通过对称性解耦设计随时间变化的约束函数,提升系统安全性与计算效率。
Decoupled Design of Time-Varying Control Barrier Functions via Equivariances
- 利用系统动态的对称性,将时变约束函数分解为静态与时变部分
- 无需重新计算基础约束函数,显著降低设计复杂度
- 适用于不确定环境中的欠驱动系统,只需知道约束变化趋势
本文提出一种系统化方法,用于设计由时不变分量和多个时变分量组成的时变控制屏障函数(CBF),该方法基于系统动力学的结构特性。首先构建一类编码系统动态能力的时不变CBF,再通过精心设计的时变变换进行增强。虽然通用的时间变换可应用于任意系统,但利用动力学中特定结构属性——尤其是对称性——可处理更广泛、更丰富的时变约束。文章展示了如何在设计中利用这些性质。所提方法将时变设计与计算成本高的基础CBF构造解耦,从而提供一种计算上更高效的时变CBF设计途径。该方法考虑输入约束和欠驱动情况,仅需对约束时变性的定性知识,适合应用于不确定性环境。
原文摘要 · Abstract (English)
This article presents a systematic method for designing time-varying Control Barrier Functions (CBF) composed of a time-invariant component and multiple time-dependent components, leveraging structural properties of the system dynamics. The method involves the construction of a specific class of time-invariant CBFs that encode the system's dynamic capabilities with respect to a given constraint, and augments them subsequently with appropriately designed time-dependent transformations. While transformations uniformly varying the time-invariant CBF can be applied to arbitrary systems, transformations exploiting structural properties in the dynamics - equivariances in particular - enable the handling of a broader and more expressive class of time-varying constraints. The article shows how to leverage such properties in the design of time-varying CBFs. The proposed method decouples the design of time variations from the computationally expensive construction of the underlying CBFs, thereby providing a computationally attractive method to the design of time-varying CBFs. The method accounts for input constraints and under-actuation, and requires only qualitative knowledge on the time-variation of the constraints making it suitable to the application in uncertain environments.
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。