An Efficient Minimum-Time Trajectory Generation Strategy for Two-Track Car Vehicles

In this paper, we propose a novel approach to compute minimum-time trajectories for a two-track car model, including tires and (quasi-static) longitudinal and lateral load transfer. Given the car model and a planar track, including lane boundaries, our goal is to find a trajectory of the car minimizing the traveling time subject to steering and tire limits. Moreover, we enforce normal force constraints to avoid wheel liftoff. Based on a projection operator nonlinear optimal control technique, we propose a minimum-time trajectory generation strategy to compute the fastest car trajectory. Numerical computations are presented on two testing scenarios, a 90° turn and a real testing track. The computations allow us to both demonstrate the efficiency and accuracy of the proposed approach and highlight important features of the minimum-time trajectories. Finally, we integrate our strategy into a commercial vehicle dynamics software, thus computing minimum-time trajectories for a complex multibody vehicle model. The matching between the predicted trajectory and the one of the commercial toolbox further highlights the effectiveness of the proposed methodology.