Research Papers

Direct Adaptive Function Approximation Techniques Based Control of Robot Manipulators

[+] Author and Article Information
Majid Moradi Zirkohi

Department of Electrical Engineering,
Behbahan Khatam Alanbia University
of Technology,
Behbahan 6361647189, Iran
e-mail: moradi@bkatu.ac.ir

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 18, 2016; final manuscript received June 10, 2017; published online September 5, 2017. Assoc. Editor: Azim Eskandarian.

J. Dyn. Sys., Meas., Control 140(1), 011006 (Sep 05, 2017) (11 pages) Paper No: DS-16-1351; doi: 10.1115/1.4037269 History: Received July 18, 2016; Revised June 10, 2017

In this paper, a simple model-free controller for electrically driven robot manipulators is presented using function approximation techniques (FAT) such as Legendre polynomials (LP) and Fourier series (FS). According to the orthogonal functions theorem, LP and FS can approximate nonlinear functions with an arbitrary small approximation error. From this point of view, they are similar to fuzzy systems and can be used as controller to approximate the ideal control law. In comparison with fuzzy systems and neural networks, LP and FS are simpler and less computational. Moreover, there are very few tuning parameters in LP and FS. Consequently, the proposed controller is less computational in comparison with fuzzy and neural controllers. The case study is an articulated robot manipulator driven by permanent magnet direct current (DC) motors. Simulation results verify the effectiveness of the proposed control approach and its superiority over neuro-fuzzy controllers.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Li, Y. , Tong, S. , and Li, T. , 2012, “ Fuzzy Adaptive Dynamic Surface Control for a Single-Link Flexible-Joint Robot,” Nonlinear Dyn., 70(3), pp. 2035–2048. [CrossRef]
Moradi Zirkohi, M. , Fateh, M. M. , and Shoorehdeli, M. A. , 2013, “ Type-2 Fuzzy Control for a Flexible-Joint Robot Using Voltage Control Strategy,” Int. J. Autom. Comput., 10(3), pp. 242–255. [CrossRef]
Fateh, M. M. , and Khorashadizadeh, S. , 2012, “ Robust Control of Electrically Driven Robots by Adaptive Fuzzy Estimation of Uncertainty,” Nonlinear Dyn., 69(3), pp. 1465–1477. [CrossRef]
Puga-Guzmán, S. , Moreno-Valenzuela, J. , and Santibáñez, V. , 2014, “ Adaptive Neural Network Motion Control of Manipulators With Experimental Evaluations,” Sci. World J., 2014, p. 694706.
Zhai, D. H. , and Xia, Y. , 2016, “ Adaptive Fuzzy Control of Multilateral Asymmetric Teleoperation for Coordinated Multiple Mobile Manipulators,” IEEE Trans. Fuzzy Syst., 24(1), pp. 57–70. [CrossRef]
Tong, S. , Shuai, S. , and Yongming, Li. , 2015, “ Fuzzy Adaptive Output Feedback Control of MIMO Nonlinear Systems With Partial Tracking Errors Constrained,” IEEE Trans. Fuzzy Syst., 23(4), pp. 729–742. [CrossRef]
Khorashadizadeh, S. , and Fateh, M. M. , 2015, “ Uncertainty Estimation in Robust Tracking Control of Robot Manipulators Using the Fourier Series Expansion,” Robotica, 35(2), pp. 310–336. [CrossRef]
Khorashadizadeh, S. , and Mahdian, M. , 2016, “ Voltage Tracking Control of DC-DC Boost Converter Using Brain Emotional Learning,” Fourth International Conference on Control, Instrumentation, and Automation (ICCIA), Qazvin, Iran, Jan. 27–28, pp. 268–272.
Tsai, Y. C. , and Huang, A. C. , 2008, “ FAT-Based Adaptive Control for Pneumatic Servo Systems With Mismatched Uncertainties,” Mech. Syst. Signal Process., 22(6), pp. 1263–1273. [CrossRef]
Huang, A. C. , Wu, S. C. , and Ting, W. F. , 2006, “ A FAT-Based Adaptive Controller for Robot Manipulators Without Regressor Matrix: Theory and Experiments,” Robotica, 24(2), pp. 205–210. [CrossRef]
Chien, M. C. , and Huang, A. C. , 2012, “ Adaptive Impedance Controller Design for Flexible-Joint Electrically-Driven Robots Without Computation of the Regressor Matrix,” Robotica, 30(1), pp. 133–144. [CrossRef]
Chien, M. C. , and Huang, A. C. , 2010, “ Design of a FAT-Based Adaptive Visual Servoing for Robots With Time Varying Uncertainties,” Int. J. Optomechatronics, 4(2), pp. 93–114. [CrossRef]
Fard, M. B. , and Khorashadizadeh, S. , 2015, “ Model Free Robust Impedance Control of Robot Manipulators Using Fourier Series Expansion,” AI & Robotics (IRANOPEN), Qazvin, Iran. Apr. 12, pp. 1–7.
Wang, C. H. , Liu, H. L. , and Lin, T. C. , 2002, “ Direct Adaptive Fuzzy-Neural Control With State Observer and Supervisory Controller for Unknown Nonlinear Dynamical Systems,” IEEE Trans. Fuzzy Syst., 10(1), pp. 39–49. [CrossRef]
Hsueh, Y. C. , and Su, S. F. , 2012, “ Learning Error Feedback Design of Direct Adaptive Fuzzy Control Systems,” IEEE Trans. Fuzzy Syst., 20(3), pp. 536–545. [CrossRef]
Li, Y. , Liand, T. , and Jing, X. , 2014, “ Indirect Adaptive Fuzzy Control for Input and Output Constrained Nonlinear Systems Using a Barrier Lyapunov Function,” Int. J. Adapt. Control Signal Process., 28(2), pp. 184–199. [CrossRef]
Boulkroune, A. , Bounar, N. , and Farza, M. , 2014, “ Indirect Adaptive Fuzzy Control Scheme Based on Observer for Nonlinear Systems: A Novel SPR-Filter Approach,” Neurocomputing, 135, pp. 378–387. [CrossRef]
Kreyszig, E. , 2007, Advanced Engineering Mathematics, Wiley, New York. [PubMed] [PubMed]
Khorashadizadeh, S. , and Fateh, M. M. , 2015, “ Robust Task-Space Control of Robot Manipulators Using Legendre Polynomials for Uncertainty Estimation,” Nonlinear Dyn., 79(2), pp. 1151–1161. [CrossRef]
Khorashadizadeh, S. , and Fateh, M. M. , 2013, “ Adaptive Fourier Series-Based Control of Electrically Driven Robot Manipulators,” Third International Conference on Control, Instrumentation, and Automation (ICCIA), Tehran, Iran, Dec. 28–30, pp. 213–218.
Spong, M. W. , Hutchinson, S. , and Vidyasagar, M. , 2006, Robot Modelling and Control, Wiley, Hoboken, NJ.
Fateh, M. M. , Azargoshasb, S. , and Khorashadizadeh, S. , 2014, “ Model-Free Discrete Control for Robot Manipulators Using a Fuzzy Estimator,” COMPEL: Int. J. Comput. Math. Electr. Electron. Eng., 33(3), pp. 1051–1067. [CrossRef]
Wang, L. X. , 1994, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice Hall, Upper Saddle River, NJ.
Slotine, J. J. , and Li, W. , 1991, Applied Nonlinear Control, Vol. 199, Prentice Hall, Englewood Cliffs, NJ.
Fateh, M. M. , 2012, “ Robust Control of Flexible-Joint Robots Using Voltage Control Strategy,” Nonlinear Dyn., 67(2), pp. 1525–1537. [CrossRef]
Shahnazi, R. , Modir Shanechi, H. , and Pariz, N. , 2008, “ Position Control of Induction and DC Servomotors: A Novel Adaptive Fuzzy PI Sliding Mode Control,” IEEE Trans. Energy Convers., 23(1), pp. 138–147. [CrossRef]
Wai, R. J. , and Chen, P. C. , 2004, “ Intelligent Tracking Control for Robot Manipulator Including Actuator Dynamics Via TSK-Type Fuzzy Neural Network,” IEEE Trans. Fuzzy Syst., 12(4), pp. 552–559. [CrossRef]


Grahic Jump Location
Fig. 5

The tracking errors using FS

Grahic Jump Location
Fig. 6

The tracking performance using FS

Grahic Jump Location
Fig. 7

Motor voltages using FS

Grahic Jump Location
Fig. 1

The tracking errors using LP

Grahic Jump Location
Fig. 2

The tracking performance using LP

Grahic Jump Location
Fig. 3

Motor voltages using LP

Grahic Jump Location
Fig. 4

The tracking errors using LP in the presence of external disturbance

Grahic Jump Location
Fig. 8

The tracking errors using FS in the presence of external disturbance

Grahic Jump Location
Fig. 9

The tracking errors of fuzzy-neural network

Grahic Jump Location
Fig. 10

The control signals of fuzzy-neural network




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In