Backup-Based Safety Filters: A Comparative Review of Backup CBF, Model Predictive Shielding, and gatekeeper

TL;DR

This paper provides a unified review and comparison of three backup-based safety filters—Backup CBF, MPS, and gatekeeper—highlighting their similarities, differences, and sources of conservatism.

Contribution

It introduces a common framework to compare these safety filters, clarifies their theoretical relationships, and discusses the conservatism inherent in their safety evaluations.

Findings

MPS is a special case of gatekeeper.

Gatekeeper relates to the interior of Backup CBF's inactive set.

Safety is often evaluated via backup maneuver feasibility.

Abstract

This paper revisits three backup-based safety filters -- Backup Control Barrier Functions (Backup CBF), Model Predictive Shielding (MPS), and gatekeeper -- through a unified comparative framework. Using a common safety-filter abstraction and shared notation, we make explicit both their common backup-policy structure and their key algorithmic differences. We compare the three methods through their filter-inactive sets, i.e., the states where the nominal policy is left unchanged. In particular, we show that MPS is a special case of gatekeeper, and we further relate gatekeeper to the interior of the Backup CBF inactive set within the implicit safe set. This unified view also highlights a key source of conservatism in backup-based safety filters: safety is often evaluated through the feasibility of a backup maneuver, rather than through the nominal policy's continued safe execution. The paper is intended as a compact tutorial and review that clarifies the theoretical connections and differences among these methods.