Lyapunov-Based Control Barrier Functions for Real-Time Safe Navigation in Three-Dimension Complex Environments

Abstract

In the field of safe navigation for mobile robots, control barrier functions (CBFs) have garnered significant attention due to their ability to transform complex safety constraints into real-time solvable optimization problems. In this letter, we propose a novel Lyapunov-based CBF framework. It offers the following key advantages: (1) Using a single Control Lyapunov Function (CLF), this method synthesizes spatially shifted CBFs to construct an expansive safe invariant set in obstacle-dense environments. (2) The framework is capable of incorporating existing approaches for constructing quadratic CLF, making it applicable to a wide range of complex nonlinear systems and enhancing its generality and extensibility. (3) It enables real-time synthesis of CBFs, and ensures safety in large-scale 3D environments through efficient CBF-based quadratic programming (CBF-QP). (4) The method ensures safety while inheriting the stability properties of the CLF, allowing the asymptotic convergence of the system state to equilibrium, thus unifying safety and motion stability. To validate efficacy, we rigorously tested the framework in both simulations and hardware experiments.