# Discovering Efficient Periodic Behaviours in Mechanical Systems via Neural Approximators

arXiv: https://arxiv.org/abs/2212.14253 · HTML: https://mlsanity.com/paper/2212.14253/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Dec 2022.

## Built on by (most cited first, 2 of 2)

- [RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations](https://mlsanity.com/paper/2305.12854/) (2023)
- [Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groups](https://mlsanity.com/paper/2401.15107/) (2024)

## Abstract (arXiv)

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.