Safety-critical control is characterized as ensuring constraint satisfaction for a given dynamical system. Recent developments in zeroing control barrier functions (ZCBFs) have provided a framework for ensuring safety of a superlevel set of a single constraint function. Euler–Lagrange systems represent many real-world systems including robots and vehicles, which must abide by safety-regulations, especially for use in human-occupied environments. These safety regulations include state constraints (position and velocity) and input constraints that must be respected at all times. ZCBFs are valuable for satisfying system constraints for general nonlinear systems, however their construction to satisfy state and input constraints is not straightforward. Furthermore, the existing barrier function methods do not address the multiple state constraints that are required for safety of Euler–Lagrange systems. In this paper, we propose a methodology to construct multiple, non-conflicting control barrier functions for Euler–Lagrange systems subject to input constraints to satisfy safety regulations, while concurrently taking into account robustness margins and sampling-time effects. The proposed approach consists of a sampled-data controller and an algorithm for barrier function construction to enforce safety (i.e. satisfy position and velocity constraints). The proposed method is validated in simulation on a 2-DOF planar manipulator.

安全关键控制的特点是确保给定动态系统的约束满足。归零控制障碍函数 (ZCBF) 的最新发展为确保单个约束函数的超级别集的安全性提供了一个框架。欧拉-拉格朗日系统代表了许多现实世界的系统，包括机器人和车辆，它们必须遵守安全法规，尤其是在有人居住的环境中使用。这些安全法规包括必须始终遵守的状态约束（位置和速度）和输入约束。ZCBF 对于满足一般非线性系统的系统约束很有价值，但是它们的构造是为了满足状态和输入约束并不简单。此外，现有的障碍函数方法没有解决欧拉-拉格朗日系统安全所需的多状态约束。在本文中，我们提出了一种方法，用于为受输入约束的欧拉-拉格朗日系统构建多个不冲突的控制障碍函数，以满足安全规定，同时考虑鲁棒性裕度和采样时间效应。所提出的方法由一个采样数据控制器和一个用于构建屏障函数的算法组成，以增强安全性（即满足位置和速度约束）。所提出的方法在 2-DOF 平面机械手的仿真中得到验证。