ATOM-CBF: Adaptive Safe Perception-Based Control under Out-of-Distribution Measurements

TL;DR

ATOM-CBF addresses safety for perception-based control under OoD measurements by introducing an adaptive perception error margin that scales with epistemic uncertainty and a safety filter that modulates conservatism in real time. It builds on MR-CBF but replaces static bounds with an OoD-aware margin $\epsilon_{\text{adapt}}(y) = \left\| \varphi_{\text{cal}} \cdot \text{Unc}(y) \right\|_2$, where $\varphi_{\text{cal}}$ is learned from a filtered calibration set. The framework supports EUQ modules such as SCOD or Deep Ensembles and formulates the safety constraint as an SOCP with a slack variable to ensure feasibility. Empirical validation on an F1Tenth vehicle with LiDAR and a quadruped with RGB images shows zero OoD collisions and highlights a safety-performance trade-off influenced by the choice of EUQ and the filtering parameter $\\gamma$. The approach provides practical safety guarantees for perception-based control without ground-truth OoD labels or prior distribution knowledge, enabling safer real-world deployment.

Abstract

Ensuring the safety of real-world systems is challenging, especially when they rely on learned perception modules to infer the system state from high-dimensional sensor data. These perception modules are vulnerable to epistemic uncertainty, often failing when encountering out-of-distribution (OoD) measurements not seen during training. To address this gap, we introduce ATOM-CBF (Adaptive-To-OoD-Measurement Control Barrier Function), a novel safe control framework that explicitly computes and adapts to the epistemic uncertainty from OoD measurements, without the need for ground-truth labels or information on distribution shifts. Our approach features two key components: (1) an OoD-aware adaptive perception error margin and (2) a safety filter that integrates this adaptive error margin, enabling the filter to adjust its conservatism in real-time. We provide empirical validation in simulations, demonstrating that ATOM-CBF maintains safety for an F1Tenth vehicle with LiDAR scans and a quadruped robot with RGB images.

Figures (8)

• Figure 1: Problem setting (left) and ATOM-CBF (right). Offline, ID data is used to train a perception module and an epistemic uncertainty quantification (EUQ) module, and compute the base error ratio, $\varphi_{\text{cal}}$. Online, ATOM-CBF is deployed in OoD settings for F1Tenth and quadruped experiments.
• Figure 2: F1/10.
• Figure 3: F1Tenth vehicle experiment with a star obstacle. All trajectories start with an identical initial condition and OoD obstacle, comparing three controller variants: CBF-QP (red), ATOM-CBF with SCOD (green), ATOM-CBF with Deep Ensemble (purple). (Left) Trajectory plot. (Middle) Time plots of true $\alpha$ (blue) vs. predicted $\hat{\alpha}$ and its prediction interval (PI). (Right) Time plots of true $h(x)$ (blue) vs. estimated $h(\hat{x})$. Perception and safety filters are engaged until the vehicle passes the obstacle, at which point the nominal controller resumes control using the ground-truth state.
• Figure 4: Quadruped crash (OoD).
• Figure 5: Violin plots comparing the epistemic uncertainty score distributions from the calibration dataset ($\mathcal{D}_{\text{cal}}$), i.e., $S_{\text{cal}}$, for each EUQ module, plotted on a log-scale. The left plot shows the distributions for Deep Ensemble, and the right plot compares SCOD using a 5,000-point sketch ("SCOD 5k") versus a 20,000-point sketch ("SCOD 20k"). Each plot further separates the distributions for the F1Tenth (light-blue background) and quadruped (light-red background) experiments.

Theorems & Definitions (6)

• definition 1
• definition 2
• definition 3
• remark 1
• remark 2
• definition 4