Optimal overtaking on a NASCAR oval

2026-06-08

Charl V. van de Merwe *

D.J.N. Limebeer *

DOI：10.1080/00423114.2026.2685177

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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.

Optimal overtaking on a NASCAR oval

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