Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-22T05:22:44.128Z Has data issue: false hasContentIssue false

Iterative learning control with feedback using Fourier series with application to robot trajectory tracking

Published online by Cambridge University Press:  09 March 2009

Jong-Woon Lee
Affiliation:
Department of Electrical EngineeringKorea Advanced Institute of Science and Technology373–1 Kusong-dongYusong-ku, Taejeon, 305–701 (Korea)
Hak-Sung Lee
Affiliation:
Department of Electrical EngineeringKorea Advanced Institute of Science and Technology373–1 Kusong-dongYusong-ku, Taejeon, 305–701 (Korea)
Zeungnam Bien
Affiliation:
Department of Electrical EngineeringKorea Advanced Institute of Science and Technology373–1 Kusong-dongYusong-ku, Taejeon, 305–701 (Korea)

Summary

The Fourier series is employed to approximate the input/output (I/O) characteristics of a dynamic system and, based on the approximation, a new learning control algorithm is proposed in order to find iteratively the control input for tracking a desired trajectory. The use of the Fourier series approximation of I/O renders at least a couple of useful consequences: the frequency characteristics of the system can be used in the controller design and the reconstruction of the system states is not required. The convergence condition of the proposed algorithm is provided and the existence and uniqueness of the desired control input is discussed. The effectiveness of the proposed algorithm is illustrated by computer simulation for a robot trajectory tracking. It is shown that, by adding a feedback term in learning control algorithm, robustness and convergence speed can be improved.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1993

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

1.Arimoto, S., Kawamura, S. and Miyazaki, F., “Bettering Operation of Robots by Learning“, J. Robotic System 1 (2), 123140 (1984).Google Scholar
2.Sugie, T. and Ono, T., “On a Learning Control LawSystem and Control 31 (2), 129135 (1987).Google Scholar
3.Bien, Z. and Huh, K.M., “Higher Order Iterative Learning Control AlgorithmIEE Proc. Part. D. 136 (3), 105112 (1989).CrossRefGoogle Scholar
4.Oh, S.R., Bien, Z. and Suh, I.H., “An Iterative Learning Control Method with Application for the Robot ManipulatorIEEE J. Robotics and Automation 4 (5), 508514 (1988).CrossRefGoogle Scholar
5.Hwang, D.H., Bien, Z. and Oh, S.R., “A Note on Iterative Learning Control Method for Discrete-Time Dynamic SystemIEE Proc. Part. D. 138 (2), 139144 (1991).CrossRefGoogle Scholar
6.Bien, Z., Hwang, D.H. and Oh, S.R., “A Nonlinear Iterative Learning Method for Robot Path ControlRobotica 9 387392 (1991).CrossRefGoogle Scholar
7.Porter, B. and Mohamed, S.S., “Iterative Learning Control of Partially Irregular Multivariate Plants with Initial Impulsive ActionInt. J. System Science 22 (3), 447454 (1991).Google Scholar
8.Craig, J.J., Adaptive Control of Mechanical Manipulators (Addison-Wesley Publishing Co., New York, NY, USA, 1988).Google Scholar
9.Togai, M. and Yamano, O., “Analysis and Design of an Optimal Control Scheme for Industrial Robots: A Discrete System Approach” Proc. 24th IEEE Conf. on Decision and Control (Ft. Lauderdale, FL, 12. 11–13, 1985) pp. 13991404.Google Scholar
10.Ishihara, T., Abe, K. and Takeda, H., “A design of discrete time repetitive control systemsTrans. Soc. Instrum. Contr. Eng. 21(1), 4349 (1986).Google Scholar
11.Lee, K.H. and Bien, Z., “Initial Condition Problem of Learning ControlIEE Proc. Part. D. 138 (6), 525528 (1991).CrossRefGoogle Scholar
12.Heinzinger, G., Fenwick, D., Paden, B. and Miyazaki, F., “Stability of Learning Control with Disturbances and Uncertain Initial ConditionsIEEE Tr. on Automatic Control 37 (1), 110114 (1992).CrossRefGoogle Scholar
13.Hauser, J.E., “Learning Control for a Class of Nonlinear Systems” Proc. 26-th IEEE Conf. Decision and Control (Los Angeles, CA, USA 1987) pp. 859860.Google Scholar
14.Arimoto, S., “Learning Control Theory for Robot MotionInt. J. Adaptive Control and Signal Processing 4 (6), 543564 (1990).CrossRefGoogle Scholar
15.Arimoto, S., “Learning For Skill Refinement in Robotic SystemsIEICE Tr. E74 (2), 235243 (1991).Google Scholar
16.Bondi, P., Casalina, G. and Gambardella, L., “On the Iterative Learning Control Theory for Robotic ManipulatorsIEEE J. Robotics and Automation, 4 (1), 1421 (1988).CrossRefGoogle Scholar
17.Lunde, E. and Balchen, J.G., “Practical Trajectory Learning Algorithms for Robot Manipulators” IEEE Conf. on Robots and Automation (05 13–18, 1990, Cincinnati, USA) pp. 15161521.Google Scholar
18.Lee, H. and Bien, Z., “Method of Computing the Inverse of a Matrix Whose Elements are a Linear Combination of Walsh functionsInt. J. Control 47 (5), 12351242 (1988).CrossRefGoogle Scholar
19.Lewis, F.L. and Mertzios, B.G., “Analysis of Singular Systems Using Orthogonal FunctionsIEEE Tr. on Automatic Control 32 (6), 527530 (1987).CrossRefGoogle Scholar
20.Razzaghi, M. and Arabshahi, A., “Analysis of Linear time-varying Systems and Bilinear Systems via Fourier SeriesInt. J. Control 50 (3), 889898 (1989).Google Scholar
21.Barnett, S., Matrices in Control Theory (Van Nostrand Reinhold, London, UK, 1971).Google Scholar
22.Kreyszig, E., Advanced Engineering Mathematics, 5-th Ed. (John Wiley and Sons, New York, NY, USA, 1983).Google Scholar
23.Chen, C.T., Linear System Theory and Design (CBS Publishing, New York, NY, USA, 1984).Google Scholar
24.Goodwin, G.C. and Sin, K.S., Adaptive Filtering, Prediction and Control (Prentice-Hall Inc., New Jersey, USA, 1984).Google Scholar
25.Craig, J.J., Introduction to Robotics: Mechanics and Control (Addison-Wesley Publishing Co., Reading, Massachusetts, USA, 1986).Google Scholar
26.Simon, D. and Isik, C., “Optimal Trigonometric Robot Joint TrajectoriesRobotica 9 379386 (1991).CrossRefGoogle Scholar
27.Hostetter, G.H., “Recursive Discrete Fourier TransformIEEE Tr. ASSP 28 (2), 184190 (1980).CrossRefGoogle Scholar
28.Bitmead, R.R., Tsoi, A.C. and Parker, P.J., “A Kalman Filtering Approach to Short-time Fourier AnalysisIEEE Tr. ASSP 34 (6), 14931501 (1986).CrossRefGoogle Scholar
29.Peyton Jones, J.C. and Billings, S.A., “Recursive Algorithm for Computing the Frequency Response of a Class of Nonlinear Difference Equation ModelInt. J. Control 50 (5), 19251940 (1989).Google Scholar
30.Nagurta, M.L. and Yen, V., “Fourier-Based Optimal Control of Nonlinear Dynamic SystemsTr. ASME J. Dynamic Systems, Measurement and Control 112, 1726 (06 1990).CrossRefGoogle Scholar