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

Taekyung Kim; Aswin D. Menon; Akshunn Trivedi; Dimitra Panagou

cs.ROApr 2, 2026

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

Authors: Taekyung Kim, Aswin D. Menon, Akshunn Trivedi, Dimitra Panagou

Organizations: Department of Robotics, University of Michigan, Ann Arbor, MI, 48109, USA · Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

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.

Figures & tables

	Backup CBF	MPS	gatekeeper
Prerequisite	Backup policy $\pi_{\textup{b}}$
Decision Variable	Control input	Boolean	Switching time
	${\bm{u}}\in\mathcal{U}$	acceptance	$T_{S}\in[0,T_{H}]$
Verification Mechanism	Enforce ( 9b )-( 9c )	Checks validity	Checks validity
	$\forall\tau\in[t,t+T_{B}]$	at $T_{S}=\Delta t$	for $\max T_{S}$
Limitation	Safety evaluation on backup		Dependency

TABLE I: Comparison overview of backup-based safety filters

Fig. 1: Recovered safe sets (light-colored regions) and filter-inactive sets (dark-colored regions) for the double-integrator example on the slice

(v_{x},v_{y})=(2,0)

. The black dashed curve shows the viability kernel obtained from HJ reachability on the full 4-dimensional state space. For each

1~\textup{m}\times 1~\textup{m}

grid of initial positions, we simulate the closed-loop system under each safety filter; green trajectories remain safe, whereas yellow trajectories indicate unsafe or infeasible rollouts.

Fig. 2: Geometric illustration of the local argument in Thm. 3 .

Fig. 3: Reach-avoid scenario with a dynamic obstacle. (a) Robot trajectories generated by Backup CBF, MPS, and gatekeeper . (b) Backup CBF value as a function of time. (c) Comparison of the certified switching time

T_{S}^{\star}

for MPS and gatekeeper .

Scenario	Method	$\pi_{\textup{nom}}$ %	Avg. $T_{S}^{\star}$ [s]	Reached Goal	Avg. Time [ms]
Reach-Avoid	$\pi_{\textup{BCBF}}$	28.8	N/A	✗	10.33
	$\pi_{\textup{MPS}}$	55.3	0.06	✗	1.31
	$\pi_{\textup{GK}}$	87.5	6.00	✓	10.86
	Parallel $\pi_{\textup{GK}}$	87.5	6.00	✓	1.30
Highway Overtake	$\pi_{\textup{BCBF}}$	60.8	N/A	✓	27.90
	$\pi_{\textup{MPS}}$	67.5	0.03	✓	2.64

TABLE II: Quantitative evaluation in the reach-avoid and highway overtake scenarios, averaged over five trials with randomly sampled initial robot conditions.

Fig. 4: Highway overtake scenario. (a) Vehicle trajectories generated by Backup CBF, MPS, and gatekeeper . (b) Backup CBF value as a function of time. (c) Comparison of the certified switching time $T_{S}^{\star}$ for MPS and gatekeeper .

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Abstract

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