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

• URL: http://arxiv.org/abs/2312.07457v3
• Date: Tue, 4 Jun 2024 13:39:17 GMT
• Title: Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling
• Authors: Daniel Ordoñez-Apraez, Vladimir Kostic, Giulio Turrisi, Pietro Novelli, Carlos Mastalli, Claudio Semini, Massimiliano Pontil,
• Abstract summary: We introduce the use of harmonic analysis to decompose the state space of symmetric robotic systems into isotypic subspaces. For linear dynamics, we characterize how this decomposition leads to a subdivision of the dynamics into independent linear systems on each subspace. Our architecture, validated on synthetic systems and the dynamics of locomotion of a quadrupedal robot, exhibits enhanced generalization, sample efficiency, and interpretability.
• Score: 24.738444847113232
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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