Quadratic programs (QP) subject to multiple time-dependent control barrier function (CBF) based constraints have been used to design safety-critical controllers. However, ensuring the existence of a solution at all times to the QP subject to multiple CBF constraints is non-trivial. We quantify the feasible solution space of the QP in terms of its volume. We introduce a novel feasible space volume monitoring control barrier function that promotes compatibility of barrier functions and, hence, existence of a solution at all times. We show empirically that our approach not only enhances feasibility but also exhibits reduced sensitivity to changes in the hyperparameters such as gains of nominal controller. Finally, paired with a global planner, we evaluate our controller for navigation among humans in the AWS Hospital gazebo environment. The proposed controller is demonstrated to outperform the standard CBF-QP controller in maintaining feasibility.

翻译：基于多个时变控制障碍函数（CBF）约束的二次规划问题（QP）已被用于设计安全关键控制器。然而，确保在任意时刻满足多个CBF约束的QP解的存在性并非易事。我们通过体积量化了QP的可行解空间，并提出一种新颖的可行空间体积监测控制障碍函数，以增强障碍函数间的相容性，从而保障解始终存在。实验表明，我们的方法不仅提高了可行性，还降低了对名义控制器增益等超参数变化的敏感性。最后，结合全局规划器，我们在AWS Hospital gazebo环境中评估了控制器在人群导航中的表现。所提出的控制器在维持可行性方面明显优于标准CBF-QP控制器。