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

Abstract

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.

Effects of Robotic Knee Exoskeleton on Human Energy Expenditure

“…Instead of a pool of adaptive oscillators in a feedback loop as in [17], and using a logic algorithm to determine the basic frequency Ω as in [16], we used a single oscillator in the loop, combined with an adaptive Fourier series [18]. By determining the basic frequency of squatting Ω, we predicted the joint positionq, and reproduced the desired torque waveform with a torque estimator.…”

“…where φ is the phase of the oscillator, q is the input signal (the knee joint angle), and K (positive constant) is the coupling strength (see [18] for parameter settings). e is the input into the oscillator, determined with a difference between the actual (q) and the estimated joint position (q).…”

“…Unlike the conventional filters, this adaptive oscillator is able to predict and estimate the output in real time, without delays between the input and the output. The only constraint is that the signal needs to be periodic or pseudoperiodic [18]. Approaches for determining the onset of periodic behavior, such as walking, are being explored [35].…”

“…On the other hand, when the participant flexes the knee (going down), the torque produced by the oscillator-based method is reduced, which eventually reduces the user's effort, as there is no need to press hard on the device to flex. A slightly spread torque on the hysteresis in the oscillator plot is a consequence of the predictive nature of the oscillator (for details see [18]). …”

“…A similar approach was used for the first layer of a two-layered movement imitation system [16]. A novel design of the first layer introduced in [18] uses a single oscillator followed by a complete Fourier series approximation with a built-in algorithm to determine the Fourier coefficients. In the paper, we test the applicability and the effectiveness of this approach on a robotic knee exoskeleton when performing periodic squatting.…”