ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks

TL;DR

The paper addresses safety filtering for autonomous systems operating with partial environmental observations. It introduces ORN-CBF, which combines Hamilton-Jacobi reachability with a hypernetwork-conditioned residual CBF to approximate the maximal safe set while ensuring the learned CBF does not intersect the observed failure set. A residual learning approach trains a simple main network to model a nonnegative residual on top of a discretized SDF, enabling high-frequency safety filtering with guarantees. Empirical results in both simulation and hardware show improved safety performance and generalization for a ground robot and a quadcopter, outperforming MPC-based baselines and demonstrating strong out-of-domain robustness.

Abstract

Control barrier functions (CBFs) have been demonstrated as an effective method for safety-critical control of autonomous systems. Although CBFs are simple to deploy, their design remains challenging, motivating the development of learning-based approaches. Yet, issues such as suboptimal safe sets, applicability in partially observable environments, and lack of rigorous safety guarantees persist. In this work, we propose observation-conditioned neural CBFs based on Hamilton-Jacobi (HJ) reachability analysis, which approximately recover the maximal safe sets. We exploit certain mathematical properties of the HJ value function, ensuring that the predicted safe set never intersects with the observed failure set. Moreover, we leverage a hypernetwork-based architecture that is particularly suitable for the design of observation-conditioned safety filters. The proposed method is examined both in simulation and hardware experiments for a ground robot and a quadcopter. The results show improved success rates and generalization to out-of-domain environments compared to the baselines.

Figures (11)

• Figure 1: Safety filtering for autonomous systems operating based on environment observations with the proposed ORN-CBF method.
• Figure 2: Illustration of the critical moment when the new observation occurs. The robot must be outside of the BRT $\mathcal{B}$ corresponding to the suddenly observed failure set $\mathcal{F}$. This can be achieved by considering all aspects such as the robot's maximal speed, observation size and update rate, maximal expected size of an obstacle, and the shape of the corresponding BRT.
• Figure 3: A detailed architecture of the ORN-CBF safety filter. Based on the observation $o$, a discretized SDF $\bar{d}$ is computed, which is then fed into the hypernetwork and the SDF interpolation function. The hypernetwork parametrizes the main network, which approximates the nonnegative residual $\hat{r}$ and its gradient $\nabla \hat{r}$. The approximate CBF value $\hat{h}$ and gradient $\nabla \hat{h}$ are obtained by subtracting $\hat{r}$ and $\nabla \hat{r}$ from interpolated SDF value $\hat{d}$ and gradient $\nabla \hat{d}$, respectively. In the end, $L_f\hat{h}$ and $L_g\hat{h}$ are computed based on $\nabla \hat{h}$ and the system dynamics and together with $\hat{h}$ provided to the CBF-QP safety filter.
• Figure 4: An example of a learned ORN-CBF for the Dubins car model.
• Figure 5: Left: Scene from the 3D simulation experiment with the ground robot in the warehouse environment. Right: The corresponding observation.