Backup-Based Safety Filters: A Comparative Review of Backup CBF, Model Predictive Shielding, and gatekeeper
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 | ||
| Decision Variable | Control input | Boolean | Switching time |
| acceptance | |||
| Verification Mechanism | Enforce ( 9b )-( 9c ) | Checks validity | Checks validity |
| at | for | ||
| Limitation | Safety evaluation on backup | Dependency | |
| Scenario | Method | % | Avg. [s] | Reached Goal | Avg. Time [ms] |
| Reach-Avoid | 28.8 | N/A | ✗ | 10.33 | |
| 55.3 | 0.06 | ✗ | 1.31 | ||
| 87.5 | 6.00 | ✓ | 10.86 | ||
| Parallel | 87.5 | 6.00 | ✓ | 1.30 | |
| Highway Overtake | 60.8 | N/A | ✓ | 27.90 | |
| 67.5 | 0.03 | ✓ | 2.64 |