  Safety is a critical issue in learning-based robotic and autonomous systems
as learned information about their environments is often unreliable and
inaccurate. In this paper, we propose a risk-aware motion control tool that is
robust against errors in learned distributional information about obstacles
moving with unknown dynamics. The salient feature of our model predictive
control (MPC) method is its capability of limiting the risk of unsafety even
when the true distribution deviates from the distribution estimated by Gaussian
process (GP) regression, within an ambiguity set. Unfortunately, the
distributionally robust MPC problem with GP is intractable because the
worst-case risk constraint involves an infinite-dimensional optimization
problem over the ambiguity set. To remove the infinite-dimensionality issue, we
develop a systematic reformulation approach exploiting modern distributionally
robust optimization techniques. The performance and utility of our method are
demonstrated through simulations using a nonlinear car-like vehicle model for
autonomous driving.
