An Overtaking Game

Overtaking in motor racing involves the optimal exploitation of the vehicle, tire, and track characteristics in a game-theoretic setting. The game described here adopts a well-known Stackelberg structure that is solved as a sequence of interlinked optimal control problems (OCPs). Intervehicular interactions are due to collision avoidance and aerodynamic drafting. In order to minimize the model complexity, drafting influences have not been included here but are discussed in detail by Limebeer and Dollar (2025). The vehicles are assumed to travel on an idealized closed-circuit track that takes the form of an elliptic cone that is reminiscent of a highly banked NASCAR oval. The track, vehicle, and overtaking game are described in detail and then tested in combination. The results show that it can be difficult to overtake a relatively underpowered car that is adept at “blocking” overtakes. It is also shown that apparently minor changes in the test conditions can lead to qualitatively different overtaking strategies. Simulation studies of this type ignore driver mistakes, or conservative or inconsistent decision-making.