KeyCLD: Learning Constrained Lagrangian Dynamics in Keypoint Coordinates from Images

Rembert Daems, Jeroen Taets, Francis wyffels, Guillaume Crevecoeur

Keywords: Lagrangian, dynamics, keypoints, images, unsupervised

TL;DR: We learn unsupervised keypoint representations as state, jointly with constrained Lagrangian dynamics, based on videos of dynamical systems.

Abstract: We present KeyCLD, a framework to learn Lagrangian dynamics from images. Learned keypoint representations derived from images are directly used as positional state vector for jointly learning constrained Lagrangian dynamics. KeyCLD is trained unsupervised end-to-end on sequences of images. Our method explicitly models the mass matrix, potential energy and the input matrix, thus allowing energy based control. We demonstrate learning of Lagrangian dynamics from images on the dm_control pendulum, cartpole and acrobot environments, wether they are unactuated, underactuated or fully actuated. Trained models are able to produce long-term video predictions, showing that the dynamics are accurately learned. Our method strongly outperforms recent works on learning Lagrangian or Hamiltonian dynamics from images. The benefits of including a Lagrangian prior and prior knowledge of a constraint function is further investigated and empirically evaluated.

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Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/keycld-learning-constrained-lagrangian/code)