A three-dimensional free-trajectory quasi-steady-state optimal-control method for minimum-lap-time of race vehicles

A method to solve minimum-lap-time problems using quasi-steady-state models and free (i.e. not predetermined) trajectory on two-dimensional tracks has been recently proposed. This work describes the extension of the method to three-dimensional tracks and builds upon g–g–g diagrams (instead of the standard g–g), to account for the effects of three-dimensionality. The main features of car and motorcycle g–g–g diagrams are discussed, to get insight into the main effects of three-dimensionality and to suggest a convenient parametrisation for the subsequent optimal control problem (OCP), whose size is not affected by the complexity of the vehicle model employed to generate the g–g–g diagrams. The application of the method to the Mugello and Barcelona–Catalunya circuits is given, with vehicle datasets resembling those of a race motorcycle (MotoGP) and a race car (Formula One). The results obtained are in line with those reported in the literature using full-dynamic models, yet such dynamic models are generally associated with the solution of much larger OCP.