Distributionally Robust Trajectory Optimization Under Uncertain Dynamics via Relative Entropy Trust-Regions

TL;DR

This paper introduces a distributionally robust trajectory optimization method that enhances control robustness against dynamics uncertainties and adversarial disturbances by using relative entropy trust-regions.

Contribution

It proposes a novel distributionally robust optimal control framework that finds worst-case dynamics and robust policies with a closed-form solution for certain systems.

Findings

Demonstrates increased robustness on linear and nonlinear examples.

Provides a closed-form backward pass for specific system classes.

Addresses vulnerabilities of data-driven approaches to uncertainties.

Abstract

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.