Rate-Tunable Control Barrier Functions: Methods and Algorithms for Online Adaptation

This paper introduces the notion of a Rate-Tunable Control Barrier Function (RT-CBF), which allows for online tuning of the response of CBF-based controllers by adapting the parameters of the class-$\mathcal{K}$ function that is involved in the CBF condition. In contrast to most existing approaches that use a fixed class-$\mathcal{K}$ function to ensure safety, we propose an online adaptation law for the parameters of class-$\mathcal{K}$ function of the CBF condition. The algorithm can also incorporate multiple higher-order CBFs and adapt their class-$\mathcal{K}$ parameters for feasibility, albeit without guarantees in theory. The simulation results verify that online adaptation helps improve the system's response in terms of the resulting trajectories being closer to a nominal reference while still being safe.