Designing Barrier Functions for Graceful Safety Control

TL;DR

This paper introduces a novel safety control framework that ensures multi-layered safety guarantees, allowing systems to gracefully handle primary safety breaches by maintaining secondary safety invariance, with applications demonstrated in collision avoidance.

Contribution

It develops a new safety constraint combining zeroing and reciprocal control barrier functions for multi-layer safety assurance in systems with relative degree 1 or 2.

Findings

The approach guarantees safety even if the primary safety layer is breached.

It provides a systematic way to design safety controllers with energy-based proofs.

Demonstrated effectiveness in a wall collision avoidance scenario.

Abstract

This paper examines the problem of achieving "grace" when controlling dynamical systems for safety, which is defined in terms of providing multi-layered safety assurances. Namely, two safety layers are created: a primary layer that represents a desirable degree of safety, and a secondary failsafe layer. Graceful control then involves ensuring that even if the primary layer is breached, the failsafe layer remains forward invariant. The paper pursues this goal by constructing a safety constraint that combines the concepts of zeroing and reciprocal control barrier functions with regard to the primary and secondary safe sets, respectively. This constraint is analogous to a stiffening spring, making it possible to construct energy-based analytical proofs of the resulting graceful safety guarantees. The proposed approach is developed for systems with a relative degree of either 1 or 2, the latter case being particularly useful for mechanical systems. We demonstrate the applicability of the method using a wall collision avoidance example. This demonstration highlights the benefits of the proposed approach compared to traditional benchmarks from the literature.