VertexCBF: Improving Neural Control Barrier Functions via Vertex-Restricted Control Search

Safe navigation of autonomous robots remains one of the core challenges in the field, especially in dynamic and uncertain environments. One prevalent approach is safety filtering based on control barrier functions (CBFs), which are easy to deploy but difficult to design. Motivated by the shortcomings of existing learning- and model-based methods, we propose a simple yet effective neural CBF design method for safe robot navigation in dynamic environments. We employ the idea of a composite CBF, where multiple neural CBFs are combined into a single CBF. Individual CBFs are trained using data generated offline via the Hamilton-Jacobi reachability framework to approximate the optimal safe set for single moving obstacles. Additionally, we use a residual neural architecture, ensuring that the estimated safe set does not intersect with the corresponding failure set. The method is extensively evaluated in simulation experiments for a ground robot and a quadrotor, comparing it against several baseline methods. The proposed method improves success rates by up to 18% over the strongest baseline, while maintaining comparable or lower path lengths and motion times. The method is also demonstrated in hardware experiments for both types of robots.

Safe navigation often relies on well-defined conditions based on the shape of robots and obstacles, and can be challenging when they have irregular geometries. While Control Barrier Functions (CBFs) offer an efficient mechanism to enforce safe set forward invariance, common shape surrogates (e.g., spheres or super-ellipsoids) either are overly conservative in unstructured scenes or require many local primitives, which inflates constraint counts and degrades real-time performance. In this paper, we introduce a novel geometry-aware Control Barrier Function (CBF) based on Bernstein-Polynomial Signed Distance Fields (BP-SDFs). It provides a unified way to represent the obstacles and robots, so as to represent the barrier function with a unified minimum distance. Benefiting from the differentiability of the Bernstein polynomials, one can easily enforce the control constraints in a closed loop. We validate the method's efficiency and performance to guarantee safety in single-robot navigation and heterogeneous multi-robot collision avoidance via simulations under different environments.

Reinforcement learning (RL), while powerful and expressive, can often prioritize performance at the expense of safety. Yet safety violations can lead to catastrophic outcomes in real-world deployments. Control Barrier Functions (CBFs) offer a principled method to enforce dynamic safety -- traditionally deployed online via safety filters. While the result is safe behavior, the fact that the RL policy does not have knowledge of the CBF can lead to conservative behaviors. This paper proposes CBF-RL, a framework for generating safe behaviors with RL by enforcing CBFs in training. CBF-RL has two key attributes: (1) minimally modifying a nominal RL policy to encode safety constraints via a CBF term, (2) and safety filtering of the policy rollouts in training. Theoretically, we prove that continuous-time safety filters can be deployed via closed-form expressions on discrete-time roll-outs. Practically, we demonstrate that CBF-RL internalizes the safety constraints in the learned policy -- both enforcing safer actions and biasing towards safer rewards -- enabling safe deployment without the need for an online safety filter. We validate our framework through ablation studies on navigation tasks and on the Unitree G1 humanoid robot, where CBF-RL enables safer exploration, faster convergence, and robust performance under uncertainty, enabling the humanoid robot to avoid obstacles and climb stairs safely in real-world settings without a runtime safety filter.