On-line frequency adaptation and movement imitation for rhythmic robotic tasks

In this paper we present a novel method to obtain the basic frequency of an unknown periodic signal with an arbitrary waveform, which can work online with no additional signal processing or logical operations. The method originates from non-linear dynamical systems for frequency extraction, which are based on adaptive frequency oscillators in a feedback loop. In previous work, we had developed a method that could extract separate frequency components by using several adaptive frequency oscillators in a loop, but that method required a logical algorithm to identify the basic frequency. The novel method presented here uses a Fourier series representation in the feedback loop combined with a single oscillator. In this way it can extract the frequency and the phase of an unknown periodic signal in real time and without any additional signal processing or preprocessing. The method determines the Fourier series coefficients and can be used for dynamic Fourier series implementation. The proposed method can be used for the control of rhythmic robotic tasks, where only the extraction of the basic frequency is crucial. For demonstration several highly non-linear and dynamic periodic robotic tasks are shown, including also a task where an electromyography (EMG) signal is used in a feedback loop.