  Trajectory optimization and model predictive control are essential techniques
underpinning advanced robotic applications, ranging from autonomous driving to
full-body humanoid control. State-of-the-art algorithms have focused on
data-driven approaches that infer the system dynamics online and incorporate
posterior uncertainty during planning and control. Despite their success, such
approaches are still susceptible to catastrophic errors that may arise due to
statistical learning biases, unmodeled disturbances, or even directed
adversarial attacks. In this paper, we tackle the problem of dynamics mismatch
and propose a distributionally robust optimal control formulation that
alternates between two relative entropy trust-region optimization problems. Our
method finds the worst-case maximum entropy Gaussian posterior over the
dynamics parameters and the corresponding robust policy. Furthermore, we show
that our approach admits a closed-form backward-pass for a certain class of
systems. Finally, we demonstrate the resulting robustness on linear and
nonlinear numerical examples.
