Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling
This addresses the problem of efficient and interpretable dynamics modeling for symmetric robotic systems, representing an incremental advance by combining harmonic analysis with existing Koopman methods.
The paper tackles the problem of modeling robotic system dynamics by introducing dynamics harmonic analysis (DHA) to decompose symmetric systems into lower-dimensional subspaces, and proposes an equivariant deep-learning architecture using Koopman operator theory. The result is enhanced generalization, sample efficiency, and interpretability with fewer parameters and computational costs, validated on synthetic systems and a quadrupedal robot.
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.