Risk-Sensitive Path Planning via CVaR Barrier Functions: Application to Bipedal Locomotion

Enforcing safety of robotic systems in the presence of stochastic uncertainty is a challenging problem. Traditionally,researchers have proposed safety in the statistical mean as a safety measure in this case. However, ensuring safety in the statistical mean is only reasonable if robot safe behavior in the large number of runs is of interest, which precludes the use of mean safety in practical scenarios. In this paper, we propose a risk sensitive notion of safety called conditional-value-at-risk (CVaR) safety, which is concerned with safe performance in the worst case realizations. We introduce CVaR barrier functions asa 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. We elucidate the proposed method by applying it to a bipedal locomotion case study.