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

Robots navigating under occlusion may enter states from which no admissible input can avoid a dynamic obstacle once it becomes visible. We present OcclusionCBF, a safety filter that extends backup control barrier functions to reachable-occupancy predictions for potentially hidden dynamic obstacles in occluded regions. The method certifies a prescribed backup rollout against collision-inflated occupancy and a verified terminal set, yielding affine constraints for minimally invasive quadratic-program filtering. We establish recursive feasibility of the resulting safety filter, and collision avoidance for every hidden-obstacle motion covered by the occupancy prediction. Randomized benchmarks, MetaUrban simulations, and hardware experiments demonstrate improved task success over reactive and occlusion-aware predictive baselines with millisecond-scale computation.

Runtime safety filters for learned manipulation policies typically define unsafe states as unions of object-wise keep-out regions. This representation can be unnecessarily restrictive for hazards that depend on a joint spatial relation, such as battery recycling, where a conductive payload can short a charged cell only when it approaches both terminals simultaneously. We study runtime filtering for this two-terminal hazard in LIBERO using frozen OpenVLA policies. We factor a runtime filter into three design choices: the predicate structure, its geometric margin, and the fallback action applied when a commanded action is rejected. We compare a conjunctive predicate, a conventional two-site keep-out, and a composite of the two. For each predicate, we vary its margin to obtain a frontier between task success and residual hazard. We then compare four fallback strategies at matched operating points: holding, retreat, sampled search, and a continuous-action barrier projection. Across three workcells, the three predicate families trace nearly identical safety--utility frontiers once each is evaluated over its own margin. In contrast, the fallback strategy has a substantially larger effect: holding reduces task success by up to 0.302 relative to retreat without reducing hazard, while both minimally invasive fallbacks leave substantially more residual hazard. This ordering transfers to a second policy and task suite, while retreat-based filtering remains effective under standing errors in the clearances available to the filter, although correlated error in the estimated payload size is more damaging than larger independent errors in terminal position. These results show that, for proximity-defined manipulation hazards, margin selection and fallback strategy can matter more than predicate structure in determining the safety--utility trade-off of a runtime filter.

Control barrier functions (CBFs) certify commands through an assumed dynamics model, so an abrupt, unmeasured regime change can undermine the certificate exactly when safety matters most. We present Look-Back Adaptive Control Barrier Functions (LBA-CBF), which rank a finite bank of candidate dynamics by recent prediction error over a short look-back window and enforce the high-order CBF condition against every model within a tolerance of the best, spanning best-fit adaptation to full-bank robust filtering. The dynamics may depend nonlinearly on the unknown parameters, and no switching model or continuously parameterized estimator is required. We prove that any feasible filtered input satisfies the true CBF condition whenever a safety-representative candidate is retained. In quadrotor simulation with abrupt wind reversals and an unknown payload, LBA-CBF is safe and reaches the goal from all random initial conditions, matching an oracle, while adaptive and robust baselines achieve 0-88% success. Banks of up to 250,000 models run inside the control loop, and Crazyflie 2.1 and F1TENTH experiments demonstrate adaptation to wind, payload release, and varying tire-road friction. Code, videos, and project details are available at: https://lla-control.github.io