提出简化版控制屏障函数，减少设计参数并保障安全
High-Order Control Barrier Functions: Insights and a Truncated Taylor-Based Formulation
- 用截断泰勒展开近似离散时间屏障条件
- 仅需一个类K函数，相对阶数升高时仍保持低复杂度
- 在避障实验中验证安全性与设计简化效果
我们分析了标准高阶控制屏障函数（HOCBF）方法的复杂性，并提出一种基于截断泰勒展开的新方法以降低设计参数数量。首先，我们推导出HOCBF方法的显式不等式条件，发现其等式条件对屏障函数值设定下限，从而调控衰减速率。接着，我们提出截断泰勒控制屏障函数（TTCBF），利用截断泰勒级数近似离散时间下的CBF条件。相较于标准HOCBF需多个类K函数导致设计参数随约束相对阶数增加而增多，TTCBF仅需一个类K函数。我们在数值避障实验中验证了理论结果，表明该方法在保证安全性的前提下显著降低了设计复杂度。
原文摘要 · Abstract (English)
We examine the complexity of the standard High-Order Control Barrier Function (HOCBF) approach and propose a truncated Taylor-based approach that reduces design parameters. First, we derive the explicit inequality condition for the HOCBF approach and show that the corresponding equality condition sets a lower bound on the barrier function value that regulates its decay rate. Next, we present our Truncated Taylor CBF (TTCBF), which uses a truncated Taylor series to approximate the discrete-time CBF condition. While the standard HOCBF approach requires multiple class K functions, leading to more design parameters as the constraint's relative degree increases, our TTCBF approach requires only one. We support our theoretical findings in numerical collision-avoidance experiments and show that our approach ensures safety while reducing design complexity.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。