Identification of the optimal trajectory for a race driver

Due to increasing demands for time and cost efficient vehicle design, numerical simulation of closed loop maneuvers has become more and more important. Therefore the driver has to be included into the modeling. In the literature driver models are generally regarded as controllers acting through throttlesteer- brake inputs on a nonlinear plant (i.e. the vehicle) with the aim to follow a planned trajectory maintaining the vehicle stability. It is thus straightforward to understand that in the case of race driver models, the generation of a proper reference trajectory is essential, since it must allow achieving the minimum lap time with respect of the circuit geometry and of the vehicle dynamic characteristics. The issues concerned with the generation of reference trajectories are ought to: the reciprocal interaction between longitudinal and lateral vehicle dynamics, the driver's maneuvers and the shape of the circuit. All these information have to be comprehensively analyzed through simplified logics in order to reduce the complexity of the problem. A methodology for identifying the trajectory allowing the minimization of the lap time is proposed in this paper. It splits the analysis into two steps: studying a geometric tool able to generate trajectories as a compromise between minimum space and minimum curvature paths; another one that according to the vehicle dynamic characteristics generates limit curves in order to obtain the speed profile associated to each trajectory. Combining the results of the developed tools the trajectory associated with the minimum lap time can thus be identified.