The safety-critical control of robotic systems often must account for multiple, potentially conflicting, safety constraints. This paper proposes novel relaxation techniques to address safety-critical control problems in the presence of conflicting safety conditions. In particular, Control Barrier Function (CBFs) provide a means to encode safety as constraints in a Quadratic Program (QP), wherein multiple safety conditions yield multiple constraints. However, the QP problem becomes infeasible when the safety conditions cannot be simultaneously satisfied. To resolve this potential infeasibility, we introduce a hierarchy between the safety conditions and employ an additional variable to relax the less important safety conditions (Relaxed-CBF-QP), and formulate a cascaded structure to achieve smaller violations of lower-priority safety conditions (Hierarchical-CBF-QP). The proposed approach, therefore, ensures the existence of at least one solution to the QP problem with the CBFs while dynamically balancing enforcement of additional safety constraints. Importantly, this paper evaluates the impact of different weighting factors in the Hierarchical-CBF-QP and, due to the sensitivity of these weightings in the observed behavior, proposes a method to determine the weighting factors via a sampling-based technique. The validity of the proposed approach is demonstrated through simulations and experiments on a quadrupedal robot navigating to a goal through regions with different levels of danger.

翻译：机器人系统的安全关键控制通常需要考虑多个可能冲突的安全约束。本文提出新颖的松弛技术，以处理存在冲突安全条件时的安全关键控制问题。具体而言，控制障碍函数(CBF)提供了一种将安全条件编码为二次规划(QP)中约束的方法，其中多个安全条件产生多个约束。然而，当安全条件无法同时满足时，QP问题将变得不可行。为解决这一潜在不可行性问题，我们在安全条件之间引入分层结构，并使用附加变量松弛次要安全条件(Relaxed-CBF-QP)，同时构建级联结构以实现对低优先级安全条件更小的违反程度(Hierarchical-CBF-QP)。因此，所提方法在动态平衡附加安全约束执行的同时，确保至少存在一个符合CBF的QP问题解。重要的是，本文评估了Hierarchical-CBF-QP中不同权重因子的影响，并针对观测行为中这些权重的敏感性，提出了一种基于采样的权重因子确定方法。通过四足机器人在不同危险等级区域中导航至目标的仿真与实验，验证了所提方法的有效性。