CBF-Based Hierarchical Quadratic Programs with Guaranteed Feasibility for Safety-Critical Systems
Junjun Xie, Liang Hu, Yunzhe Tan, Jun Yang
AI summary
Problem
Existing CBF-based QP methods often suffer from infeasibility or overly conservative relaxations when handling multiple constraints, input limits, and performance objectives simultaneously, compromising safety or navigability in complex environments
Approach
The authors propose a hierarchical optimization framework that prioritizes safety constraints in a top-level sub-problem, then sequentially optimizes performance and minimizes control input in lower levels, ensuring feasibility is never sacrificed
Key results
- Theoretical proof of guaranteed feasibility under arbitrary CBF and input constraints
- Unified formulation exposing root causes of infeasibility and performance loss in prior QP methods
- CDT-based geometric approximation for representing irregular obstacles via multiple simple CBFs
- Real-world robot navigation validation in cluttered and dynamic environments
Why it matters
Provides a robust, scalable control framework for autonomous systems and robotics to safely navigate complex, unstructured environments without compromising feasibility or safety guarantees
Abstract
Control Barrier Function (CBF) based quadratic pro- grams (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 rep- resentation 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. Note to Practitioners—This paper is motivated by the need to ensure safety and solution feasibility for safe-critical systems with multiple constraints, such as safe navigation through irregular or dynamic obstacles. Control Barrier Functions (CBFs) have emerged as a promising approach for enforcing safety in optimization-based control, but existing approaches face feasibility issues as constraint complexity grows, especially when considering input limitations and performance goals as well. In practice, a single constraint is often insufficient to represent safety requirements, such as autonomous navigation among irregular or dynamic obstacles. To overcome these issues, this paper provides a hierarchical optimization framework that prioritizes safety yet improving other performance. It guarantees feasibility under any number of constraints, and models safety in complex environments accurately through multiple, easily constructed CBFs. The proposed method is applied to safe navigation tasks involving irregular and dynamic obstacles, showing that our algorithm achieves safe and reliable navigation in challenging scenarios. These results demonstrate the practical value of the framework and its potential for broader application to safety- critical systems operating in uncertain and/or unstructured real- world environments.