Optimal overtaking on a NASCAR oval

This paper presents a framework for simulating minimum-time overtaking manoeuvres between two race cars on a three-dimensional (3D) race track. The overtaking problem is formulated as a dynamic game while avoiding collisions. To accurately capture the influence of track geometry on vehicle behaviour, recent developments in track-surface modelling are incorporated. The simulations are performed on the Darlington Raceway, which is characterised by significant camber angles and large lateral camber angle variations. A realistic overtaking scenario comprises identical cars, with the lead car fitted with worn tyres that degrade its performance. Two key challenges are addressed: the formulation of a geometry-based inequality constraint to prevent inter-vehicular collisions, and the implementation of interlaced receding-horizon optimal control problems that constitute a Stackelberg game. The game comprises continuous moves that are played simultaneously and discretely.