Non-smooth Control Barrier Functions for Stochastic Dynamical Systems

TL;DR

This paper extends Control Barrier Functions to stochastic systems with non-smooth safe sets, providing formal safety guarantees and demonstrating effectiveness through simulations in uncertain environments.

Contribution

It introduces a novel framework that combines stochastic control and non-smooth safe set descriptions within the CBF methodology, addressing limitations of previous deterministic and smooth-set assumptions.

Findings

Formal safety guarantees for stochastic systems

Effective handling of complex, non-smooth safety specifications

Successful numerical simulations in uncertain scenarios

Abstract

Uncertainties arising in various control systems, such as robots that are subject to unknown disturbances or environmental variations, pose significant challenges for ensuring system safety, such as collision avoidance. At the same time, safety specifications are getting more and more complex, e.g., by composing multiple safety objectives through Boolean operators resulting in non-smooth descriptions of safe sets. Control Barrier Functions (CBFs) have emerged as a control technique to provably guarantee system safety. In most settings, they rely on an assumption of having deterministic dynamics and smooth safe sets. This paper relaxes these two assumptions by extending CBFs to encompass control systems with stochastic dynamics and safe sets defined by non-smooth functions. By explicitly considering the stochastic nature of system dynamics and accommodating complex safety specifications, our method enables the design of safe control strategies in uncertain and complex systems. We provide formal guarantees on the safety of the system by leveraging the theoretical foundations of stochastic CBFs and non-smooth safe sets. Numerical simulations demonstrate the effectiveness of the approach in various scenarios.