Zero-Order Control Barrier Functions for Sampled-Data Systems with State and Input Dependent Safety Constraints

TL;DR

This paper introduces a zero-order control barrier function (ZOCBF) for sampled-data systems that guarantees safety without differentiation, effectively handling complex safety constraints dependent on states and inputs.

Contribution

The paper presents a novel ZOCBF formulation that generalizes existing methods, enabling safety enforcement in sampled-data systems with high-relative degree and state-input dependent constraints without differentiation.

Findings

Successfully applied to collision avoidance scenarios

Effective in rollover prevention on uneven terrains

No differentiation required for ZOCBF condition

Abstract

We propose a novel zero-order control barrier function (ZOCBF) for sampled-data systems to ensure system safety. Our formulation generalizes conventional control barrier functions and straightforwardly handles safety constraints with high-relative degrees or those that explicitly depend on both system states and inputs. The proposed ZOCBF condition does not require any differentiation operation. Instead, it involves computing the difference of the ZOCBF values at two consecutive sampling instants. We propose three numerical approaches to enforce the ZOCBF condition, tailored to different problem settings and available computational resources. We demonstrate the effectiveness of our approach through a collision avoidance example and a rollover prevention example on uneven terrains.