کنترل تطبیقی ​​یادگیری تکراری برای جرثقیل ربات: نتایج تجربی

In this paper, two adaptive iterative learning control schemes, proposed by A. Tayebi [2004, Automatica, 40(7), 1195–1203], are tested experimentally on a five-degrees-of-freedom (5-DOF) robot manipulator CATALYST5. The control strategy consists of using a classical PD feedback structure plus an additional iteratively updated term designed to cope with the unknown parameters and disturbances. The control implementation is very simple in the sense that the knowledge of the robot parameters is not needed, and the only requirement on the PD and learning gains is the positive definiteness condition. Furthermore, in contrast with classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the adaptive control schemes tested in this paper involve just one or two iterative variables.

It is well known that robot manipulators are generally used in repetitive tasks (e.g., automotive manufacturing industries). Therefore, it is interesting to take advantage of the fact that the reference trajectory is repeated over a given operation time. In this context, iterative learning control (ILC) techniques can be applied in order to enhance the tracking performance from operation to operation. Since the early works of Arimoto et al. (1984), Casalino and Bartolini (1984) and Craig (1984), several ILC schemes for robot manipulators have been proposed in the literature (see for instance Arimoto, 1996; Bondi et al., 1988; Luca et al., 1992; Horowitz, 1993 and Kavli, 1992; Kawamura et al., 1988; Moon et al., 1997). These ILC algorithms, whether developed for the linearized model or the nonlinear model, are generally based upon the contraction mapping approach and require a certain a priori knowledge of the system dynamics. On the other hand, another type of ILC algorithms have been developed using Lyapunov and Lyapunov-like methods. In fact in French and Rogers (2000), a standard Lyapunov design is used to solve ILC problems. The idea consists to use a standard adaptive controller and to start the parameter estimates with their final values obtained at the preceding iteration. In the same spirit, Choi and Lee (2000) proposed an adaptive ILC for uncertain robot manipulators, where the uncertain parameters are estimated along the time horizon whereas the repetitive disturbances are compensated along the iteration horizon. However, as in standard adaptive control design, this technique requires the unknown system parameters to be constant. In Ham et al. (1995), Ham et al. (2000), Kuc et al. (1991), Xu (2002), Xu et al. (2000) and Xu and Tan (2001), several ILC algorithms have been proposed based upon the use of a positive-definite Lyapunov-like sequence which is made monotonically decreasing along the iteration axis via a suitable choice of the control input. In contrast with the standard adaptive control, this technique is shown to be able to handle systems with time-varying parameters since the adaptation law in this case is nothing else but a discrete integration along the iteration axis. Based on this approach, Kuc et al. (1991) proposed an ILC scheme for the linearized robot manipulator model, while in (Ham et al., 2000; Xu et al., 2000) nonlinear ILC schemes have been proposed for the nonlinear model. Again these control laws require a certain a priori knowledge of the system dynamics. In Tayebi (2004), a simple ILC scheme, for the position tracking problem of rigid robot manipulators without any a priori knowledge on the system parameters, has been proposed. The control strategy consists of a PD term plus an additional iterative term introduced to cope with the unknown parameters and disturbances. The proof of convergence is based upon the use of a Lyapunov-like positive definite sequence, which is made monotonically decreasing through an adequate choice of the control law and the iterative adaptation rule. In contrast with classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the proposed control strategy uses one or two iterative variables, which is interesting from a practical point of view since it contributes considerably to memory space saving. In this framework, the acceleration measurements and the bounds of the robot parameters are not needed and the only requirement on the control gains is the positive definiteness condition. In this paper, we present some experimental results on a 5-DOF robot manipulator CATALYST5, confirming the effectiveness of the control strategy proposed in Tayebi (2004).

Two adaptive ILC schemes, proposed in Tayebi (2004), have been successfully tested on a 5-DOF robot manipulator CATALYST5. The control schemes consist of a PD feedback plus an additional adaptive term introduced to cope with the unknown parameters and disturbances. The overall control strategy is very simple to implement since no a priori knowledge of the robot parameters is needed, and the only requirement on the control gains is the positive definiteness condition. Another clear advantage of this approach is the fact that it uses just one or two iterative variables, which helps to reduce the memory space requirements in practical implementations. During our several tests, we noticed that the cut-off frequency of the low pass filter, used to generate the joint velocities from the joint positions, plays a crucial role. In fact, from a theoretical point of view, a high cut-off frequency would result in a good approximation of the derivative action and hence would lead to a good performance. However, according to our experiments, we noticed that at high cut-off frequencies the robot joints start to vibrate after a certain number of iterations forcing us to stop the learning process. This is mainly due to the fact that the noise amplification, caused by the derivative action, is accumulating through the iterative process (see Figs. 6, 7, 10 and 11). By gradually reducing the cut-off frequency, we noticed a considerable improvement in the tracking performance in terms of measurement noise rejection. However, a very low cut-off frequency would result in a bad approximation of the joint velocity and therefore the stability and convergence of the iterative process are not guaranteed any more. We also noticed that the convergence rates could be improved by increasing the learning gain as seen from the results of experiments 1 and 2. However, the noise level increases with the learning gain causing the joints to vibrate earlier in the iteration domain as evidenced by the two experiments. In fact, in the first experiment we had to stop the learning process at the 25th iteration while for the second experiment we were able to go to the 50th iteration without any problem. A potential solution to this crucial problem, related to the use of the filtered derivative also known as the “dirty derivative”, is to design P-type iterative parametric updating rules that do not require the joint velocities measurements. In this case, the noise effect will be reduced considerably, but will not be totally eliminated since the joint positions measurements are also noisy, and there will be an accumulation of noise from iteration to iteration. Consequently, it is important to stop the learning process after a certain number of iterations once the tracking error reaches a certain acceptable level. The theoretical implications of this crucial problem will be investigated in our future research work.