Hostname: page-component-5b777bbd6c-gtgcz Total loading time: 0 Render date: 2025-06-21T22:20:51.416Z Has data issue: false hasContentIssue false
  • English
  • Français

An Adaptive Regressor-Free Fourier Series-Based Tracking Controller for Robot Manipulators: Theory and Experimental Evaluation

Published online by Cambridge University Press:  17 February 2021

Jorge Villalobos-Chin Open the ORCID record for Jorge Villalobos-Chin [Opens in a new window]  and
Víctor Santibáñez
Jorge Villalobos-Chin*
Affiliation:
Tecnológico Nacional de México/Instituto Tecnológico de la Laguna, Apdo. Postal 49, Adm. 1, Torreón, Coahuila27000, Mexico, E-mail: vsantiba@itlalaguna.edu.mx
Víctor Santibáñez
Affiliation:
Tecnológico Nacional de México/Instituto Tecnológico de la Laguna, Apdo. Postal 49, Adm. 1, Torreón, Coahuila27000, Mexico, E-mail: vsantiba@itlalaguna.edu.mx
*
*Corresponding author. E-mail: jorgevillaloboschin@hotmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

In this article, we propose a nonlinear Proportional+Derivative (PD) tracking controller with adaptive Fourier series compensation. The proposed controller uses a regressor-free adaptive scheme that relies on a trigonometric polynomial with varying coefficients to solve the control problem. Asymptotic convergence of the position and velocity errors is proven via a formal stability analysis based on Lyapunov and LaSalle theory for discontinuous systems. The proposed controller is validated on a 2-degrees of freedom robot manipulator. The experimental results validate the theoretically obtained results and reflect the effect of certain parameters in the transient behavior of the error dynamics. Certain robustness properties are also observed.

Keywords

FourierRobotic manipulatorAdaptive controlDiscontinuous control
Type
Reply
Information
Robotica , Volume 39 , Issue 11 , November 2021 , pp. 1981 - 1996
Copyright
© The Author(s), 2021. 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.)

Article purchase

Temporarily unavailable

Footnotes

†

This project was partially supported by Conacyt and TecNM Projects.

References

Kelly, R., Santibáñez, V. and Loría, A., Control of Robot Manipulators in Joint Space (Springer, London, 2005).Google Scholar
Khorashadizadeh, S. and Majidi, M.-H., “Chaos synchronization using the Fourier series expansion with application to secure communications,” AEU Int. J. Electron. Commun. 82, 37–44 (2017).CrossRefGoogle Scholar
Tsai, Y.-C. and Huang, A.-C., “Fat-based adaptive control for pneumatic servo systems with mismatched uncertainties,” Mech. Syst. Signal Process. 22(6), 1263–1273 (2008).CrossRefGoogle Scholar
Khorashadizadeh, S. and Fateh, M. M., “Adaptive Fourier Series-Based Control of Electrically Driven Robot Manipulators,” The 3rd International Conference on Control, Instrumentation, and Automation (2013).CrossRefGoogle Scholar
Labiod, S., Boubertakh, H. and Guerra, T., “Fourier Series-Based Adaptive Tracking Control for Robot Manipulators,” 3rd International Conference on Systems and Control (2013).CrossRefGoogle Scholar
Huang, A., Wu, S. and Ting, W., “A FAT-based adaptive controller for robot manipulators without regressor matrix: Theory and experiments,” Robotica 24(2), 205–210 (2006).CrossRefGoogle Scholar
Huang, A.-C. and Chen, Y.-C., “Adaptive sliding control for single-link flexible-joint robot with mismatched uncertainties,” IEEE Trans. Control Syst. Tech. 12(5), 770–775 (2004).CrossRefGoogle Scholar
Zarei, R. and Khorashadizadeh, S., “Direct adaptive model-free control of a class of uncertain nonlinear systems using Legendre polynomials,” Trans. Inst. Meas. Control 41(11), 3081–3091 (2019).CrossRefGoogle Scholar
Huang, A. and Chien, M., Adaptive Control of Robot Manipulators: A Unified Regressor-Free Approach (World Scientific Publications, Singapore, 2010).Google Scholar
Kai, C. and Huang, A., “A regressor-free adaptive controller for robot manipulators without Slotine and Li’s modification,” Robotica 31(7), 1051–1058 (2013). doi: 10.1017/S0263574713000301.CrossRefGoogle Scholar
Gholipour, R. and Fateh, M. M., “Observer-Based Robust Task-Space Control of Robot Manipulators Using Legendre Polynomial,” 2017 Iranian Conference on Electrical Engineering (ICEE), Tehran (2017) pp. 766–771.CrossRefGoogle Scholar
Gholipour, R. and Fateh, M. M., “Adaptive task-space control of robot manipulators using the Fourier series expansion without task-space velocity measurements,” Measurement 123, 285–292 (2018).CrossRefGoogle Scholar
Chien, M. and Huang, A., “FAT-Based Adaptive Visual Servoing for Robots with Time Varying Uncertainties,” 2009 IEEE International Conference on Robotics and Automation, Kobe (2009) pp. 3700–3705.Google Scholar
Puga-Guzmán, S., Moreno-Valenzuela, J. and Santibáñez, V., “Adaptive neural network motion control of manipulators with experimental evaluations,” Sci. World J. 2014, 1–13 (2014).Google Scholar
Rudin, W., Principles of Mathematical Analysis (McGraw-Hill Book Company, New York, 1976).Google Scholar
Wilcox, H. J. and Myers, D. L., An Introduction to Lebesgue Integration and Fourier Series (Dover Publication, New York, 2009).Google Scholar
Bacciotti, A. and Rosier, L., Liapunov Functions and Stability in Control Theory (Springer, Berlin Heidelberg, 2005).CrossRefGoogle Scholar
Orlov, Y. V., Discontinuous Systems: Lyapunov Analysis and Robust Synthesis Under Uncertainty Conditions (Springer, London, 2009).Google Scholar
Fischer, N., Kamalapurkar, R. and Dixon, W. E., “Lasalle-Yoshizawa corollaries for nonsmooth systems,” IEEE Trans. Autom. Control 58(9), 2333–2338 (2013).Google Scholar
Guo, Z. and Huang, L., “Generalized Lyapunov method for discontinuous systems,” Nonlinear Anal. Theory Methods Appl. 71(7–8), 3083–3092 (2009).CrossRefGoogle Scholar
Reyes, F. and Kelly, R., “Experimental evaluation of identification schemes on a direct drive robot,” Robotica 15(5), 563–571 (1997).CrossRefGoogle Scholar
Reyes, F. and Kelly, R., “Experimental evaluation of model-based controllers on a direct-drive robot arm,” Mechatronics 11(3), 267–282 (2001).CrossRefGoogle Scholar
Zavala-Río, A., Mendoza, M., Santibáñez, V. and Reyes, F., “An output-feedback PID-type global regulator for robot manipulators with bounded inputs,” IFAC-PapersOnLine 48(19), 87–93 (2015), 11th IFAC Symposium on Robot Control SYROCO 2015.CrossRefGoogle Scholar
Campa, R., Kelly, R. and Santibañez, V., “Windows-based real-time control of direct-drive mechanisms: Platform description and experiments,” Mechatronics 14(9), 1021–1036 (2004).CrossRefGoogle Scholar