Robust lap-time simulation

Lap-time simulation is an important computational tool for many motor racing teams, but the assumption of ideal operating conditions and a ‘perfect’ racing driver is usually made. The aim of this paper is to extend lap-time simulation to include robustness to disturbances on the vehicle and robustness to mistakes by the driver. A previously developed receding-horizon model predictive control with a convex optimisation method for lap-time simulation is extended with a tube-based technique for robust model predictive control. A linear quadratic regulator compensatory controller maintains the vehicle close to the nominal vehicle path and speed trajectories in the presence of disturbances to the vehicle. An ensemble of disturbed trajectories defines a tube of trajectories, which is then used to modify the nominal vehicle path so that the track boundary constraints are satisfied in the presence of the disturbances. The lap time versus r.m.s. steering velocity curves for two different vehicle models demonstrate the expected trade-off: a decrease in the activity of the compensatory steering control increases the tube width, which leads to a longer lap time. The technique has application to designing and setting up cars to perform well in the presence of disturbances.