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

Timo Nachstedt,Poramate Manoonpong,Christian Tetzlaff

doi:10.3389/fnbot.2017.00014

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.

Highlights

Rhythmic processes are of central importance for many aspects of biological life (Winfree, 1967; Barkai and Leibler, 2000; Goldbeter et al, 2012)
We find that the Adaptation through Fast Dynamical Coupling” (AFDC) mechanism clearly outperforms standard adaptive frequency oscillators (AFOs) within the tested frequency interval covering two orders of magnitudes
Transferring key concepts of biological solutions for complex control problems to robotic applications has been proven to be a promising approach regarding the adaptivity, robustness, versatility and agility found in biological organisms (Pfeifer et al, 2007)

Summary

Introduction

Rhythmic processes are of central importance for many aspects of biological life (Winfree, 1967; Barkai and Leibler, 2000; Goldbeter et al, 2012). Examples include the cardiac rhythm, various circadian rhythms and, in particular, all forms of biological locomotion like walking, flying or swimming. The latter are controlled by specific neural circuits, so called central pattern generators. CPGs can be described as nonlinear oscillators which have been used in numerous applications for different variants of robotic control problems (Nakamura et al, 2007; Ijspeert, 2008; Pinto et al, 2012; Nassour et al, 2014; Santos et al, 2017). Compared to purely reflexive control schemes (Foth and Bässler, 1985; Cruse et al, 1995), oscillatorcontrolled robots enable more stable and robust locomotion (Kimura et al, 2001; Righetti and Ijspeert, 2008)

Methods

Results

Conclusion