Implementation of a Transverse MPC Controller on a Simulated Autonomous Vehicle Model

This thesis develops a transverse Model Predictive Control strategy for minimumtime racing applications, where the vehicle dynamics are reformulated with respect to the arc length to explicitly optimize the progression along a reference track. The approach leverages curvilinear coordinates to separate longitudinal advancement from lateral deviation, enabling the controller to regulate motion directly in the spatial domain without relying on time-parameterized trajectories. A curvaturebased soft-minimum operator is introduced to construct a reasonably smooth and anticipative upper bound on the admissible velocity, with the goal of constructing a velocity profile as realistic as possible. The proposed controller is first evaluated on a unicycle model through numerical Python-based simulations and subsequently validated in the high-fidelity CarRealTime environment by supplying only the curvature-dependent velocity profile to the native driver. Two soft-minimum tunings (aggressive and safe) are compared across nominal and challenging circuit configurations, highlighting their respective advantages and limitations in terms of performance, robustness and adherence to the reference path.