Safe Control for Nonlinear Systems with Stochastic Uncertainty via Risk Control Barrier Functions

TL;DR

This paper develops a risk-sensitive safety framework for nonlinear stochastic systems using risk control barrier functions, enabling safety guarantees under uncertainty with practical validation on a cart-pole system.

Contribution

It introduces risk control barrier functions (RCBFs) for stochastic systems, extending safety guarantees to risk-sensitive contexts with finite-time reachability analysis.

Findings

RCBFs ensure invariance in a coherent risk sense.

The framework guarantees finite-time reachability under stochastic uncertainty.

Validated effectiveness on a cart-pole system in safety-critical scenarios.

Abstract

Guaranteeing safety for robotic and autonomous systems in real-world environments is a challenging task that requires the mitigation of stochastic uncertainties. Control barrier functions have, in recent years, been widely used for enforcing safety related set-theoretic properties, such as forward invariance and reachability, of nonlinear dynamical systems. In this paper, we extend this rich framework to nonlinear discrete-time systems subject to stochastic uncertainty and propose a framework for assuring risk-sensitive safety in terms of coherent risk measures. To this end, we introduce risk control barrier functions (RCBFs), which are compositions of barrier functions and dynamic, coherent risk measures. We show that the existence of such barrier functions implies invariance in a coherent risk sense. Furthermore, we formulate conditions based on finite-time RCBFs to guarantee finite-time reachability to a desired set in the coherent risk. Conditions for risk-sensitive safety and finite-time reachability of sets composed of Boolean compositions of multiple RCBF are also formulated. We show the efficacy of the proposed method through its application to a cart-pole system in a safety-critical scenario.