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Robust adaptive controller–observer scheme for robot manipulators: a Bernstein–Stancu approach

Published online by Cambridge University Press:  28 September 2021

Alireza Izadbakhsh Open the ORCID record for Alireza Izadbakhsh [Opens in a new window]  and
Nazila Nikdel
Alireza Izadbakhsh*
Affiliation:
Department of Electrical Engineering, Garmsar Branch, Islamic Azad University, Garmsar, Iran
Nazila Nikdel
Affiliation:
Faculty of Electrical and Computer Engineering, Urmia University, Urmia, Iran
*
*Corresponding author. E-mail: izadbakhsh_alireza@hotmail.com
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Abstract

This article introduces a robust adaptive controller–observer structure for robotic manipulators such that the need for joints speed measurement is removed. Besides, it is presumed that the system model has uncertainties and is subject to disturbances, and the proposed method must eliminate the impact of these factors on the system response. According to this, for the first time in the robotics field, a model-free scheme is developed based on the Bernstein–Stancu polynomial. The universal approximation property of the Bernstein–Stancu polynomial enables it to accurately estimate the lumped uncertainty, including unmodeled dynamics and disturbances. Moreover, to increase the efficiency of the controller–observer structure, adaptive rules have been proposed to update polynomial coefficients. The boundedness of all system errors is proven using the Lyapunov theorem. Finally, the proposed robust Adaptive controller–observer is applied on a planer robot, and the results are precisely analyzed. The results of the proposed approach are also compared with two state-of-art powerful approximation methods.

Keywords

function approximation techniquesBernstein–Stancu operatorcontroller–observer structureadaptive control
Type
Research Article
Information
Robotica , Volume 40 , Issue 5 , May 2022 , pp. 1309 - 1325
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Kali, Y., Saad, M. and Benjelloun, K., Optimal super-twisting algorithm with time delay estimation for robot manipulators based on feedback linearization. Robot Auton Syst. 108, 87–99 (2018). https://doi.org/10.1016/j.robot.2018.07.004.CrossRefGoogle Scholar
Silva, F. F. and Adorno, B. V., Whole-body control of a mobile manipulator using feedback linearization and dual quaternion algebra. J Intell Robot Syst. 91(2), 249–262 (2018). https://doi.org/10.1007/s10846-017-0686-3.CrossRefGoogle Scholar
Taira, Y., Sagara, S. and Oya, M., Model-based motion control for underwater vehicle-manipulator systems with one of the three types of servo subsystems. Artif Life Robotics. 25(1), 133–148 (2020). https://doi.org/10.1007/s10015-019-00564-8.CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., Single-loop PID controller design for electrical flexible-joint robots. J Braz. Soc. Mech. Sci. Eng. 42, 91 (2020). https://doi.org/10.1007/s40430-020-2172-25.CrossRefGoogle Scholar
Izadbakhsh, A., Khorashadizadeh, S. and Kheirkhahan, P., Real-time Fuzzy Fractional-order control of Electrically driven flexible-joint robots, AUT Journal of Modeling, and Simulation, (2018). DOI: 10.22060/MISCJ.2018.13523.5075.Google Scholar
Izadbakhsh, A. and Khorashadizadeh, S., Neural control of robot manipulators considering motor voltage saturation: performance evaluation and experimental validation, COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 40(1), 27–29 (2021). https://doi.org/10.1108/COMPEL-03-2020-0127.CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator, International Journal of Robust and Nonlinear Control 30, 2719–2735 (2020).CrossRefGoogle Scholar
Wang, X., Liu, X., Chen, L. and Hu, H., Deep-learning damped least squares method for inverse kinematics of redundant robots. Measurement 171, 108821 (2021). https://doi.org/10.1016/j.measurement.2020.108821.CrossRefGoogle Scholar
Xian, B., De Queiroz, M. S., Dawson, D. M. and McIntyre, M. L., Output feedback variable structure-like control of nonlinear mechanical systems. In 42nd IEEE Int. Conf. Decision and Control 1, 368–373 (2003). https://doi.org/10.1109/CDC.2003.1272589.CrossRefGoogle Scholar
Ortega, R., Perez, J. A., Nicklasson, P. J. and Sira-Ramirez, H. J., Passivity-based control of Euler-Lagrange systems: Mechanical, electrical and electromechanical applications. Springer Science & Business Media; 2013. https://doi.org/10.1007/978-1-4471-3603-3.Google Scholar
Antonelli, G., Caccavale, F., Chiaverini, S. and Villani, L., Tracking control for underwater vehicle-manipulator systems with velocity estimation. IEEE J. Ocean. Eng. 25(3), 399–413 (2000). https://doi.org/10.1109/48.855403.CrossRefGoogle Scholar
Yang, Z., Peng, J. and Liu, Y., Adaptive neural network force tracking impedance control for uncertain robotic manipulator based on nonlinear velocity observer. Neurocomputing 331, 263–280 (2019). https://doi.org/10.1016/j.neucom.2018.11.068.CrossRefGoogle Scholar
Tuan, D. M. and Hieu, P. D., Adaptive Position/Force Control for Robot Manipulators Using Force and Velocity Observer. J. Electr. Eng. Technol. 14(6), 2575–2582 (2019). https://doi.org/10.1007/s42835-019-00281-z.CrossRefGoogle Scholar
Shojaei, K., Kazemy, A. and Chatraei, A., An Observer-Based Neural Adaptive PID2 Controller for Robot Manipulators Including Motor Dynamics with a Prescribed Performance. IEEE/ASME Trans Mechatron 2020; https://doi.org/10.1109/TMECH.2020.3028968.Google Scholar
Van, M. and Ge, S. S., Adaptive fuzzy integral sliding mode control for robust fault tolerant control of robot manipulators with disturbance observer. IEEE Trans Fuzzy Syst. 2020; https://doi.org/10.1109/TFUZZ.2020.2973955.Google Scholar
Shang, Y., Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies. Appl. Math. Comput. 273, 1234–1245 (2016). https://doi.org/10.1016/j.amc.2015.08.115.Google Scholar
Shang, Y., Consensus of noisy multiagent systems with Markovian switching topologies and time-varying delays. Math. Probl. Eng. 2015, 1–13 (2015). https://doi.org/10.1155/2015/453072.Google Scholar
Hu, Y., Dian, S., Guo, R., Li, S. and Zhao, T., Observer-based dynamic surface control for flexible-joint manipulator system with input saturation and unknown disturbance using type-2 fuzzy neural network. Neurocomputing 436, 162–173 (2021). https://doi.org/10.1016/j.neucom.2020.12.121.CrossRefGoogle Scholar
Wu, Y., Huang, R., Li, X. and Liu, S., Adaptive neural network control of uncertain robotic manipulators with external disturbance and time-varying output constraints. Neurocomputing 323, 108–116 (2019). https://doi.org/10.1016/j.neucom.2018.09.072.CrossRefGoogle Scholar
Izadbakhsh, A. and Kheirkhahan, P., An alternative stability proof for “Adaptive Type-2 fuzzy estimation of uncertainties in the control of electrically flexible-joint robots”, Journal of Vibration and Control 25(5), 977–983 (2019).CrossRefGoogle Scholar
Haonan, S., Xingling, S. and Wendong, Z., Fuzzy rule-based neural appointed-time control for uncertain nonlinear systems with aperiodic samplings. Expert Syst Appl. 170, 114504 (2021). https://doi.org/10.1016/j.eswa.2020.114504.CrossRefGoogle Scholar
Izadbakhsh, A., Robust adaptive control of voltage saturated flexible joint robots with experimental evaluations, AUT Journal of Modeling, and Simulation 50(1), 31–38 (2018).Google Scholar
Kheirkhahan, P. and Izadbakhsh, A., Observer-based adaptive fractional-order control of flexible-joint robots using the Fourier series expansion: theory and experiment. J Braz Soc Mech Sci Eng. 42(10), 1–0 (2020). https://doi.org/10.1007/s40430-020-02590-1.CrossRefGoogle Scholar
Izadbakhsh, A., Kheirkhahan, P. and Khorashadizadeh, S., FAT-based robust adaptive control of electrically driven robots in interaction with environment, Robotica 37(5), 779–800 (2019). 12.CrossRefGoogle Scholar
Izadbakhsh, A., Khorashadizadeh, S. and Kheirkhahan, P. Tracking control of electrically driven robots using a model free observer. Robotica 37(4), 729–755 (2019).CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., Robust task-space control of robot manipulators using differential equations for uncertainty estimation. Robotica 35(9), 1923 (2017). https://doi.org/10.1017/S0263574716000588.CrossRefGoogle Scholar
Izadbakhsh, A., Akbarzadeh kalat, A. and Khorashadizadeh, S., (2021) Observer-based adaptive control for HIV infection therapy using the Baskakov operator, Biomedical Signal Processing and Control, 65.CrossRefGoogle Scholar
Izadbakhsh, A., FAT-based robust adaptive control of electrically driven robots without velocity measurements. Nonlinear Dynamics. 89(1), 289–304 (2017). https://doi.org/10.1007/s11071-017-3454-9.CrossRefGoogle Scholar
Stancu, D. D., Approximation of functions by a new class of linear polynomial operators. Rev. Roumaine Math. Pures Appl. 13(8), 1173–1194 (1968).Google Scholar
Izadbakhsh, A. and Khorashadizadeh, S., Polynomial-Based Robust Adaptive Impedance Control of Electrically Driven Robots. Robotica, 1–21 (2020). doi: 10.1017/S0263574720001009.Google Scholar
Dawson, D. M., Qu, Z. and Carroll, J. J., Tracking control of rigid-link electrically–driven robot manipulators. Int J Control. 56(5), 991–1006 (1992). https://doi.org/10.1080/00207179208934354.CrossRefGoogle Scholar
Shang, Y., Fixed-time group consensus for multi-agent systems with non-linear dynamics and uncertainties. IET Control Theory Appl. 12(3), 395–404 (2018). https://doi.org/10.1049/iet-cta.2017.1021.CrossRefGoogle Scholar
Izadbakhsh, A. and Rafiei, S. M. R., Endpoint perfect tracking control of robots – A robust non inversion-based approach, International Journal of Control, Automation, and Systems, Springer, 7(6), 888–898 (2009).CrossRefGoogle Scholar
Izadbakhsh, A. Khorashadizadeh, S. and Ghandali, S., Robust Adaptive Impedance Control of Robot Manipulators Using Szasz-Mirakyan Operator as universal Approximator, ISA Transactions 106, 1–11 (2020).CrossRefGoogle ScholarPubMed