Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916273576738816 |
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| author | Ordoñez-Apraez, Daniel Kostic, Vladimir Turrisi, Giulio Novelli, Pietro Mastalli, Carlos Semini, Claudio Pontil, Massimiliano |
| author_facet | Ordoñez-Apraez, Daniel Kostic, Vladimir Turrisi, Giulio Novelli, Pietro Mastalli, Carlos Semini, Claudio Pontil, Massimiliano |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_07457 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling Ordoñez-Apraez, Daniel Kostic, Vladimir Turrisi, Giulio Novelli, Pietro Mastalli, Carlos Semini, Claudio Pontil, Massimiliano Robotics Artificial Intelligence Machine Learning Systems and Control 43-08 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. |
| title | Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling |
| topic | Robotics Artificial Intelligence Machine Learning Systems and Control 43-08 |
| url | https://arxiv.org/abs/2312.07457 |