无需微分的零阶安全约束方法，提升采样系统安全性
Zero-Order Control Barrier Functions for Sampled-Data Systems with State and Input Dependent Safety Constraints
- 用采样点间差值替代微分，实现零阶安全约束
- 可处理状态与输入共同依赖的复杂安全约束
- 适用于资源受限场景，已在避障与防翻滚中验证
本文提出一种新型零阶控制屏障函数（ZOCBF），用于保证采样数据系统的安全性。该方法推广了传统控制屏障函数，能直接处理高相对阶或显式依赖系统状态与输入的安全约束。所提ZOCBF条件无需任何微分运算，仅需计算两个连续采样时刻的ZOCBF值之差。针对不同问题设置和计算资源，我们提出了三种数值实现方法。通过碰撞避免与不平地形上的翻滚预防实例，验证了该方法的有效性。
原文摘要 · Abstract (English)
We propose a novel zero-order control barrier function (ZOCBF) for sampled-data systems to ensure system safety. Our formulation generalizes conventional control barrier functions and straightforwardly handles safety constraints with high-relative degrees or those that explicitly depend on both system states and inputs. The proposed ZOCBF condition does not require any differentiation operation. Instead, it involves computing the difference of the ZOCBF values at two consecutive sampling instants. We propose three numerical approaches to enforce the ZOCBF condition, tailored to different problem settings and available computational resources. We demonstrate the effectiveness of our approach through a collision avoidance example and a rollover prevention example on uneven terrains.
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