis, M. J. Rutherford, and M. Stefanovic, “Comparison of Controller Performance for UGV-Landing Platform Self-Leveling,” 2020 28th Mediterranean Conference on Control and Automation (MED), pp. 471–478, Sep. 2020, doi: 10.1109/med48518.2020.9182837.
J. Wu, Z. Jin, A. Liu, and L. Yu, “Vision-based neural predictive tracking control for multi-manipulator systems with parametric uncertainty,” ISA Transactions, vol. 110, pp. 247–257, Apr. 2021, doi: 10.1016/j.isatra.2020.10.057.
W. Xu, P. Yan, F. Wang, H. Yuan, and B. Liang, “Vision-based simultaneous measurement of manipulator configuration and target pose for an intelligent cable-driven robot,” Mechanical Systems and Signal Processing, vol. 165, p. 108347, Feb. 2022, doi: 10.1016/j.ymssp.2021.108347.
M. Noaman, M. Qasim, and O. Ismael, “Landmarks exploration algorithm for mobile robot indoor localization using VISION sensor,” Journal of Engineering Science and Technology, vol. 16, no. 4, pp. 3165–3184, 2021.
K. Jayaswal, D. K. Palwalia, and S. Kumar, “Performance investigation of PID controller in trajectory control of two-link robotic manipulator in medical robots,” Journal of Interdisciplinary Mathematics, vol. 24, no. 2, pp. 467–478, Feb. 2021, doi: 10.1080/09720502.2021.1893444.
P. Chotikunnan and R. Chotikunnan, “Dual Design PID Controller for Robotic Manipulator Application,” Journal of Robotics and Control (JRC), vol. 4, no. 1, pp. 23–34, Feb. 2023, doi: 10.18196/jrc.v4i1.16990.
M. J. Mohamed, B. K. Oleiwi, L. H. Abood, A. T. Azar, and I. A. Hameed, “Neural fractional order PID controllers design for 2-link rigid robot manipulator,” Fractal and Fractional, vol. 7, no. 9, p. 693, 2023.
S. Luo, M. Cheng, R. Ding, F. Wang, B. Xu, and B. Chen, “Human–Robot Shared Control Based on Locally Weighted Intent Prediction for a Teleoperated Hydraulic Manipulator System,” IEEE/ASME Transactions on Mechatronics, vol. 27, no. 6, pp. 4462–4474, Dec. 2022, doi: 10.1109/tmech.2022.3157852.
D. Rakita, B. Mutlu, M. Gleicher, and L. M. Hiatt, “Shared control–based bimanual robot manipulation,” Science Robotics, vol. 4, no. 30, May 2019, doi: 10.1126/scirobotics.aaw0955.
M. Qasim and O. Y. Ismael, “Shared Control of a Robot Arm Using BCI and Computer Vision,” Journal Européen des Systèmes Automatisés, vol. 55, no. 1, pp. 139–146, Feb. 2022, doi: 10.18280/jesa.550115.
A. Liu, H. Zhao, T. Song, Z. Liu, H. Wang, and D. Sun, “Adaptive control of manipulator based on neural network,” Neural Computing and Applications, vol. 33, no. 9, pp. 4077–4085, Nov. 2020, doi: 10.1007/s00521-020-05515-0.
F. Luan, J. Na, Y. Huang, and G. Gao, “Adaptive neural network control for robotic manipulators with guaranteed finite-time convergence,” Neurocomputing, vol. 337, pp. 153–164, Apr. 2019, doi: 10.1016/j.neucom.2019.01.063.
Q. Zhou, S. Zhao, H. Li, R. Lu, and C. Wu, “Adaptive Neural Network Tracking Control for Robotic Manipulators With Dead Zone,” IEEE Transactions on Neural Networks and Learning Systems, vol. 30, no. 12, pp. 3611–3620, Dec. 2019, doi: 10.1109/tnnls.2018.2869375.
L. Dai, Y. Yu, D.-H. Zhai, T. Huang, and Y. Xia, “Robust Model Predictive Tracking Control for Robot Manipulators With Disturbances,” IEEE Transactions on Industrial Electronics, vol. 68, no. 5, pp. 4288–4297, May 2021, doi: 10.1109/tie.2020.2984986.
M. Krämer, C. Rösmann, F. Hoffmann, and T. Bertram, “Model predictive control of a collaborative manipulator considering dynamic obstacles,” Optimal Control Applications and Methods, vol. 41, no. 4, pp. 1211–1232, Apr. 2020, doi: 10.1002/oca.2599.
O. Y. Ismael, M. N. Noaman, and I. K. Abdullah, “Fick’s Law Algorithm Based-Nonlinear Model Predictive Control of Twin Rotor MIMO System,” Journal of Robotics and Control (JRC), vol. 5, no. 3, pp. 694–705, 2024, doi: 10.18196/jrc.v5i3.21725.
M. Elsisi, K. Mahmoud, M. Lehtonen, and M. M. F. Darwish, “Effective Nonlinear Model Predictive Control Scheme Tuned by Improved NN for Robotic Manipulators,” IEEE Access, vol. 9, pp. 64278–64290, 2021, doi: 10.1109/access.2021.3075581.
M. S. Qasim, A. B. Ayoub, and A. I. Abdulla, “NMPC Based-Trajectory Tracking and Obstacle Avoidance for Mobile Robots,” International Journal of Robotics and Control Systems, vol. 4, no. 4, pp. 2026–2040, Nov. 2024, doi: 10.31763/ijrcs.v4i4.1605.
M. J. Mahmoodabadi and N. Nejadkourki, “Trajectory Tracking of a Flexible Robot Manipulator by a New Optimized Fuzzy Adaptive Sliding Mode-Based Feedback Linearization Controller,” Journal of Robotics, vol. 2020, pp. 1–12, Jul. 2020, doi: 10.1155/2020/8813217.
M. Bagheri, P. Naseradinmousavi, and M. Krstić, “Feedback linearization based predictor for time delay control of a high-DOF robot manipulator,” Automatica, vol. 108, p. 108485, Oct. 2019, doi: 10.1016/j.automatica.2019.06.037.
O. Y. Ismael, M. Qasim, M. N. Noaman, and A. Kurniawan, “Salp Swarm Algorithm-Based Nonlinear Robust Control of Magnetic Levitation System Using Feedback Linearization Approach,” Proceedings of the 3rd International Conference on Electronics, Communications and Control Engineering, pp. 58–64, Apr. 2020, doi: 10.1145/3396730.3396734.
S. J. Gambhire, D. R. Kishore, P. S. Londhe, and S. N. Pawar, “Review of sliding mode based control techniques for control system applications,” International Journal of Dynamics and Control, vol. 9, no. 1, pp. 363–378, May 2020, doi: 10.1007/s40435-020-00638-7.
J. Hu, X. Zhang, D. Zhang, Y. Chen, H. Ni, and H. Liang, “Finite-time adaptive super-twisting sliding mode control for autonomous robotic manipulators with actuator faults,” ISA Transactions, vol. 144, pp. 342–351, Jan. 2024, doi: 10.1016/j.isatra.2023.10.028.
O. Y. Ismael, M. Qasim, and M. N. Noaman, “Equilibrium Optimizer-Based Robust Sliding Mode Control of Magnetic Levitation System,” Journal Européen des Systèmes Automatisés, vol. 54, no. 1, pp. 131–138, Feb. 2021, doi: 10.18280/jesa.540115.
T. N. Truong, A. T. Vo, and H.-J. Kang, “A Backstepping Global Fast Terminal Sliding Mode Control for Trajectory Tracking Control of Industrial Robotic Manipulators,” IEEE Access, vol. 9, pp. 31921–31931, 2021, doi: 10.1109/access.2021.3060115.
A. Q. Al-Dujaili, A. Falah, A. J. Humaidi, D. A. Pereira, and I. K. Ibraheem, “Optimal super-twisting sliding mode control design of robot manipulator: Design and comparison study,” International Journal of Advanced Robotic Systems, vol. 17, no. 6, Nov. 2020, doi: 10.1177/1729881420981524.
Y. Guo and B.-L. Ma, “Global sliding mode with fractional operators and application to control robot manipulators,” International Journal of Control, vol. 92, no. 7, pp. 1497–1510, Nov. 2017, doi: 10.1080/00207179.2017.1398417.
A. T. Vo and H.-J. Kang, “A Novel Fault-Tolerant Control Method for Robot Manipulators Based on Non-Singular Fast Terminal Sliding Mode Control and Disturbance Observer,” IEEE Access, vol. 8, pp. 109388–109400, 2020, doi: 10.1109/access.2020.3001391.
J. Liu, L. Wu, C. Wu, W. Luo, and L. G. Franquelo, “Event-triggering dissipative control of switched stochastic systems via sliding mode,” Automatica, vol. 103, pp. 261–273, May 2019, doi: 10.1016/j.automatica.2019.01.029.
S. Mobayen, O. Mofid, S. U. Din, and A. Bartoszewicz, “Finite-Time Tracking Controller Design of Perturbed Robotic Manipulator Based on Adaptive Second-Order Sliding Mode Control Method,” IEEE Access, vol. 9, pp. 71159–71169, 2021, doi: 10.1109/access.2021.3078760.
T. N. Truong, A. T. Vo, and H.-J. Kang, “Neural network-based sliding mode controllers applied to robot manipulators: A review,” Neurocomputing, vol. 562, p. 126896, Dec. 2023, doi: 10.1016/j.neucom.2023.126896.
E. A. Alandoli and T. S. Lee, “A Critical Review of Control Techniques for Flexible and Rigid Link Manipulators,” Robotica, vol. 38, no. 12, pp. 2239–2265, May 2020, doi: 10.1017/s0263574720000223.
S. Jung, “Improvement of Tracking Control of a Sliding Mode Controller for Robot Manipulators by a Neural Network,” International Journal of Control, Automation and Systems, vol. 16, no. 2, pp. 937–943, Apr. 2018, doi: 10.1007/s12555-017-0186-z.
A. S. Poznyak, A. V. Nazin, and H. Alazki, “Integral Sliding Mode Convex Optimization in Uncertain Lagrangian Systems Driven by PMDC Motors: Averaged Subgradient Approach,” IEEE Transactions on Automatic Control, vol. 66, no. 9, pp. 4267–4273, Sep. 2021, doi: 10.1109/tac.2020.3032088.
B. Özyer “Adaptive fast sliding neural control for robot manipulator,” Turkish Journal of Electrical Engineering and Computer Sciences, vol. 28, no. 6, Nov. 2020, doi: 10.3906/elk-2001-129.
O. Eray and S. Tokat, “The design of a fractional-order sliding mode controller with a time-varying sliding surface,” Transactions of the Institute of Measurement and Control, vol. 42, no. 16, pp. 3196–3215, Aug. 2020, doi: 10.1177/0142331220944626.
V. Utkin, J. Guldner, and J. Shi. Sliding Mode Control in Electro-Mechanical Systems. CRC Press, 2017, doi: 10.1201/9781420065619.
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