Control Barrier Function-Based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria

Control Lyapunov functions (CLFs) and control barrier (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs), guaranteeing safety in the form trajectory invariance with respect a given set. In this letter, we show that framework can introduce equilibrium points (particularly at boundary set) other than minimum function into closed-loop system. We derive explicit conditions under which these undesired equilibria (which even appear simple case linear systems just one convex unsafe are asymptotically stable. To address issue, propose an extension QP-based controller unifying CLFs CBFs such resulting system trajectories avoid undesirable problem on The solution is illustrated design collision-free controller.