A Free-Trajectory Quasi-steady-state Optimal-Control Method for Minimum-Time Problems of Cars and Motorcycles

Minimum-lap-time problems are commonly solved employing quasi-steady-state models on a predetermined trajectory or dynamic models on a free (non-predetermined) trajectory. The current work deals with a third approach, that combines a free-trajectory minimum-lap-time method, together with a quasi-steady-state description of the vehicle. The method is based on the computation of the well known g-g diagrams, which summarise the quasi-steady-state performance of the vehicle. This information is employed for the solution of an optimal-control problem, that allows to determine the optimal trajectory. Numerical models of high complexity can be employed, since all their features (e.g. tyre limits, power limits, aerodynamic drag and downforce, suspensions, etc.) are included in the related g-g diagrams, and do not affect the complexity of the optimal control problem that need be solved. The method allows to employ even experimental g-g diagrams in place of numerical ones, and is suitable for application to both cars and motorcycles.