Risk-Aware Motion Planning and Control Using CVaR-Constrained Optimization

Astghik Hakobyan, Gyeong Chan Kim, Insoon Yang

Abstract: We propose a risk-aware motion planning and decision-making method that systematically adjusts the safety and conservativeness in an environment with randomly moving obstacles. The key component of this method is the conditional value-at-risk (CVaR) used to measure the safety risk that a robot faces. Unlike chance constraints, CVaR constraints are coherent, convex, and distinguish between tail events. We propose a two-stage method for safe motion planning and control: A reference trajectory is generated by using RRT* in the first stage, and then a receding horizon controller is employed to limit the safety risk by using CVaR constraints in the second stage. However, the second stage problem is nontrivial to solve, as it is a triple-level stochastic program. We develop a computationally tractable approach through 1) a reformulation of the CVaR constraints; 2) a sample average approximation; and 3) a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">linearly constrained</i> mixed integer convex program formulation. The performance and utility of this risk-aware method are demonstrated via simulation using a 12-dimensional model of quadrotors.