CBF-Based Hierarchical Quadratic Programs with Guaranteed Feasibility for Safety-Critical Systems (I)

Abstract

Control Barrier Function (CBF) based quadratic programs (QPs) have become an effective method for enforcing safety in safety-critical systems and robotics. However, these methods often suffer from infeasibility or overly conservative relaxations when handling multiple constraints, potentially compromising safety. In this paper, we propose a hierarchical framework called ``Safety-first" for control design, which simultaneously incorporates performance objectives formulated using Control Lyapunov Functions (CLFs), and safety guarantees via CBFs with input constraints. Unlike existing approaches, the proposed method guarantees solution feasibility while achieving improved performance, and it is scalable to an arbitrary number of CBF constraints. This scalability enables more precise and flexible representation of complex safety requirements using multiple simple CBFs. For application to mobile robot navigation, we employ Constrained Delaunay Triangulation (CDT) to construct multiple CBFs that approximate irregularly-shaped obstacles. Real-world experiments in cluttered and dynamic environments demonstrate that the Safety-first algorithm achieves safe navigation, validating both the theoretical guarantee and practical advantages over existing methods.