Timely Activation of Safety Filters via One-Step Reachability Expansion

Robots must complete their tasks and maintain the achieved outcomes while avoiding safety failures at all times. Strict reach-avoid-stay (sRAS) formalizes this requirement: safely reaching a target and remaining there indefinitely after first entry. We propose an sRAS Q-control barrier function (CBF) safety filter for high-dimensional black-box systems under bounded uncertainty. Our construction combines a stay value encoding safe permanent residence in a target subset with a reach-avoid value encoding safe reachability of this subset while avoiding target states from which safe permanent residence cannot be guaranteed. We prove that these values jointly yield a valid robust discrete-time CBF and lift them to state-action Q-functions for runtime intervention. For exact values and under a measure-zero condition, our filter preserves sRAS feasibility from almost every winnable initial state and keeps the system safely within the target after first entry, against all admissible uncertainty realizations. We adopt reachability-based adversarial reinforcement learning for scalable value approximation using only black-box interactions. Notably, neither synthesis nor deployment of our filter requires known dynamics, affine structure, value derivatives, or hand-designed barriers. We validate our framework in quadruped gap jumping in simulation and hardware, where the robot crosses the gap, lands safely, and remains safe afterward. Simulated F1TENTH races further demonstrate safe overtaking and lead retention.

Safety filters have been shown to be effective tools to ensure the safety of control systems with unsafe nominal policies. To address scalability challenges in traditional synthesis methods, learning-based approaches have been proposed for designing safety filters for systems with high-dimensional state and control spaces. However, the inevitable errors in the decisions of these models raise concerns about their reliability and the safety guarantees they offer. This paper presents Adaptive Conformal Filtering (ACoFi), a method that combines learned Hamilton-Jacobi reachability-based safety filters with adaptive conformal inference. Under ACoFi, the filter dynamically adjusts its switching criteria based on the observed errors in its predictions of the safety of actions. The range of possible safety values of the nominal policy's output is used to quantify uncertainty in safety assessment. The filter switches from the nominal policy to the learned safe one when that range suggests it might be unsafe. We show that ACoFi guarantees that the rate of incorrectly quantifying uncertainty in the predicted safety of the nominal policy is asymptotically upper bounded by a user-defined parameter. This gives a soft safety guarantee rather than a hard safety guarantee. We evaluate ACoFi in a Dubins car simulation and a Safety Gymnasium environment, empirically demonstrating that it significantly outperforms the baseline method that uses a fixed switching threshold by achieving higher learned safety values and fewer safety violations, especially in out-of-distribution scenarios.

Ensuring robot safety in unknown, dynamic environments is a fundamental requirement. It involves inferring the states of an unknown and time-varying number of moving objects from noisy, incomplete measurements. We address safe control under the induced multi-object state uncertainty with a risk-aware belief control barrier function (BCBF) framework. The uncertainty is captured by a random finite set (RFS) belief, estimated by a sequential Monte Carlo probability hypothesis density (SMC-PHD) filter that represents it with a set of particles. Building directly on these particles, we construct a nonsmooth BCBF, establish forward invariance of the safe set under continuous prediction, and derive an explicit condition under which discrete updates preserve safety. Simulation and real-world underwater experiments demonstrate the effectiveness and efficiency of the proposed approach.