Models and methodology for optimal vehicle maneuvers applied to a hairpin turn

There is currently a strongly growing interest in obtaining optimal control solutions for vehicle maneuvers, both in order to understand optimal vehicle behavior and to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is nontrivial to find the right mix of models, formulations, and optimization tools to get useful results for the above purposes. Here, a platform is developed based on a state-of-the-art optimization tool together with adoption of existing vehicle models, where especially the tire models are in focus. A minimum-time formulation is chosen to the purpose of gaining insight in at-the-limit maneuvers, with the overall aim of possibly finding improved principles for future active safety systems. We present optimal maneuvers for different tire models with a common vehicle motion model, and the results are analyzed and discussed. Our main result is that a few-state single-track model combined with different tire models is able to replicate the behavior of experienced drivers. Further, we show that the different tire models give quantitatively different behavior in the optimal control of the vehicle in the maneuver.