Safety-critical Control with Control Barrier Functions: A Hierarchical Optimization Framework

The control barrier function (CBF) has become a fundamental tool in safety-critical systems design since its invention. Typically, the quadratic optimization framework is employed to accommodate CBFs, control Lyapunov functions (CLFs), other constraints and nominal control design. However, the constrained optimization framework involves hyper-parameters to tradeoff different objectives and constraints, which, if not well-tuned beforehand, impact system performance and even lead to infeasibility. In this paper, we propose a hierarchical optimization framework that decomposes the multi-objective optimization problem into nested optimization sub-problems in a safety-first approach. The new framework addresses potential infeasibility on the premise of ensuring safety and performance as much as possible and applies easily in multi-certificate cases. With vivid visualization aids, we systematically analyze the advantages of our proposed method over existing QP-based ones in terms of safety, feasibility and convergence rates. Moreover, two numerical examples are provided that verify our analysis and show the superiority of our proposed method.