We propose a learning-based Control Barrier Function (CBF) to reduce conservatism in collision avoidance of car-like robots. Traditional CBFs often use Euclidean distance between robots' centers as safety margin, neglecting headings and simplifying geometries to circles. While this ensures smooth, differentiable safety functions required by CBFs, it can be overly conservative in tight environments. To address this limitation, we design a heading-aware safety margin that accounts for the robots' orientations, enabling a less conservative and more accurate estimation of safe regions. Since the function computing this safety margin is non-differentiable, we approximate it with a neural network to ensure differentiability and facilitate integration with CBFs. We describe how we achieve bounded learning error and incorporate the upper bound into the CBF to provide formal safety guarantees through forward invariance. We show that our CBF is a high-order CBF with relative degree two for a system with two robots whose dynamics are modeled by the nonlinear kinematic bicycle model. Experimental results in overtaking and bypassing scenarios reveal a 33.5 % reduction in conservatism compared to traditional methods, while maintaining safety. Code: https://github.com/bassamlab/sigmarl

翻译：本文提出一种基于学习的控制屏障函数（CBF）方法，以降低类汽车机器人在避障过程中的保守性。传统CBF通常将机器人中心间的欧氏距离作为安全裕度，忽略航向角并将几何形状简化为圆形。虽然这种方法能保证CBF所需的光滑可微安全函数，但在狭窄环境中可能过于保守。为克服该局限，我们设计了一种航向感知安全裕度，该裕度综合考虑机器人的朝向信息，从而实现对安全区域更精确且保守性更低的估计。由于计算该安全裕度的函数不可微，我们采用神经网络进行近似以保证可微性，并实现与CBF框架的集成。我们阐述了如何实现有界学习误差，并将误差上界纳入CBF框架，通过前向不变性提供形式化的安全保证。针对采用非线性运动学自行车模型的双机器人系统，我们证明所提出的CBF是具有二阶相对度的高阶CBF。超车与绕行场景的实验结果表明，在保证安全性的前提下，该方法相比传统方法将保守性降低了33.5%。代码：https://github.com/bassamlab/sigmarl