Distributionally robust model predictive control for collision avoidance in the presence of stochastic obstacles

Abstract

This article focuses on distributionally robust controller design for safe navigation in the presence of dynamic and stochastic obstacles, where the true probability distributions associated with the disturbances are unknown. Although the true probability distributions are considered to be unknown, they are considered to belong to a set of probability distributions known as the ambiguity set. This ambiguity set includes all the probability distributions that share the same first two moments. In this article, the safe navigation problem has been defined by an optimal control problem with probabilistic collision avoidance constraint. To ensure satisfaction of this probabilistic constraint in the presence of disturbances whose true probability distributions are known, this constraint has been enforced in a distributionally robust sense. A computationally tractable control approach has been presented in this article that exploits techniques from robust optimization methods. Simulation results show the effectiveness of the proposed method.