Risk-Averse Planning via CVaR Barrier Functions: Application to Bipedal Robot Locomotion
This addresses safety for robotic systems in uncertain environments, representing an incremental improvement over traditional mean-based safety measures.
The paper tackles the problem of ensuring safety under stochastic uncertainty by proposing a risk-sensitive notion called conditional-value-at-risk (CVaR) safety, which focuses on worst-case scenarios, and introduces CVaR barrier functions to enforce it, with application to bipedal robot locomotion.
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 in this case. 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 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 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. We elucidate the proposed method by applying it to a bipedal robot locomotion case study.