Lyapunov-Based Control Barrier Functions for Real-Time Safe Navigation in Three-Dimension Complex Environments
Fuwei Zhang, Zhiwei Hou
AI summary
Problem
Existing safe navigation methods struggle to guarantee real-time collision avoidance and asymptotic stability simultaneously for high-dimensional nonlinear robots in large-scale, obstacle-dense environments due to computational bottlenecks and offline synthesis requirements.
Approach
The method exploits system translational symmetry to dynamically generate and switch between multiple spatially shifted Control Barrier Functions from a single Control Lyapunov Function, integrated into a real-time quadratic programming safety filter.
Key results
- Unifies safety and asymptotic stability within a single coherent control framework
- Decouples computational load from environmental scale via online local synthesis
- Achieves real-time safe navigation in cluttered 2D and 3D environments with aggressive inputs
- Demonstrates superior efficiency and scalability over offline Lyapunov-based CBF-QP baselines
Why it matters
Provides a computationally tractable and theoretically rigorous safety filter for deploying autonomous robots in complex, large-scale operational spaces.
Abstract
In the field of safe navigation for mobile robots, con- trol 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.