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Adaptive iterative learning control for robot manipulators. (English) Zbl 1051.93038

Summary: We propose some adaptive iterative learning control (ILC) schemes for trajectory tracking of rigid robot manipulators, with unknown parameters, performing repetitive tasks. The proposed control schemes are based upon the use of a proportional-derivative (PD) feedback structure, for which an iterative term is added to cope with the unknown parameters and disturbances. The control design is very simple in the sense that the only requirement on the PD and learning gains is the positive definiteness condition and the bounds of the robot parameters are not needed. In contrast to classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the second controller proposed in this paper uses just two iterative variables, which is an interesting fact from a practical point of view since it contributes considerably to memory space saving in real-time implementations. We also show that it is possible to use a single iterative variable in the control scheme if some bounds of the system parameters are known. Furthermore, the resetting condition is relaxed to a certain extent for a certain class of reference trajectories. Finally, simulation results are provided to illustrate the effectiveness of the proposed controllers.

MSC:

93B51 Design techniques (robust design, computer-aided design, etc.)
93C85 Automated systems (robots, etc.) in control theory
93C40 Adaptive control/observation systems
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[1] Arimoto, S., Control theory of non-linear mechanical systems (1996), Oxford Science Publications: Oxford Science Publications Oxford, UK · Zbl 0857.93002
[2] Arimoto, S.; Kawamura, S.; Miyazaki, F., Bettering operation of robots by learning, Journal of Robotic Systems, 1, 123-140 (1984)
[3] Bondi, P.; Casalino, G.; Gambardella, L., On the iterative learning control theory for robotic manipulators, IEEE Journal of Robotics and Automation, 4, 1, 14-22 (1988)
[4] Cao, W.-J.; Xu, J.-X., On functional approximation of the equivalent control using learning variable structure control, IEEE Transactions on Automatic Control, 47, 5, 824-830 (2002) · Zbl 1364.93880
[5] Casalino, G., & Bartolini, G. (1984). A learning procedure for the control of movements of robotic manipulators. IASTED symposium on robotics and automation; Casalino, G., & Bartolini, G. (1984). A learning procedure for the control of movements of robotic manipulators. IASTED symposium on robotics and automation
[6] Choi, J. Y.; Lee, J. S., Adaptive iterative learning control for uncertain robotic systems, IEE-Proceedings Control Theory and Applications, 147, 2, 217-223 (2000)
[7] Craig, J. J. (1984). Adaptive control of manipulators through repeated trials. Proceedings of the American control conference; Craig, J. J. (1984). Adaptive control of manipulators through repeated trials. Proceedings of the American control conference
[8] De Luca, A.; Paesano, G.; Ulivi, G., A frequency domain approach to learning controlImplementation for a robot manipulator, IEEE Transactions On Industrial Electronics, 39, 1, 1-10 (1992)
[9] French, M.; Rogers, E., Nonlinear iterative learning by an adaptive Lyapunov technique, International Journal of Control, 73, 10, 840-850 (2000) · Zbl 1006.93596
[10] Ham, C.; Qu, Z.; Johnson, R., A nonlinear iterative learning control for robot manipulators in the presence of actuator dynamics, International Journal of Robotics and Automation, 15, 3, 119-130 (2000)
[11] Ham, C., Qu, Z. H., & Kaloust, J. H. (1995). Nonlinear learning control for a class of nonlinear systems based on Lyapunov’s direct method. Proceedings of the American control conference; Ham, C., Qu, Z. H., & Kaloust, J. H. (1995). Nonlinear learning control for a class of nonlinear systems based on Lyapunov’s direct method. Proceedings of the American control conference
[12] Horowitz, R., Learning control of robot manipulators, ASME Journal of Dynamic Systems Measurements and Control, 115, 402-411 (1993) · Zbl 0775.93151
[13] Kavli, T., Frequency domain synthesis of trajectory learning controller for robot manipulators, Journal of Robotic Systems, 9, 5, 663-680 (1992) · Zbl 0775.68021
[14] Kawamura, S.; Miyazaki, F.; Arimoto, S., Realization of robot motion based on a learning method, IEEE Transactions on Systems, man and cybernetics, 18, 1, 126-134 (1988)
[15] Kuc, T. Y.; Nam, K.; Lee, J. S., An iterative learning control of robot manipulators, IEEE Transactions on Robotics and Automation, 7, 6, 835-841 (1991)
[16] Moon, J. H., Doh, T. Y., & Chung, M. J. (1997). An iterative learning control scheme for manipulators. In Proceedings of international conference on intelligent robots and systems; Moon, J. H., Doh, T. Y., & Chung, M. J. (1997). An iterative learning control scheme for manipulators. In Proceedings of international conference on intelligent robots and systems
[17] Slotine, J. J.; Li, W., On the adaptive control of robot manipulators, International Journal of Robotics Research, 6, 49-59 (1987)
[18] Slotine, J. J.; Li, W., Applied nonlinear control (1991), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0753.93036
[19] Spong, M. W.; Vidyasagar, M., Robot dynamics and control (1989), Wiley: Wiley New York
[20] Takegaki, M.; Arimoto, S., A new feedback method for dynamic control of manipulators, Journal of Dynamic Systems, Measurement and Control, 103, 119-125 (1981) · Zbl 0473.93012
[21] Tomei, P., Adaptive PD controller for robot manipulators, IEEE Transactions on Robotics and Automation, 7, 565-570 (1991)
[22] Xu, J.-X., The frontiers of iterative learning control—Part II, Journal of Systems, Control and Information, 46, 5, 233-243 (2002)
[23] Xu, J.-X.; Badrinath, V.; Qu, Z., Robust learning control for robotic manipulators with an extension to a class of nonlinear systems, International Journal of Control, 73, 10, 858-870 (2000) · Zbl 1006.93557
[24] Xu, J.-X.; Tan, Y., A suboptimal learning control scheme for nonlinear systems with time-varying parametric uncertainties, Journal of Optimal Control-Applications and Theory, 22, 111-126 (2001) · Zbl 1069.93510
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