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 Massimiliano Pontil
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 system dynamics. Our architecture, validated on synthetic systems and
the dynamics of locomotion of a quadrupedal robot, demonstrates enhanced
generalization, sample efficiency, and interpretability, with less trainable
parameters and computational costs.