Impacts of g-g-v Constraints Formulations on Online Minimum-Time Vehicle Trajectory Planning

Abstract: The g-g-v diagram is a popular representation of a vehicle’s maximum longitudinal and lateral accelerations, as a function of its speed. Recently, g-g-v diagrams have been used as performance constraints for online minimum-time vehicle trajectory planning with economic nonlinear model predictive control (E-NMPC). However, in the related literature, the modeling accuracy of the g-g-v formulations was often compromised in favor of computational efficiency for online E-NMPC. This paper compares various formulations of the g-g-v constraints, evaluating their accuracy, computational efficiency and impact on the lap times, when applied by an artificial race driver (ARD) to control a sports car model on a circuit. Also, we propose a new g-gv diagram formulation, based on convex polytopic and non-convex polynomial constraints. Our formulation yields improved modeling accuracy while preserving a low computational burden for online E-NMPC. Finally, we analyze the vehicle trajectories, to understand how ARD achieves lower lap times through an improved knowledge of the maximum performance.