Work

Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling

Year: 2023

Type: preprint

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 fewer trainable parameters and computational costs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2312.07457

Authors: Ordoñez-Apraez, Daniel, Kostic, Vladimir, Turrisi, Giulio, Novelli, Pietro, Mastalli, Carlos, Semini, Claudio, Pontil, Massimiliano

Institutions: Italian Institute of Technology, Heriot-Watt University, University College London

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: European Commission

OpenAlex ID: W4389712899

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