  The autonomous driving industry is continuously dealing with safety-critical
scenarios, and nonlinear model predictive control (NMPC) is a powerful control
strategy for handling such situations. However, standard safety constraints are
not scalable and require a long NMPC horizon. Moreover, the adoption of NMPC in
the automotive industry is limited by the heavy computation of numerical
optimization routines. To address those issues, this paper presents a real-time
capable NMPC for automated driving in urban environments, using control barrier
functions (CBFs). Furthermore, the designed NMPC is based on a novel
collocation transcription approach, named RESAFE/COL, that allows to reduce the
number of optimization variables while still guaranteeing the continuous time
(nonlinear) inequality constraints satisfaction, through regional convex hull
approximation. RESAFE/COL is proven to be 5 times faster than multiple shooting
and more tractable for embedded hardware without a decrease in the performance,
nor accuracy and safety of the numerical solution. We validate our NMPC-CBF
with RESAFE/COL on digital twins of the vehicle and the urban environment and
show the safe controller's ability to improve crash avoidance by 91\%.
Supplementary visual material can be found at https://youtu.be/_EnbfYwljp4.
