  In this paper, we extend a framework that we developed earlier for
coordination of connected and automated vehicles (CAVs) at a signal-free
intersection by integrating a safety layer using control barrier functions.
First, in our motion planning module, each CAV computes the optimal control
trajectory using simple vehicle dynamics. The trajectory does not make any of
the state, control, and safety constraints active. A vehicle-level tracking
controller employs a combined feedforward-feedback control law to track the
resulting optimal trajectory from the motion planning module. Then, a
barrier-certificate module, acting as a middle layer between the vehicle-level
tracking controller and physical vehicle, receives the control law from the
vehicle-level tracking controller and using realistic vehicle dynamics ensures
that none of the state, control, and safety constraints becomes active. The
latter is achieved through a quadratic program, which can be solved efficiently
in real time. We demonstrate the effectiveness of our extended framework
through a numerical simulation.
