A Curvilinear Abscissa Approach for the Lap Time Optimization of Racing Vehicles

The optimal control and lap time optimization of vehicles such as racing cars and motorcycle is a challenging problem, in particular the approach adopted in the problem formulation has a great impact on the actual possibility of solving such problem by using numerical techniques. This paper illustrates a methodology which combines some modelling technique which have been found to be numerically efficient. The methodology is based on the 3D curvilinear coordinates technique for the road modelling, the moving frame approach for the derivation of the vehicle equations of motion, the replacement of the time with the position along the track as new independent variable and the formulation and the solution of the minimum lap time problem by means of the indirect approach. The case study of a GT car is presented and simulation examples are given and discussed.