Abstract
To improve control performance in robotic systems with faults and unknown uncertainties, a fault-tolerant control (FTC) system based on a wavelet type-2 fuzzy brain emotional learning controller (WT2FBC) is developed in this research. Type-2 fuzzy logic systems can handle uncertainties better than type-1 fuzzy logic systems, so they can solve some uncertain complex problems more accurate. Given its fast learning and problem-solving capabilities, the proposed WT2FBC is an important fuzzy neural network. The next step is to investigate how a WT2FBC-based FTC system can help solve the puzzles that plague the robotic systems. To achieve FTC, a control system with a computed torque controller and the WT2FBC estimator is provided. If the robotic system ever exhibits faults, it can consult an online fault estimator built on WT2FBC, and then compensates the faults. For more efficient, the total number of fuzzy rules of WT2FBC can be dynamically adjusted using a self-organizing algorithm based on the technique for order of preference by similarity to ideal solution. Simulations of a biped robot and a two-link manipulator robot have demonstrated the effectiveness of the proposed control algorithm.
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References
Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M., Schröder, J.: Diagnosis and Fault-Tolerant Control. Springer, New York (2006)
Khalastchi, E., Kalech, M.: On fault detection and diagnosis in robotic systems. ACM Comput. Surv. 51(1), 1–24 (2018)
Hwang, C.-L., Yu, W.-S.: Tracking and cooperative designs of robot manipulators using adaptive fixed-time fault-tolerant constraint control. IEEE Access 8, 56415–56428 (2020)
Zhang, Y., Zhu, W., Rosendo, A.: QR code-based self-calibration for a fault-tolerant industrial robot arm. IEEE Access 7, 73349–73356 (2019)
Wu, H.-M., Karkoub, M.: Hierarchical fuzzy sliding-mode adaptive control for the trajectory tracking of differential-driven mobile robots. Int. J. Fuzzy Syst. 21(1), 33–49 (2019)
Li, K., Wen, R.: Robust control of a walking robot system and controller design. Procedia Eng. 174, 947–955 (2017)
Taherkhorsandi, M., Mahmoodabadi, M., Talebipour, M., Castillo-Villar, K.: Pareto design of an adaptive robust hybrid of PID and sliding control for a biped robot via genetic algorithm optimization. Nonlinear Dyn. 79(1), 251–263 (2015)
Gil, C.R., Calvo, H., Sossa, H.: Learning an efficient gait cycle of a biped robot based on reinforcement learning and artificial neural networks. Appl. Sci. 9(3), 502 (2019)
Fuentes-Alvarez, R., et al.: Assistive robotic exoskeleton using recurrent neural networks for decision taking for the robust trajectory tracking. Expert Syst. Appl. 193, 116482 (2022)
Lin, J.-L., Hwang, K.-S., Jiang, W.-C., Chen, Y.-J.: Gait balance and acceleration of a biped robot based on Q-learning. IEEE Access 4, 2439–2449 (2016)
Lin, C.-M., Ramarao, R., Gopalai, S.-H.: Self-organizing adaptive fuzzy brain emotional learning control for nonlinear systems. Int. J. Fuzzy Syst. 21(7), 1989–2007 (2019)
Huynh, T.T., Lin, C.M., Le, T.L., Vu, V.P., Chao, F.: Self-organizing double function-link fuzzy brain emotional control system design for uncertain nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. 52(3), 1852–1868 (2020)
Lin, C.-M., Chen, C.-H.: Robust fault-tolerant control for a biped robot using a recurrent cerebellar model articulation controller. IEEE Trans. Syst. Man Cybern. 37(1), 110–123 (2007)
Lin, C.-M., Boldbaatar, E.-A.: Fault accommodation control for a biped robot using a recurrent wavelet Elman neural network. IEEE Syst. J. 11(4), 2882–2893 (2015)
Sabzehzar, A., Shan, W., Panahi, M.S., Saremi, O.: An improved extended classifier system for the real-time-input real-time-output (XCSRR) stability control of a biped robot. Procedia Comput. Sci. 61, 492–499 (2015)
Zhang, S., Yang, P., Kong, L., Chen, W., Fu, Q., Peng, K.: Neural networks-based fault tolerant control of a robot via fast terminal sliding mode. IEEE Trans. Syst. Man Cybern. Syst. 51(7), 4091–4101 (2021)
Furukawa, J.-I., Noda, T., Teramae, T., Morimoto, J.: Fault tolerant approach for biosignal-based robot control. Adv. Robot. 29(7), 505–514 (2015)
Vemuri, A.T., Polycarpou, M.M.: Neural-network-based robust fault diagnosis in robotic systems. IEEE Trans. Neural Netw. 8(6), 1410–1420 (1997)
Nguyen, V.-C., Vo, A.-T., Kang, H.-J.: A finite-time fault-tolerant control using non-singular fast terminal sliding mode control and third-order sliding mode observer for robotic manipulators. IEEE Access 9, 31225–31235 (2021). https://doi.org/10.1109/ACCESS.2021.3059897
Wu, Y., Yao, L.: Fault diagnosis and fault tolerant control for manipulator with actuator multiplicative fault. Int. J. Control Automat. Syst. 19, 980–987 (2021)
LeDoux, J.E., Phelps, E.: A: Emotional networks in the brain. In: Lewis, M., Haviland-Jones, J.M., Barrett, L.F. (eds.) Handbook of Emotions, pp. 159–179. Guilford Press, New York (2008)
Dolan, R.J.: The human amygdala and orbital prefrontal cortex in behavioural regulation. Philos. Trans. R. Soc. Lond. B Biol. Sci. 362(1481), 787–799 (2007)
Moren, J.: Emotion and learning: a computational model of the amygdala. Cybern. Syst. 32(6), 611–636 (2001)
Guo, G.L., Lin, C.M., Cho, H.Y., Pham, D.H., Huynh, T.T., Chao, F.: Decoupled sliding mode control of underactuated nonlinear systems using a fuzzy brain emotional cerebellar model control system. Int. J. Fuzzy Syst. 25, 15–28 (2022). https://doi.org/10.1007/s40815-022-01378-w
Nguyen, H.B., Lin, C.M., Huynh, T.T., Cho, H.Y., Pham, D.H., Chao, F., Thanh, H.L.N.N.: Fuzzy hybrid neural network control for uncertainty nonlinear systems based on enhancement search algorithm. Int. J. Fuzzy Syst. (2022). https://doi.org/10.1007/s40815-022-01374-0
Lin, C.-M., Pham, D.-H., Huynh, T.-T.: Encryption and decryption of audio signal and image secure communications using chaotic system synchronization control by tsk fuzzy brain emotional learning controllers. IEEE Trans. Cybern. (2022). https://doi.org/10.1109/TCYB.2021.3134245
Lin, C.-M., Pham, D.-H., Huynh, T.-T.: Synchronization of chaotic system using a brain-imitated neural network controller and its applications for secure communications. IEEE Access 9, 75923–75944 (2021). https://doi.org/10.1109/ACCESS.2021.3080696
Zhou, H., Zhang, Y., Duan, W., Zhao, H.: Nonlinear systems modelling based on self-organizing fuzzy neural network with hierarchical pruning scheme. Appl. Soft Comput. 95, 106516 (2020)
Huynh, T.-T., Lin, C.-M., Le, T.-L., Cho, H.-Y., Pham, T.-T.T., Chao, F.: A new self-organizing fuzzy cerebellar model articulation controller for uncertain nonlinear systems using overlapped Gaussian membership functions. IEEE Trans. Ind. Electron. 67(11), 9671–9682 (2019)
Huynh, T.-T., Le, T.-L., Lin, C.-M.: A TOPSIS multi-criteria decision method-based intelligent recurrent wavelet CMAC control system design for MIMO uncertain nonlinear systems. Neural Comput. Appl. 32(8), 4025–4043 (2020)
Mendel, J.: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Englewood Cliffs (2001)
Sun, M.: A Barbalat-like lemma with its application to learning control. IEEE Trans. Autom. Control 54(9), 2222–2225 (2009)
Pham, D.-H., Lin, C.-M., Giap, V.N., Huynh, T.-T., Cho, H.-Y.: Wavelet interval type-2 Takagi-Kang-Sugeno hybrid controller for time-series prediction and chaotic synchronization. IEEE Access 10, 104313–104327 (2022). https://doi.org/10.1109/ACCESS.2022.3210260
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This research was supported by the Ministry of Science and Technology of Taiwan, under Grant: MOST 109-2221-E-155-027-MY3.
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Pham, DH., Huynh, TT. & Lin, CM. Fault-Tolerant Control for Robotic Systems Using a Wavelet Type-2 Fuzzy Brain Emotional Learning Controller and a TOPSIS-Based Self-organizing Algorithm. Int. J. Fuzzy Syst. 25, 1727–1741 (2023). https://doi.org/10.1007/s40815-023-01516-y
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DOI: https://doi.org/10.1007/s40815-023-01516-y