  Successful robotic operation in stochastic environments relies on accurate
characterization of the underlying probability distributions, yet this is often
imperfect due to limited knowledge. This work presents a control algorithm that
is capable of handling such distributional mismatches. Specifically, we propose
a novel nonlinear MPC for distributionally robust control, which plans locally
optimal feedback policies against a worst-case distribution within a given KL
divergence bound from a Gaussian distribution. Leveraging mathematical
equivalence between distributionally robust control and risk-sensitive optimal
control, our framework also provides an algorithm to dynamically adjust the
risk-sensitivity level online for risk-sensitive control. The benefits of the
distributional robustness as well as the automatic risk-sensitivity adjustment
are demonstrated in a dynamic collision avoidance scenario where the predictive
distribution of human motion is erroneous.
