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Autonomous vehicles are going to soon travel on our roads. For this reason, studying effective planning and control algorithms for self-driving cars is of paramount importance. Applying such studies in racing scenarios has two main advantages: first, to be competitive, the developed solutions are forced to be capable of controlling the vehicle at high speeds and close to its handling limits. Furthermore, racing is a protected environment, that helps the experimentation of innovative solutions.

This dissertation focuses on one of the core layers that any autonomous driving application needs: the trajectory-planning module. The inputs to our planning algorithm are a representation of the track, an offline-computed trajectory, and a list of opponent vehicles to be avoided and overtaken. The proposed algorithm is capable of computing overtaking trajectories that fully exploit the grip limits of the vehicle. We split the trajectory computation into two phases: first, we generate a collision-free path; then, an optimal speed profile is computed, trying to minimize the time to transverse the planned path, while respecting the handling limits of the vehicle.

The effectiveness of the designed solution has been demonstrated both in simulation and on an experimental autonomous racing vehicle during several racing events of the Roborace Season Beta championship.