The best race driver is the one that, with a given vehicle, is able to drive on a given track in the shortest possible time. Thus, the only target is the lap time. A race driver model has to do the same. The first step towards this target is to decide which trajectory to follow. In fact, the optimal trajectory is the best compromise between the shortest track and the track that allows to achieve the highest speeds (least curvature track). Thus, the problem of trajectory planning is a bounded optimisation problem that has to take into account not only the geometry of the circuit but also the dynamics of the vehicle. A simplified vehicle dynamic model is used for this purpose. Due to the fact that the vehicle will be driven at its limit performances, although simplified the model has to correctly reproduce the maximum possible acceleration, a function of the vehicle speed, the maximum possible deceleration, again a function of the vehicle speed, and the maximum lateral acceleration, a function of both the vehicle speed and the steering angle. Knowing the trajectory, the vehicle model allows to determine the lap time. Through an optimisation algorithm it is therefore possible to determine the best compromise between shortest track and track with the minimum curvature, i.e. the trajectory (in terms of track and speed profile) that allows to minimise the time lap.
It is important to point out that the model is able to consider the whole track and not only a portion of it thus allowing to determine the overall best solution.