Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling
Abstract
We introduce the use of harmonic analysis to decompose the state space of symmetric robotic systems into orthogonal isotypic subspaces. These are lower-dimensional spaces that capture distinct, symmetric, and synergistic motions. For linear dynamics, we characterize how this decomposition leads to a subdivision of the dynamics into independent linear systems on each subspace, a property we term dynamics harmonic analysis (DHA). To exploit this property, we use Koopman operator theory to propose an equivariant deep-learning architecture that leverages the properties of DHA to learn a global linear model of the system dynamics. Our architecture, validated on synthetic systems and the dynamics of locomotion of a quadrupedal robot, exhibits enhanced generalization, sample efficiency, and interpretability, with less trainable parameters and computational costs.
Cite
Text
Ordoñez-Apraez et al. "Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling." Proceedings of the 6th Annual Learning for Dynamics & Control Conference, 2024.Markdown
[Ordoñez-Apraez et al. "Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling." Proceedings of the 6th Annual Learning for Dynamics & Control Conference, 2024.](https://mlanthology.org/l4dc/2024/ordonezapraez2024l4dc-dynamics/)BibTeX
@inproceedings{ordonezapraez2024l4dc-dynamics,
title = {{Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling}},
author = {Ordoñez-Apraez, Daniel and Kostic, Vladimir and Turrisi, Giulio and Novelli, Pietro and Mastalli, Carlos and Semini, Claudio and Pontil, Massimilano},
booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference},
year = {2024},
pages = {1318-1329},
volume = {242},
url = {https://mlanthology.org/l4dc/2024/ordonezapraez2024l4dc-dynamics/}
}