Three-dimensional fixed-trajectory approaches to the minimum-lap time of road vehicles

Minimum-lap-time simulations with quasi-steady-state models and predefined trajectory have been in use for many years. However, most of the published works deal with two-dimensional roads and employ the so-called apex-finding method. This paper focuses on the application to three-dimensional roads, both with an extension of the ‘apex-finding’ approach to three-dimensional scenarios and with an optimal control method. Both approaches are based on g–g–g diagrams, i.e. the three-dimensional extension of the well-known g–g maps. In addition, under the assumption that the predefined trajectory is determined from noisy data (e.g. logged from the real vehicle), the three-dimensional trajectory reconstruction problem is addressed, to find a smooth and drift-free racing line to be used in the minimum-time simulation – again an optimal control approach is employed for the trajectory reconstruction. Examples of application are given both for a car and a motorcycle.