Evolutionary Parameter Estimation of Coupled Non-linear Oscillators

Abstract

In nature, nonlinear oscillators are observed attached to the joints of the animal’s legs as they move. In this paper, a system identification method based on evolutionary computation applied to coupled nonlinear oscillators is presented. As an initial reference, is a coupled non-linear oscillator designed from a Central Pattern Generator, developed for a quadruped robot with three joints per leg, and electronically tuned. The method of identification is based on the MAGO evolutionary algorithm to minimize the error in the magnitude and in the phase shift of the signals. The procedure consists of two stages: coarse-tuning and fine-tuning. With a new parameterization of the same oscillator developed for the quadruped robot, the goodness of the identification method is revealed. The method is validated by parameterizing the Van der Pol Oscillator. The results are very satisfactory. The problem to be solved is to find a mathematical model that synthesizes the observed movement of a quadruped as it moves. From the images of the oscillations generated by the hip, knee and ankle of a horse, a system of coupled nonlinear differential equations is found that reproduce the movement of the quadruped with an approximation of more than 95%.