AI 中文总结
本文针对控制障碍函数存在的无记忆算子易受高频噪声影响的问题，提出时空变换方法设计STT-CBF，经仿真验证其可实现100%安全率并大幅降低控制抖动，适用于物理机器人平台。
AI 中文摘要
控制障碍函数（CBFs）、其高阶变体（HOCBFs）及指数型CBFs（ECBFs）是用于强制执行非线性安全约束的标准几何工具。CBFs及其变体为非线性安全提供了简洁的几何框架，但从数学角度看，它们可简化为受零记忆核限制的连续时间卷积。在存在高频测量噪声的情况下，这些无记忆算子会充当不合适的滤波器，导致控制剧烈抖动，并因二次规划（QP）不可行而可能丧失主动控制权限。为解决这一结构局限性，本文提出一种时空变换，将动态时间滤波直接嵌入安全约束综合过程。通过设计合适的时空核，该方法可在保留仿射控制权限的同时固有地衰减高频噪声。关键在于，我们证明了所设计的STT-CBF的鲁棒前向不变性。对三阶系统的蒙特卡洛仿真表明，与传统参数化障碍方法相比，所提框架实现了100%的安全率，同时将控制总变差降低了99%以上，减轻了硬件风险，可在物理机器人平台上实现可靠部署。
英文摘要
Control Barrier Functions (CBFs), their High-Order variants (HOCBFs) and Exponential CBFs (ECBFs) are standard geometric tools for enforcing nonlinear safety constraints. CBFs, and their variants, offer an elegant geometric framework for nonlinear safety, yet mathematically, they reduce to continuous-time convolutions restricted by zero-memory kernels. In the presence of high-frequency measurement noise, these memoryless operators act as improper filters, leading to significant control chattering and the potential loss of active control authority due to Quadratic Program (QP) infeasibility. To address this structural limitation, this paper introduces a space-time transform that embeds dynamic temporal filtering directly into the safety constraint synthesis. By designing a proper spatio-temporal kernel, this approach inherently attenuates high-frequency noise while preserving affine control authority. Crucially, we prove the robust forward invariance of the designed STT-CBF. Monte Carlo simulations of a third-order system demonstrate that the proposed framework achieves a 100% safety rate while reducing control total variation by over 99% compared to conventional parameterized barrier methods, mitigating hardware hazards and enabling reliable deployment on physical robotic platforms.
Comments12 pages, 1 figure
