Safe Control for Navigation in Cluttered Space Using Multiple Lyapunov-Based Control Barrier Functions

Control barrier functions (CBFs) are powerful tools for ensuring safety in controlled systems, commonly employed through the construction of a safety filter using quadratic programming (QP), known as CBF-QP. However, synthesizing a CBF specifically for the navigation tasks of mobile robots, where safety is crucial, poses challenges due to the complexity of the operating environments. In addition to that, the CBF synthesis should be repeated for every new environment, further escalating the computational burden. In this letter, we introduce Lyapunov-based CBFs, which is a CBF built solely from a control Lyapunov function (CLF). By utilizing multiple Lyapunov-based CBFs as building blocks to create a large control invariant set, we formulate a CBF-QP-like safety filter to ensure safety in cluttered environments. The proposed safety filter inherits the favorable characteristics of CBF-QP such as fast computation and safety guarantee, and can adapt to diverse environments without the need for burdensome resynthesis of a new environment-specific CBF. We demonstrate the effectiveness of the proposed approach through multiple simulation and real-world experiments, whose results show that the proposed safety filter was successful in providing safety for the robot even in complex workspaces with many obstacles.