标题： 固定时间收敛保证对于高阶控制屏障函数 显示英文标题

标题： Fixed time convergence guarantees for Higher Order Control Barrier Functions

摘要： 我们提出了一种设计高阶控制屏障函数（CBFs）的新方法，该方法保证在用户指定的有限时间内收敛到安全集。传统的高阶控制屏障函数（HOCBFs）确保渐近安全，但缺乏固定时间收敛的机制，这在时间敏感和安全关键的应用中至关重要，例如自主导航。相比之下，我们的方法使用特征多项式中的重根施加结构化的微分约束，从而实现具有精确收敛时间的显式多项式解。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的条件，并为二阶系统提供了显式公式。我们的方法在三个机器人系统上进行了评估——一个质点模型、一个全向车和一个自行车模型，并与现有的HOCBF方法进行了比较。结果表明，即使传统方法失效时，我们的公式也能可靠地在所需时间内强制收敛。这项工作提供了一个可行且稳健的框架，用于具有可证明的有限时间安全保证的实时控制。 显示英文摘要

摘要： 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.