A Data Driven Vector Field Oscillator with Arbitrary Limit Cycle Shape

TL;DR

This paper introduces a novel 2D vector field oscillator capable of generating any non-self-intersecting periodic signal by matching its limit cycle to the desired shape, enhancing cyclic motion modeling.

Contribution

It presents a new oscillator design that can characterize arbitrary periodic signals with stable limit cycles, adaptable to various cyclic motions.

Findings

Successfully matches limit cycle to arbitrary shapes

Ensures bounded output and derivatives

Verified through simulations

Abstract

Cyclic motions in vertebrates, including heart beating, breathing and walking, are derived by a network of biological oscillators having fascinating features such as entrainment, environment adaptation, and robustness. These features encouraged engineers to use oscillators for generating cyclic motions. To this end, it is crucial to have oscillators capable of characterizing any periodic signal via a stable limit cycle. In this paper, we propose a 2-dimensional oscillator whose limit cycle can be matched to any periodic signal depicting a non-self-intersecting curve in the state space. In particular, the proposed oscillator is designed as an autonomous vector field directed toward the desired limit cycle. To this purpose, the desired reference signal is parameterized with respect to a state-dependent phase variable, then the oscillator's states track the parameterized signal. We also present a state transformation technique to bound the oscillator's output and its first time derivative. The soundness of the proposed oscillator has been verified by carrying out a few simulations.