  We demonstrate model-based, visual robot manipulation of linear deformable
objects. Our approach is based on a state-space representation of the physical
system that the robot aims to control. This choice has multiple advantages,
including the ease of incorporating physics priors in the dynamics model and
perception model, and the ease of planning manipulation actions. In addition,
physical states can naturally represent object instances of different
appearances. Therefore, dynamics in the state space can be learned in one
setting and directly used in other visually different settings. This is in
contrast to dynamics learned in pixel space or latent space, where
generalization to visual differences are not guaranteed. Challenges in taking
the state-space approach are the estimation of the high-dimensional state of a
deformable object from raw images, where annotations are very expensive on real
data, and finding a dynamics model that is both accurate, generalizable, and
efficient to compute. We are the first to demonstrate self-supervised training
of rope state estimation on real images, without requiring expensive
annotations. This is achieved by our novel self-supervising learning objective,
which is generalizable across a wide range of visual appearances. With
estimated rope states, we train a fast and differentiable neural network
dynamics model that encodes the physics of mass-spring systems. Our method has
a higher accuracy in predicting future states compared to models that do not
involve explicit state estimation and do not use any physics prior, while only
using 3\% of training data. We also show that our approach achieves more
efficient manipulation, both in simulation and on a real robot, when used
within a model predictive controller.
