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

arXiv:2604.02401 · cs.RO, cs.SY, eess.SY · Submitted 2026-04-02 · Read on arXiv

cs.RO, cs.SY, eess.SY

Submitted: 2026-04-02

Updated: 2026-09-18

Comments: 2026 IEEE Conference on Decision and Control (CDC). Project page: https://www.taekyung.me/backup-safety-filters

Project page: https://www.taekyung.me/backup-safety-filters

License: http://creativecommons.org/licenses/by/4.0/

The gist: 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.

Terminology

Model Predictive Shielding — 9× in this paper
Abstraction — 6× in this paper · explained in 1 episode
Conference on Decision and Control — 5× in this paper
Reinforcement Learning — 5× in this paper · explained in 4 episodes
American Control Conference — 3× in this paper
Verification — 3× in this paper · explained in 2 episodes
Closed-Loop System — 2× in this paper · explained in 4 episodes
Accuracy — 1× in this paper · explained in 1 episode
Adaptation — 1× in this paper · explained in 1 episode
Control Barrier Functions (CBFs) — 1× in this paper · explained in 4 episodes
Deep Reinforcement Learning — 1× in this paper · explained in 2 episodes
Paper Review — 1× in this paper · explained in 2 episodes
Reinforcement Learning (RL) — 1× in this paper · explained in 24 episodes
Steering — 1× in this paper · explained in 2 episodes
Unified Framework — 1× in this paper · explained in 5 episodes

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.

Terminology

Abstract

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