Leveraging randomized smoothing for optimal control of nonsmooth dynamical systems

Optimal control (OC) algorithms such as differential dynamic programming (DDP) take advantage of the derivatives of the dynamics to control physical systems efficiently. Yet, these algorithms are prone to failure when dealing with non-smooth dynamical systems. This can be attributed to factors such as the existence of discontinuities in the dynamics derivatives or the presence of non-informative gradients. On the contrary, reinforcement learning (RL) algorithms have shown better empirical results in scenarios exhibiting non-smooth effects (contacts, frictions, etc.). Our approach leverages recent works on randomized smoothing (RS) to tackle non-smoothness issues commonly encountered in optimal control and provides key insights on the interplay between RL and OC through the prism of RS methods. This naturally leads us to introduce the randomized Differential Dynamic Programming (RDDP) algorithm accounting for deterministic but non-smooth dynamics in a very sample-efficient way. The experiments demonstrate that our method can solve classic robotic problems with dry friction and frictional contacts, where classical OC algorithms are likely to fail, and RL algorithms require, in practice, a prohibitive number of samples to find an optimal solution.