Wasserstein Distributionally Robust Motion Planning and Control with Safety Constraints Using Conditional Value-at-Risk

In this paper, we propose an optimization-based decision-making tool for safe motion planning and control in an environment with randomly moving obstacles. The unique feature of the proposed method is that it limits the risk of unsafety by a pre-specified threshold even when the true probability distribution of the obstacles' movements deviates, within a Wasserstein ball, from an available empirical distribution. Another advantage is that it provides a probabilistic out-of-sample performance guarantee of the risk constraint. To develop a computationally tractable method for solving the distributionally robust model predictive control problem, we propose a set of reformulation procedures using (i) the Kantorovich duality principle, (ii) the extremal representation of conditional value-at-risk, and (iii) a geometric expression of the distance to the union of halfspaces. The performance and utility of this distributionally robust method are demonstrated through simulations using a 12D quadrotor model in a 3D environment.

I. Introduction

Safety is one of the most fundamental challenges in the operation of robots and autonomous systems in practical environments, which are uncertain and dynamic. In particular, the unpredicted motion of objects and agents often risks the collision-free navigation of mobile robots. To gather information about an obstacle’s uncertain movement, it is typical to use (historical) sample data of its motion. The main goal of this work is to develop an optimization-based method for risk-aware motion planning and control by incorporating data about moving obstacles into the robot’s decision-making in a distributionally robust manner.