This paper develops a hybrid iterative learning control (ILC) algorithm which uses both tracking and contour errors as correction signals during the learning process. The tracking, contour and combined ILCs are first introduced and analyzed. A hybrid ILC is then proposed to predict contour errors based on the identified models and then used to determine whether the tracking or contour errors should be utilized for the correction signals. The criteria for selecting different signals are based on the predicted root mean square (RMS) value of the contour errors for non-uniform rational B-spline (NURBS) curves. Simulations performed on a butterfly trajectory represented by NURBS curves show that the hybrid ILC adopts tracking errors as correction signals for the first five iterations, even if the contour error RMS values are used as the objective function. As the iterations evolve, the hybrid ILC switches from using tracking errors to using contour errors as correction signals. Geometric interpretations are given to illustrate the switching behavior. It is shown that the hybrid ILC can significantly reduce contour errors as compared to the process without learning. Finally, validation experiments using the butterfly curve show that the hybrid ILC outperforms the tracking, contour and combined ILCs algorithms.

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This paper presents a learning algorithm which is based on the iterative learning control (ILC) and tracking/contour error formulation. The contour errors of the free form curve are computed and feedback as the correction signal to generate a new command. It is shown that learning using the tracking error can result in different performance for the free form curve. A modified ILC method is proposed to overcome the problem. It shows that the convergence rate and error performance can be improved by choosing the appropriate weighting during the iteration. Simulations are conducted to validate the proposed ILC scheme. The results show that the modified ILC can perform better than the traditional ILC using the tracking error alone.

In this paper, a novel algorithm (ILC-EMD) which integrates iterative learning control (ILC) with empirical mode decomposition (EMD) is proposed to improve learning process. To explain the divergence behavior under the conventional ILC, the EMD is utilized to decompose the tracking error signal into 11 intrinsic mode model (IMFs). By observing the root means square (RMS) of the IMFs during iterations, the first IMF is determined to be the undesired signal which could not be reduced by learning process. By using ILC-EMD, it can filter out the undesired signal and prevent the amplification effect. Experimental results on tracking the butterfly NURBS curve validate the effectiveness of the ILC-EMD algorithm.