Auxiliary- Variable Adaptive Control Barrier Functions for Safety Critical Systems

It has been shown that optimizing quadratic costs for affine control systems subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBFs). One of the main challenges in this method is that the CBF-based QPs can easily become infeasible under tight control bounds, especially when the control bounds are time-varying. The recently proposed adaptive CBFs have addressed such infeasibility issues, but require extensive and non-trivial hyperparameter tuning and may introduce overshooting control near the boundaries of the safe sets. In this paper, we propose a new type of adaptive CBFs called Auxiliary-Variable Adaptive CBFs (AVCBFs). Specifically, we introduce an auxiliary variable that multiplies each CBF, and define dynamics for the auxiliary variable to adapt it in constructing the corresponding CBF constraint. In this way, we improve the feasibility of the CBF -based QPs while avoiding extensive parameter tuning with non-overshooting control. We demonstrate the advantages of using AVCBFs and compare them with existing techniques on an Adaptive Cruise Control (ACC) problem with time-varying control bounds.