  Optimal control is a successful approach to generate motions for complex
robots, in particular for legged locomotion. However, these techniques are
often too slow to run in real time for model predictive control or one needs to
drastically simplify the dynamics model. In this work, we present a method to
learn to predict the gradient and hessian of the problem value function,
enabling fast resolution of the predictive control problem with a one-step
quadratic program. In addition, our method is able to satisfy constraints like
friction cones and unilateral constraints, which are important for high
dynamics locomotion tasks. We demonstrate the capability of our method in
simulation and on a real quadruped robot performing trotting and bounding
motions.
