Designing Barrier Functions for Graceful Safety Control

Yejin Moon; Gabor Orosz; Hosam K. Fathy

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arXiv · 2603.03497

Designing Barrier Functions for Graceful Safety Control

Yejin Moon·Gabor Orosz·Hosam K. Fathy

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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.

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Yejin Moon, Gabor Orosz, Hosam K. Fathy. 2026-03-03. Designing Barrier Functions for Graceful Safety Control. https://arxiv.org/abs/2603.03497

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