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Predicting the 3D rotational dynamics of a freely rotating rigid body is challenging when only image observations are available, as the mass distribution inside the body, which determines the dynamics, is not visible from the exterior.
The authors present a multi-stage neural network model that maps individual images to a low-dimensional latent representation homeomorphic to the special orthogonal group SO(3), which represents the orientation of the rigid body.
The model then computes angular velocities from latent pairs and predicts future latent states using the Hamiltonian equations of motion, with a learned moment-of-inertia tensor.
Finally, the predicted latent representations are mapped back to image sequences, allowing long-term prediction of the rigid body's motion.
The authors create several synthetic datasets of rotating objects (cubes, prisms, satellites) with uniform and non-uniform mass distributions to evaluate their model.
The proposed model outperforms baseline methods, including a Hamiltonian Generative Network, by a factor of 2 in terms of mean squared error on the test datasets.
The use of the Hamiltonian formalism provides interpretability, as the learned latent representation corresponds to the configuration space of the rigid body.
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by Justice Maso... о arxiv.org 04-12-2024
https://arxiv.org/pdf/2308.14666.pdfГлибші Запити