  Ensuring safety for vehicle overtaking systems is one of the most fundamental
and challenging tasks in autonomous driving. This task is particularly
intricate when the vehicle must not only overtake its front vehicle safely but
also consider the presence of potential opposing vehicles in the opposite lane
that it will temporarily occupy. In order to tackle the overtaking task in such
challenging scenarios, we introduce a novel integrated framework tailored for
vehicle overtaking maneuvers. Our approach integrates the theories of
varying-level control barrier functions (CBF) and time-optimal model predictive
control (MPC). The main feature of our proposed overtaking strategy is that it
is safe-by-construction, which enables rigorous mathematical proof and
validation of the safety guarantees. We show that the proposed framework is
applicable when the opposing vehicle is either fully autonomous or driven by
human drivers. To demonstrate our framework, we perform a set of simulations
for overtaking scenarios under different settings. The simulation results show
the superiority of our framework in the sense that it ensures collision-free
and achieves better safety performance compared with the standard MPC-based
approach without safety guarantees.
