Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-30T05:19:44.331Z Has data issue: false hasContentIssue false
  • English
  • Français

FAT-based robust adaptive controller design for electrically direct-driven robots using Phillips q-Bernstein operators

Published online by Cambridge University Press:  15 March 2022

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

Abstract

This article proposes a robust and adaptive controller for industrial robot arms with multiple degrees of freedom without the need for velocity measurement. Many of the controllers designed for manipulators are model-based and require detailed knowledge of the system model. In contrast to these methods, this paper proposes a model-free controller using the Philips q-Bernstein operator as universal approximator. The designed controller can approximate uncertainties including external disturbances and unmodeled dynamics based on its universal approximation capability. Besides, most of the controllers revealed for robot arms are torque-based, which is not a realistic presumption from a practical point of view. In the proposed control method, the voltage applied to the actuator is considered as the control signal. However, unlike many voltage-based methods, the need to know the exact models of the system and the actuator has been eliminated in the presented method. Also, adaptive rules are extracted during the Lyapunov analysis to ensure system stability. Finally, to analyze the performance of the presented controller, this method is simulated for an industrial robot arm, and the results are analyzed. The proposed methodology is also compared to those of a strong state-of-the-art approximator, the Chebyshev neural network.

Keywords

function approximation techniqueindustrial manipulatoruncertaintiesPhilips q-Bernstein operatoradaptive controlChebyshev neural network
Type
Research Article
Information
Robotica , Volume 40 , Issue 10 , October 2022 , pp. 3415 - 3434
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Korayem, M. H., Nekoo, S. R. and Kazemi, S., “Finite-time feedback linearization (FTFL) controller considering optimal gains on mobile mechanical manipulators,” J. Intell. Robot. Syst. 94(3), 727–744 (2019).CrossRefGoogle Scholar
Dumlu, A., Erentürk, K., Kaleli, A. and Ayten, K. K., “A comparative study of two model-based control techniques for the industrial manipulator,” Robotica 35(10), 2036–2055 (2017).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 Robot. 25(1), 133–148 (2020).CrossRefGoogle Scholar
Izadbakhsh, A., Khorashadizadeh, S. and Kheirkhahan, P., “Real-time fuzzy fractional-order control of electrically driven flexible-joint robots,” AUT J. Model. Simul. 52(1) (2020). doi: 10.22060/MISCJ.2018.13523.5075.Google Scholar
Ahmed, S., Wang, H. and Tian, Y., “Adaptive fractional high-order terminal sliding mode control for nonlinear robotic manipulator under alternating loads,” Asian J. Control 23(4), 1900–1910 (2021).CrossRefGoogle Scholar
Li, C., Liu, F., Wang, Y. and Buss, M., “Concurrent learning-based adaptive control of an uncertain robot manipulator with guaranteed safety and performance,” IEEE Trans. Syst. Man Cybern. Syst. (2021). doi: 10.1109/TSMC.2021.3064971.Google Scholar
Khan, M. U. and Kara, T., “Adaptive control of a two-link flexible manipulator using a type-2 neural fuzzy system,” Arab. J. Sci. Eng. 45(3), 1949–1960 (2020).CrossRefGoogle Scholar
Chen, S., Zhao, Z., Zhu, D., Zhang, C. and Li, H. X., “Adaptive robust control for a spatial flexible Timoshenko manipulator subject to input dead-zone,” IEEE Trans. Syst. Man Cybern. Syst. 52(3), 1395–1404 (2022). doi: 10.1109/TSMC.2020.3020326.CrossRefGoogle Scholar
Shang, Y., Leader-following consensus problems with a time-varying leader under measurement noises (2011). arXiv preprint arXiv:0909.4349.Google Scholar
Izadbakhsh, A. and Nikdel, N., “Robust adaptive controller-observer scheme for robot manipulators: A Bernstein-Stancu approach,” Robotica 2015, 1–17 (2021). doi: 10.1017/S0263574721001120.Google Scholar
Abadi, A. S. S., Hosseinabadi, P. A. and Mekhilef, S., “Fuzzy adaptive fixed-time sliding mode control with state observer for a class of high-order mismatched uncertain systems,” Int. J. Control, Autom. Syst. 18(10), 2492–2508 (2020).CrossRefGoogle Scholar
Ahmed, S., Ahmed, A., Mansoor, I., Junejo, F. and Saeed, A., “Output feedback adaptive fractional-order super-twisting sliding mode control of robotic manipulator,” Iran. J. Sci. Technol. Trans. Electr. Eng. 45(1), 335–347 (2021).CrossRefGoogle Scholar
Liu, H., Sun, J., Nie, J. and Zou, L., “Observer-based adaptive second-order non-singular fast terminal sliding mode controller for robotic manipulators,” Asian J. Control 23(4), 1845–1854 (2021).CrossRefGoogle Scholar
Niu, B., Ahn, C. K., Li, H. and Liu, M., “Adaptive control for stochastic switched non lower triangular nonlinear systems and its application to a one-link manipulator,” IEEE Trans. Syst. Man Cybern. Syst. 48(10), 1701–1714 (2017).10.1109/TSMC.2017.2685638CrossRefGoogle Scholar
Fan, Y., An, Y., Wang, W. and Yang, C., “TS fuzzy adaptive control based on small gain approach for an uncertain robot manipulators,” Int. J. Fuzzy Syst. 22(3), 930–942 (2020).CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Polynomial-based robust adaptive impedance control of electrically driven robots,” Robotica 39, 1–21 (2020). doi: 10.1017/S0263574720001009.Google Scholar
Bao, J., Wang, H. and Xiaoping Liu, P., “Adaptive finite-time tracking control for robotic manipulators with funnel boundary,” Int. J. Adapt. Control Signal Process 34(5), 575–589 (2020).CrossRefGoogle Scholar
Truong, L. V., Huang, S. D., Yen, V. T. and Van Cuong, P., “Adaptive trajectory neural network tracking control for industrial robot manipulators with deadzone robust compensator,” Int. J. Control Autom. Syst. 18(9), 2423–2434 (2020).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,”” J. Vib. Control 25(5), 977–983 (2019).CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Neural control of robot manipulators considering motor voltage saturation: performance evaluation and experimental validation,” COMPEL - Int. J. Comput. Math. Electr. Electron. Eng. 40(1), 27–29 (2021). doi: 10.1108/COMPEL-03-2020-0127.CrossRefGoogle Scholar
Izadbakhsh, A. and Kheirkhahan, P., “On the voltage-based control of robot manipulators revisited,” Int. J. Control Autom. Syst. 16(4), 1887–1894 (2018).CrossRefGoogle Scholar
Izadbakhsh, A., “FAT-based robust adaptive control of electrically driven robots without velocity measurements,” Nonlinear Dyn. 89(1), 289–304 (2017).CrossRefGoogle Scholar
Izadbakhsh, A., Zamani, I. and Khorashadizadeh, S., “Szász-Mirakyan-based adaptive controller design for chaotic synchronization,” Int. J. Robust Nonlinear Control 31(5), 1689–1703 (2020).CrossRefGoogle 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), 1–10 (2020).CrossRefGoogle Scholar
Deylami, A. and Izadbakhsh, A., “FAT-based robust adaptive control of cooperative multiple manipulators without velocity measurement,” Robotica 25, 1–31 (2021). doi: 10.1017/S0263574721001338.Google Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Robust impedance control of robot manipulators using differential equations as universal approximator,” Int. J. Control 91(10), 2170–2186 (2018).CrossRefGoogle Scholar
Yang, T., Sun, N., Fang, Y., Xin, X. and Chen, H., “New adaptive control methods for n-link robot manipulators with online gravity compensation: design and experiments,” IEEE Trans. Ind. Electron. 69(1), 539–548 (2021).CrossRefGoogle Scholar
Beckers, T., Umlauft, J. and Hirche, S., “Stable model-based control with Gaussian process regression for robot manipulators,” IFAC-PapersOnLine 50(1), 3877–3884 (2017).CrossRefGoogle Scholar
Abooee, A., MoravejKhorasani, M. and Haeri, M., “Finite time control of robotic manipulators with position output feedback,” Int. J. Robust Nonlinear Control 27(16), 2982–2999 (2017).CrossRefGoogle Scholar
Zhang, H., Fang, H., Zou, Q. and Zhang, D., “Dynamic modeling and adaptive robust synchronous control of parallel robotic manipulator for industrial application,” Complexity 2020(11), 1–23 (2020). doi: 10.1155/2020/5640246.Google Scholar
Phillips, G. M., “Bernstein polynomials based on the q-integers, the heritage of P.L. Chebyshev,” Ann. Numer. Math. 4, 511–518 (1997).Google Scholar
Khan, K., Lobiyal, D. K. and Kilicman, A., A de Casteljau algorithm for Bernstein type polynomials based on (p,q)-integers, 2015). arXiv preprint arXiv:1507.04110.Google Scholar
Phillips, G. M., “A generalization of the Bernstein polynomials based on the q-integers,” ANZIAM J 42(1), 79–86 (2000).CrossRefGoogle Scholar
Izadbakhsh, A., Khorashadizadeh, S. and Ghandali, S., “Robust adaptive impedance control of robot manipulators using Szasz-Mirakyan operator as universal approximator,” ISA Trans. 106(5), 1–11 (2020).CrossRefGoogle ScholarPubMed
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).CrossRefGoogle Scholar
Spong, M. W., Hutchinson, S. and Vidyasagar, M.. Robot Modeling and Control, vol. 3 (Wiley, New York, 2006) pp. 75–118.Google Scholar
Izadbakhsh, A. and Fateh, M. M., “Robust Lyapunov-based control of flexible-joint robots using voltage control strategy,” Arabian J. Sci. Eng. 39(4), 3111–3121 (2014).CrossRefGoogle Scholar
Izadbakhsh, A., “Robust control design for rigid-link flexible-joint electrically driven robot subjected to constraint: Theory and experimental verification,” Nonlinear Dyn. 85(2), 751–765 (2016).CrossRefGoogle Scholar
Sciavicco, L. and Siciliano, B.. Modelling and Control of Robot Manipulators (Springer Science & Business Media, 2001).Google Scholar
Shang, Y., “Finite-time consensus for multi-agent systems with fixed topologies,” Int. J. Syst. Sci. 43(3), 499–506 (2012).CrossRefGoogle Scholar
Shang, Y., “Couple-group consensus of continuous-time multi-agent systems under Markovian switching topologies,” J. Franklin Inst. 352(11), 4826–4844 (2015).CrossRefGoogle Scholar
Huang, A. C. and Chien, M. C.. Adaptive Control of Robot Manipulators: A Unified Regressor-Free Approach (World Scientific, 2010).CrossRefGoogle Scholar
Patra, J. C. and Kot, A. C., “Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks,” IEEE Trans. Syst. Man Cybern. Syst. 32(4), 505–511 (2002).CrossRefGoogle ScholarPubMed
Purwar, S., Kar, I. N. and Jha, A. N., “Adaptive output feedback tracking control of robot manipulators using position measurements only,” Expert Syst. Appl. 34(4), 2789–2798 (2008).CrossRefGoogle Scholar
Stewart, G. W.. Introduction to Matrix Computations (Elsevier, 1973).Google Scholar