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In many real-world settings, image observations of freely rotating 3D rigidbodies, such as satellites, may be available when low-dimensional measurementsare not. However, the high-dimensionality of image data precludes the use ofclassical estimation techniques to learn the dynamics and a lack ofinterpretability reduces the usefulness of standard deep learning methods. Inthis work, we present a physics-informed neural network model to estimate andpredict 3D rotational dynamics from image sequences. We achieve this using amulti-stage prediction pipeline that maps individual images to a latentrepresentation homeomorphic to $\mathbf{SO}(3)$, computes angular velocitiesfrom latent pairs, and predicts future latent states using the Hamiltonianequations of motion with a learned representation of the Hamiltonian. Wedemonstrate the efficacy of our approach on a new rotating rigid-body datasetwith sequences of rotating cubes and rectangular prisms with uniform andnon-uniform density.

Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Body