Control barrier functions (CBFs) provide a principled framework for safety-critical control, but their construction typically requires an explicit and differentiable description of the safe or unsafe region. It becomes challenging for data-defined unsafe regions that may evolve over time. This paper proposes SafeLink, a data-driven CBF construction and adaptation method based on a cost-sensitive random vector functional link (RVFL) network. SafeLink introduces asymmetric misclassification costs to promote conservative unsafe-region representation while preserving a closed-form solution. We establish the Lipschitz continuity of the learned CBF and its derivatives, and derive sufficient conditions for conservative unsafe-region coverage and the corresponding interval-wise safety guarantees. Analytical updates are further developed for adjusting the misclassification cost and for incrementally adding or decrementally removing samples, avoiding full retraining when the unsafe region changes. Experiments on a two-link manipulator demonstrate that SafeLink rapidly adapts to evolving unsafe regions, enables collision-free target reaching, and achieves substantially lower update runtimes than baselines.
As the number of autonomous robots continues to grow, safety becomes increasingly important. Control barrier functions (CBFs) provide a theoretically grounded framework for ensuring safety, but existing design methods often face limitations in effectiveness, scalability, or interpretability, and may result in overly conservative safe sets. In this paper, we propose \emph{VertexCBF}, a framework for learning neural CBFs in a scalable, systematic, and explainable way. We approximate the stationary Hamilton--Jacobi value function using a neural network trained via a combination of physics-informed and sparsely supervised learning. By exploiting control-affine dynamics and a convex polytope control set, under which the Hamiltonian is maximized at the control vertices, we efficiently generate supervision points via GPU-parallel vertex-restricted tree search, while a residual architecture guarantees that the learned CBF is never larger than the specified constraint function. We evaluate the method on 15 systems and compare it against relevant baselines, showing that it reliably recovers large safe sets where the baselines are conservative or fail completely. In addition, we perform a hardware experiment in which a mobile robot safely avoids pedestrians using a neural CBF trained with our method.
Inverse Reinforcement Learning (IRL) algorithms are powerful tools for learning from and generalizing expert demonstrations, but they often rely on unconstrained exploration, rendering them unsafe for real-world deployment. Meanwhile, Control Barrier Functions (CBFs) can guarantee the safety of control systems, but the analytical design of CBFs can be time-consuming and esoteric. In this work, we address these limitations jointly by constraining reward function candidacy during IRL to the space of CBFs, yielding a formulation that exhibits safe online control with continuous experiential improvement. Crucially, this framework enables the data-driven recovery of barrier functions directly from unlabeled expert observations. We demonstrate that the recovered barrier function is robust to unsafe states entirely absent from the expert data. Furthermore, we benchmark our method against standard IRL baselines in a simulated navigation environment, demonstrating improved safety performance. Finally, we investigate the trade-offs of planning-based versus policy-based IRL methods across both simulation and a real world obstacle avoidance task.
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.