Conventional neural network (NN)-based imitation learning methods for variable-speed motion either restricted their scope to interpolated speeds, or generated unpredictable motions when extrapolating beyond trained velocity ranges. Variable-frequency imitation learning (VFIL) enabled extrapolations of speeds by linking the NN model's sampling frequency to the motion frequency, whereas its open-loop configuration caused frequency errors, especially in the extrapolated high-frequency settings. This study proposes variable-frequency imitation learning with iterative learning control (VFILC) based on a combination of VFIL and iterative learning control (ILC) with both feedforward and feedback parts, the former taking advantage of VFIL and the latter adjusting the frequency errors. The experimental results showed that the proposed method successfully and accurately extrapolated motion speeds and reduced frequency errors in all three tasks, and that the feedback especially reduced the frequency errors by a remarkable 81% in the wiping task and 50% in the shaking task, both compared to simple feedforward VFIL, when extrapolating at double the average speed in the training data. The proposed method also improved accuracy by 27% compared with VFIL even at an interpolated frequency for a contact-rich mixing task affected by complex friction traits.

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