From Pixels to Torques with Linear Feedback

We demonstrate the effectiveness of simple observer-based linear feedback policies for "pixels-to-torques" control of robotic systems using only a robot-facing camera. Specifically, we show that the matrices of an image-based Luenberger observer (linear state estimator) for a "student" output-feedback policy can be learned from demonstration data provided by a "teacher" state-feedback policy via simple linear-least-squares regression. The resulting linear output-feedback controller maps directly from high-dimensional raw images to torques while being amenable to the rich set of analytical tools from linear systems theory, allowing us to enforce closed-loop stability constraints in the learning problem. We also investigate a nonlinear extension of the method via the Koopman embedding. Finally, we demonstrate the surprising effectiveness of linear pixels-to-torques policies on a cartpole system, both in simulation and on real hardware. The policy successfully executes both stabilizing and swing-up trajectory-tracking tasks using only camera feedback while subject to model mismatch, process and sensor noise, perturbations, and occlusions. Open-source code for all experiments can be found here: https://roboticexplorationlab.org/projects/linear_pixels_to_torques.html