Preventing Inactive CBF Safety Filters Caused by Invalid Relative Degree Assumptions

TL;DR

This paper addresses the issue of inactive control barrier function (CBF) safety filters caused by invalid assumptions about system relative degree, proposing a mitigation strategy and validating it through simulations and quadrotor experiments.

Contribution

It introduces a novel mitigation approach using multiple CBFs and derives an upper bound on sampling time to ensure safety under sampled-data control.

Findings

Mitigation strategy reduces safety filter inactivity.

Derived upper bound on sampling time for safety.

Validated effectiveness through simulations and quadrotor tests.

Abstract

Control barrier function (CBF) safety filters emerged as a popular framework to certify and modify potentially unsafe control inputs, for example, provided by a reinforcement learning agent or a non-expert user. Typical CBF safety filter designs assume that the system has a uniform relative degree. This assumption is restrictive and is frequently overlooked in practice. When violated, the assumption can cause the safety filter to become inactive, allowing large and possibly unsafe control inputs to be applied to the system. In discrete-time implementations, the inactivity issue is often manifested as chattering close to the safety boundary and/or constraint violations. In this work, we provide an in-depth discussion on the safety filter inactivity issue, propose a mitigation strategy based on multiple CBFs, and derive an upper bound on the sampling time for safety under sampled-data control. The effectiveness of our proposed method is validated through both simulation and quadrotor experiments.