提出高阶安全控制方法，实现无人机导航中稳定与安全的协同控制
Optimal Safety Control using High-Order Control Barrier Functions
- 设计新型高阶控制屏障函数，显式构造安全控制器
- 结合高阶控制李雅普诺夫函数，实现系统稳定与安全的同步保障
- 在四旋翼飞行器导航中验证方法有效性，适用于高安全要求场景
本文针对非线性控制系统中的最优安全控制问题，提出新型高阶控制屏障函数（HOCBFs）。不同于传统的零化型HOCBF，本文推导出两种新形式的HOCBF，并以显式方式设计安全控制器。随后，采用向量李雅普诺夫函数方法，提出一种新的高阶控制李雅普诺夫函数（HOCLF），用于解决稳定控制问题。文中讨论了所提方法与现有HOCBF之间的关系，并分析了HOCLF与HOCBF的兼容性，以确保稳定性和安全性目标同时达成，从而建立最优控制器。最后，通过四旋翼飞行器导航问题的数值实验，验证了所提方法的有效性。
原文摘要 · Abstract (English)
This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.
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