Learning Cost Functions for Reinforced Learned Controllers in a Quadrupedal Robot

In this work, we will consider a reinforced learning controller developed for a quadrupedal robot and we learn for which cost function such a controller is an optimal control. In particular, we will transform the learning problem into a quadratic programming problem and solve it to obtain the learned cost function. Our approach is based on second-order Lagrangian mechanics since we will use that an optimal control problem is equivalent to a second-order variational problem. We also obtain error bounds for the approximation of the cost function.