Safety is a fundamental requirement of many robotic systems. Control barrier function (CBF)-based approaches have been proposed to guarantee the safety of robotic systems. However, the effectiveness of these approaches highly relies on the choice of CBFs. Inspired by the universal approximation power of neural networks, there is a growing trend toward representing CBFs using neural networks, leading to the notion of neural CBFs (NCBFs). Current NCBFs, however, are trained and deployed in benign environments, making them ineffective for scenarios where robotic systems experience sensor faults and attacks. In this paper, we study safety-critical control synthesis for robotic systems under sensor faults and attacks. Our main contribution is the development and synthesis of a new class of CBFs that we term fault tolerant neural control barrier function (FT-NCBF). We derive the necessary and sufficient conditions for FT-NCBFs to guarantee safety, and develop a data-driven method to learn FT-NCBFs by minimizing a loss function constructed using the derived conditions. Using the learned FT-NCBF, we synthesize a control input and formally prove the safety guarantee provided by our approach. We demonstrate our proposed approach using two case studies: obstacle avoidance problem for an autonomous mobile robot and spacecraft rendezvous problem, with code available via https://github.com/HongchaoZhang-HZ/FTNCBF.

翻译：安全性是许多机器人系统的基本要求。基于控制障碍函数（CBF）的方法已被提出用于保障机器人系统的安全性，然而该类方法的有效性高度依赖于CBF的选择。受神经网络通用逼近能力的启发，利用神经网络表示CBF已成为发展趋势，由此引出神经CBF（NCBF）的概念。然而，现有NCBF均在无干扰环境中训练与部署，这使得它们在机器人系统遭遇传感器故障与攻击时失效。本文研究传感器故障与攻击下机器人系统的安全关键控制综合问题。我们的主要贡献在于开发并综合了一类新型CBF，即所提出的容错神经控制障碍函数（FT-NCBF）。我们推导了FT-NCBF保障安全性的充要条件，并通过最小化基于该条件构建的损失函数，开发了一种数据驱动的FT-NCBF学习方法。利用学习得到的FT-NCBF，我们综合了控制输入，并严格证明了该方法提供的安全保障。通过两个案例研究（自主移动机器人避障问题和航天器交会问题）验证了所提方法的有效性，相关代码见https://github.com/HongchaoZhang-HZ/FTNCBF。