VertexCBF：通过顶点受限控制搜索改进神经控制障碍函数
VertexCBF: Improving Neural Control Barrier Functions via Vertex-Restricted Control Search
- Technical University of Berlin（柏林工业大学）
- AUMOVIO
- Technical University of Applied Sciences Augsburg（奥格斯堡应用技术大学）
- Robotics Institute Germany (RIG)（德国机器人研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出VertexCBF框架，通过顶点受限树搜索和残差架构学习神经控制障碍函数，在15个系统及硬件实验中可靠恢复大安全集，优于保守或失败的基线方法。
AI中文摘要：
随着自主机器人数量持续增长，安全性变得日益重要。控制障碍函数（CBFs）为保障安全性提供了理论严谨的框架，但现有设计方法在有效性、可扩展性或可解释性方面往往存在局限，且可能导致过于保守的安全集。本文提出VertexCBF，一种以可扩展、系统且可解释的方式学习神经CBF的框架。我们利用物理信息与稀疏监督学习相结合的训练方式，用神经网络逼近稳态Hamilton-Jacobi值函数。通过利用控制仿射动力学和凸多面体控制集（在此条件下Hamiltonian在控制顶点处取得最大值），我们借助GPU并行的顶点受限树搜索高效生成监督点，同时残差架构保证学习到的CBF不大于指定的约束函数。我们在15个系统上评估了该方法，并与相关基线进行比较，表明它能可靠地恢复较大的安全集，而基线方法则表现保守或完全失败。此外，我们进行了硬件实验，在该实验中移动机器人使用我们方法训练的神经CBF安全地避开了行人。
英文摘要：
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.
