This paper presents two new control approaches for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including linear and quadratic programs subject to affine constraints, which are shown to be feasible. The first control method relies on a soft-minimum barrier function that is constructed using a finite-time-horizon prediction of the system trajectories under a known backup control. The main result shows that the control is continuous and satisfies the actuator constraints, and a subset of the safe set is forward invariant under the control. Next, we extend this method to allow from multiple backup controls. This second approach relies on a combined soft-maximum/soft-minimum barrier function, and it has properties similar to the first. We demonstrate these controls on numerical simulations of an inverted pendulum and a nonholonomic ground robot.

中文翻译：

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软最小和软最大安全栅功能，确保在执行约束下实现安全


本文提出了两种新的控制方法，以保证安全（保持在安全集中），但受致动器约束（控制在凸多面体中）。控制信号是使用实时优化计算的，包括受仿射约束的线性和二次规划，这些约束被证明是可行的。第一种控制方法依赖于软最小障碍函数，该函数使用已知备份控制下系统轨迹的有限时间范围预测构建。主要结果表明，该控件是连续的，并且满足 actuator 约束，并且安全集的一个子集在控件下是前向不变的。接下来，我们将此方法扩展为允许来自多个备份控件。第二种方法依赖于组合的软-最大值/-软-最小值障碍函数，并且它具有与第一种方法类似的属性。我们在倒立摆和非完整地面机器人的数值仿真中演示了这些控制。