  With the increasing emphasis on the safe autonomy for robots, model-based
safe control approaches such as Control Barrier Functions have been extensively
studied to ensure guaranteed safety during inter-robot interactions. In this
paper, we introduce the Parametric Control Barrier Function (Parametric-CBF), a
novel variant of the traditional Control Barrier Function to extend its
expressivity in describing different safe behaviors among heterogeneous robots.
Instead of assuming cooperative and homogeneous robots using the same safe
controllers, the ego robot is able to model the neighboring robots' underlying
safe controllers through different Parametric-CBFs with observed data. Given
learned parametric-CBF and proved forward invariance, it provides greater
flexibility for the ego robot to better coordinate with other heterogeneous
robots with improved efficiency while enjoying formally provable safety
guarantees. We demonstrate the usage of Parametric-CBF in behavior prediction
and adaptive safe control in the ramp merging scenario from the applications of
autonomous driving. Compared to traditional CBF, Parametric-CBF has the
advantage of capturing varying drivers' characteristics given richer
description of robot behavior in the context of safe control. Numerical
simulations are given to validate the effectiveness of the proposed method.
