Dynamics harmonic analysis of robotic systems: Application in data-driven Koopman modelling

Daniel Ordoñez-Apraez, Vladimir Kostic, Giulio Turrisi, Pietro Novelli, Carlos Mastalli, Claudio Semini, Massimilano Pontil
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:1318-1329, 2024.

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 this Paper

BibTeX
@InProceedings{pmlr-v242-ordonez-apraez24a, title = {Dynamics harmonic analysis of robotic systems: {A}pplication in data-driven {K}oopman modelling}, author = {Ordo\~{n}ez-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}, pages = {1318--1329}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/ordonez-apraez24a/ordonez-apraez24a.pdf}, url = {https://proceedings.mlr.press/v242/ordonez-apraez24a.html}, 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.} }
Endnote
%0 Conference Paper %T Dynamics harmonic analysis of robotic systems: Application in data-driven Koopman modelling %A Daniel Ordoñez-Apraez %A Vladimir Kostic %A Giulio Turrisi %A Pietro Novelli %A Carlos Mastalli %A Claudio Semini %A Massimilano Pontil %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-ordonez-apraez24a %I PMLR %P 1318--1329 %U https://proceedings.mlr.press/v242/ordonez-apraez24a.html %V 242 %X 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.
APA
Ordoñez-Apraez, D., Kostic, V., Turrisi, G., Novelli, P., Mastalli, C., Semini, C. & Pontil, M.. (2024). Dynamics harmonic analysis of robotic systems: Application in data-driven Koopman modelling. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:1318-1329 Available from https://proceedings.mlr.press/v242/ordonez-apraez24a.html.

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