提出可保证有限时间内到达安全区的高阶安全函数方法。
Fixed time convergence guarantees for Higher Order Control Barrier Functions
- 通过特征多项式重根构造微分约束，实现闭式解。
- 在3个机器人模型上验证，可精确在指定时间收敛。
- 适合自动驾驶等对时效性要求高的安全控制场景。
我们提出一种新型高阶控制屏障函数（HOCBF）设计方法，可保证系统在用户指定的有限时间内收敛至安全集。传统HOCBF仅能保证渐近安全，缺乏固定时间收敛机制，而这在自主导航等时敏、高危应用中至关重要。本文通过在特征多项式中引入重根，施加结构化微分约束，获得闭式多项式解，实现精确预定时间收敛。我们推导了确保前向不变性和固定时间可达性的屏障函数及其导数条件，并给出了二阶系统的显式表达。在点质量模型、全向移动机器人和自行车模型三个机器人系统上进行了评估，与现有HOCBF方法对比，结果表明本方法即使在传统方法失效时仍能可靠实现期望时间内的收敛。该工作为实时控制提供了可计算且鲁棒的有限时间安全保证框架。
原文摘要 · Abstract (English)
We present a novel method for designing higher-order Control Barrier Functions (CBFs) that guarantee convergence to a safe set within a user-specified finite. Traditional Higher Order CBFs (HOCBFs) ensure asymptotic safety but lack mechanisms for fixed-time convergence, which is critical in time-sensitive and safety-critical applications such as autonomous navigation. In contrast, our approach imposes a structured differential constraint using repeated roots in the characteristic polynomial, enabling closed-form polynomial solutions with exact convergence at a prescribed time. We derive conditions on the barrier function and its derivatives that ensure forward invariance and fixed-time reachability, and we provide an explicit formulation for second-order systems. Our method is evaluated on three robotic systems - a point-mass model, a unicycle, and a bicycle model and benchmarked against existing HOCBF approaches. Results demonstrate that our formulation reliably enforces convergence within the desired time, even when traditional methods fail. This work provides a tractable and robust framework for real-time control with provable finite-time safety guarantees.
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