Comparison of direct and indirect methods for minimum lap time optimal control problems

Minimum lap time simulations are especially important in the design, optimisation and setup of race vehicles. Such problems usually come in different flavours, e.g. quasi-steady state models vs. full dynamic models and pre-defined (fixed) trajectory problems vs. free trajectory problems. This work is focused on full dynamic models with free trajectory. Practical solution techniques include direct methods (i.e. solution of an nonlinear programming problem problem, widespread approach) and indirect method (i.e. based on Pontryagin's principle, less common, yet quite efficient in some cases). In this contribution the performance of the direct and indirect methods are compared in a number of vehicle-related problems.