用物理神经网络自动构建安全控制函数，适配复杂系统。
Neural Control Barrier Functions from Physics Informed Neural Networks
- 基于泊松方程的神经网络框架，自动生成安全控制函数。
- 在3个系统上验证，实现高维场景下的安全导航。
- 支持自定义安全区域，比传统方法更灵活实用。
随着自主系统在日常生活中的广泛应用，确保其安全性至关重要。控制屏障函数（CBFs）已成为保障安全的有效工具，但针对特定应用手动设计仍具挑战性。随着深度学习的发展，近期研究尝试使用神经网络合成CBFs，即神经CBFs。本文提出一种新型神经CBFs，基于物理启发的神经网络框架，将佐沃夫偏微分方程（Zubov's PDE）引入安全语境中，提供了一种可扩展的方法，适用于高维系统。此外，通过采用互逆CBFs而非零化CBFs，该框架允许用户灵活定义安全区域。为验证方法有效性，本文在三个不同系统上进行了案例研究：倒立摆、自主地面导航及障碍物密集环境中的空中导航。
原文摘要 · Abstract (English)
As autonomous systems become increasingly prevalent in daily life, ensuring their safety is paramount. Control Barrier Functions (CBFs) have emerged as an effective tool for guaranteeing safety; however, manually designing them for specific applications remains a significant challenge. With the advent of deep learning techniques, recent research has explored synthesizing CBFs using neural networks-commonly referred to as neural CBFs. This paper introduces a novel class of neural CBFs that leverages a physics-inspired neural network framework by incorporating Zubov's Partial Differential Equation (PDE) within the context of safety. This approach provides a scalable methodology for synthesizing neural CBFs applicable to high-dimensional systems. Furthermore, by utilizing reciprocal CBFs instead of zeroing CBFs, the proposed framework allows for the specification of flexible, user-defined safe regions. To validate the effectiveness of the approach, we present case studies on three different systems: an inverted pendulum, autonomous ground navigation, and aerial navigation in obstacle-laden environments.
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