  This paper presents a multi-layer motion planning and control architecture
for autonomous racing, capable of avoiding static obstacles, performing active
overtakes, and reaching velocities above 75 $m/s$. The used offline global
trajectory generation and the online model predictive controller are highly
based on optimization and dynamic models of the vehicle, where the tires and
camber effects are represented in an extended version of the basic Pacejka
Magic Formula. The proposed single-track model is identified and validated
using multi-body motorsport libraries which allow simulating the vehicle
dynamics properly, especially useful when real experimental data are missing.
The fundamental regularization terms and constraints of the controller are
tuned to reduce the rate of change of the inputs while assuring an acceptable
velocity and path tracking. The motion planning strategy consists of a
Fren\'et-Frame-based planner which considers a forecast of the opponent
produced by a Kalman filter. The planner chooses the collision-free path and
velocity profile to be tracked on a 3 seconds horizon to realize different
goals such as following and overtaking. The proposed solution has been applied
on a Dallara AV-21 racecar and tested at oval race tracks achieving lateral
accelerations up to 25 $m/s^{2}$.
