Fast Dynamical Coupling Enhances Frequency Adaptation of Oscillators for Robotic Locomotion Control

Abstract

Rhythmic neural signals serve as basis of many brain processes, in particular of locomotion control and generation of rhythmic movements. It has been found that specific neural circuits, named central pattern generators (CPGs), are able to autonomously produce such rhythmic activities. In order to tune, shape and coordinate the produced rhythmic activity, CPGs require sensory feedback, i.e., external signals. Nonlinear oscillators are a standard model of CPGs and are used in various robotic applications. A special class of nonlinear oscillators are adaptive frequency oscillators (AFOs). AFOs are able to adapt their frequency toward the frequency of an external periodic signal and to keep this learned frequency once the external signal vanishes. AFOs have been successfully used, for instance, for resonant tuning of robotic locomotion control. However, the choice of parameters for a standard AFO is characterized by a trade-off between the speed of the adaptation and its precision and, additionally, is strongly dependent on the range of frequencies the AFO is confronted with. As a result, AFOs are typically tuned such that they require a comparably long time for their adaptation. To overcome the problem, here, we improve the standard AFO by introducing a novel adaptation mechanism based on dynamical coupling strengths. The dynamical adaptation mechanism enhances both the speed and precision of the frequency adaptation. In contrast to standard AFOs, in this system, the interplay of dynamics on short and long time scales enables fast as well as precise adaptation of the oscillator for a wide range of frequencies. Amongst others, a very natural implementation of this mechanism is in terms of neural networks. The proposed system enables robotic applications which require fast retuning of locomotion control in order to react to environmental changes or conditions.