Curved-ribbon-based track modelling for minimum lap-time optimisation

Abstract Three-dimensional road models for vehicular minimum-lap-time manoeuvring are typically based on curvilinear coordinates and generalizations of the Frenet–Serret formulae. These describe as a parametrized ‘ribbon’, which can be described in terms three curvature variables. In this abstraction is assumed laterally flat. While class appropriate many situations, not always case. research we extend laterally-flat ribbon-type model to include lateral curvature. This accommodates case camber change across track. Lateral-position-dependent introduced generalisation that required some race tracks. A track with constructed using high-resolution LiDAR measurement data. ideas demonstrated NASCAR raceway, characterized by large changes angle ( $$\approx 10^\circ$$ ? 10 ? ) parts free-trajectory optimization employed solve optimal control problem. The calculations highlight practically observed importance variations.