从轨迹数据学习稳定性证书，无需模型也能保证机器人安全
Learning Stability Certificate for Robotics in Real-World Environments
- 用神经网络参数化李雅普诺夫函数，通过乔列斯基分解确保正定性
- 允许可控的不满足条件，实现在噪声数据下高置信度稳定认证
- 无需系统模型或控制算法即可验证机器人安全性，适合真实场景
稳定性证书在保障机器人系统安全与可靠性方面至关重要。然而，对于复杂未知系统，传统方法需明确系统动力学知识，往往难以实现。本文提出一种新框架，直接从轨迹数据中学习李雅普诺夫函数，使无需详细系统模型即可对自主系统进行稳定性认证。通过将李雅普诺夫候选函数用神经网络参数化，并利用乔列斯基分解确保其正定性，该方法可自动判断系统在给定轨迹下的稳定性。针对真实世界数据中的噪声问题，允许受控地违反稳定性条件，重点保持认证过程的高置信度。实验表明，该框架能提供数据驱动的稳定性保证，为动态真实环境中的机器人系统安全认证提供稳健方法。该方法无需访问内部控制算法，适用于行为不透明或专有的系统场景。相关工具已开源：https://github.com/HansOersted/stability。
原文摘要 · Abstract (English)
Stability certificates play a critical role in ensuring the safety and reliability of robotic systems. However, deriving these certificates for complex, unknown systems has traditionally required explicit knowledge of system dynamics, often making it a daunting task. This work introduces a novel framework that learns a Lyapunov function directly from trajectory data, enabling the certification of stability for autonomous systems without needing detailed system models. By parameterizing the Lyapunov candidate using a neural network and ensuring positive definiteness through Cholesky factorization, our approach automatically identifies whether the system is stable under the given trajectory. To address the challenges posed by noisy, real-world data, we allow for controlled violations of the stability condition, focusing on maintaining high confidence in the stability certification process. Our results demonstrate that this framework can provide data-driven stability guarantees, offering a robust method for certifying the safety of robotic systems in dynamic, real-world environments. This approach works without access to the internal control algorithms, making it applicable even in situations where system behavior is opaque or proprietary. The tool for learning the stability proof is open-sourced by this research: https://github.com/HansOersted/stability.
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