Discovering Efficient Periodic Behaviours in Mechanical Systems via Neural Approximators

TL;DR

This paper introduces a neural network-based optimization method to induce and classify periodic behaviors in conservative mechanical systems, leveraging eigenmanifold theory for efficient periodic task execution.

Contribution

It develops a novel neural approximation approach to induce desired oscillations in mechanical systems using eigenmanifold theory and gradient descent optimization.

Findings

Successful simulation validation of the proposed method

Effective classification of nonlinear oscillations

Potential for efficient periodic task execution in mechanical systems

Abstract

It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the system. The classification of these periodic behaviours and their geometric characterisation are in an on-going secular debate, which recently led to the so-called eigenmanifold theory. The eigenmanifold characterises nonlinear oscillations as a generalisation of linear eigenspaces. With the motivation of performing periodic tasks efficiently, we use tools coming from this theory to construct an optimization problem aimed at inducing desired closed-loop oscillations through a state feedback law. We solve the constructed optimization problem via gradient-descent methods involving neural networks. Extensive simulations show the validity of the approach.