Risk-Averse Control via CVaR Barrier Functions: Application to Bipedal Robot Locomotion

Abstract

Enforcing safety in the presence of stochastic uncertainty is a challenging problem. Traditionally, researchers have proposed safety in the statistical mean as a safety measure for systems subject to stochastic uncertainty. However, ensuring safety in the statistical mean is only reasonable if system's safe behavior in the large number of runs is of interest, which precludes the use of mean safety in practical scenarios. In this letter, we propose a risk sensitive notion of safety called conditional-value-at-risk (CVaR) safety. We introduce CVaR barrier functions as a tool to enforce CVaR-safety and propose conditions for their Boolean compositions. Given a legacy controller, we show that we can design a minimally interfering CVaR-safe controller via solving difference convex programs (DCPs). We elucidate the proposed method by applying it to a bipedal robot locomotion case study.