This paper presents methodologies for ensuring forward invariance of sublevel sets of constraint functions with high-relative-degree with respect to the system dynamics and in the presence of input constraints. We show that such constraint functions can be converted into special Zeroing Control Barrier Functions (ZCBFs), which, by construction, generate sufficient conditions for rendering the state always inside a sublevel set of the constraint function in the presence of input constraints. We present a general form for one such ZCBF, as well as a special case applicable to a specific class of systems. We conclude with a comparison of system trajectories under the two ZCBFs developed and prior literature, and a case study for an asteroid observation problem using quadratic-program based controllers to enforce the ZCBF condition.

中文翻译：

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输入约束下的高相对度控制障碍函数

本文提出了在系统动力学和存在输入约束的情况下确保具有高相关度的子级约束函数集的前向不变性的方法。我们表明，此类约束函数可以转换为特殊的归零控制障碍函数 (ZCBF)，通过构造，它可以生成充分条件，以便在存在输入约束的情况下始终在约束函数的子级集内呈现状态。我们提出了一个此类 ZCBF 的一般形式，以及适用于特定类别系统的特殊情况。我们最后比较了两个 ZCBF 和先前文献下的系统轨迹，以及使用基于二次规划的控制器来执行 ZCBF 条件的小行星观测问题的案例研究。