A study of a robust and accurate framework for Minimum-time optimal control of high-performance cars: from coaching professional drivers to autonomous racing.

In motorsport, simulating road vehicles driving at the limit of handling is a valuable tool to study and optimize their overall performance during the design and set-up phases. Along with Quasi-Steady-State optimization, optimal control (OC) is the most utilized technique to simulate the control and states of a vehicle during minimum-time maneuvers and has been used for offline lap-time optimization for more than twenty years now. Since the first applications of optimal control in this field, it has been clear that the solution of the minimum-time optimization does not represent a model of the human driver but instead substitutes him/her. However, the common points or divergences between the minimum-time strategy of human race drivers and the OC one are still unclear. Moreover, it seems that in the literature there is no agreement about what vehicle models must be used, and in general the choice of one model or the other is not clearly justified. Finally, thanks to the rise in popularity of autonomous driving and racing, optimal control has been used as path planner for automated vehicles: %nonetheless, the application of free-trajectory real-time nonlinear optimal control in Model Predictive Control (MPC) schemes, where the optimal controls are directly fed to the vehicle, is still an unexplored topic. nonetheless, the application of free-trajectory real-time nonlinear optimal control in Model Predictive Control (MPC) schemes, where the optimal controls are computed from a single optimization and directly fed to the vehicle, is a topic still open for exploration. The first aim of this thesis is to provide an objective comparison of several vehicle, tire, powertrain and road models to be used in minimum-time OC. In the first part of this work we thus detail several models of the vehicle and its subsystems. We then solve minimum-time OC problems on a series of test tracks adopting most of the model combinations and discuss the differences in the solutions. We then draw conclusions on the best model combinations to obtain realistic and reliable minimum-time maneuvers. The second part of the thesis aims to prove that the solutions of minimum-time OC problems are indeed different from the driving behavior of professional drivers, but they can be employed to coach the human driver and improve his/her racing performance. After modeling a high-performance vehicle manufactured by Ferrari, we again use optimal control to compute minimum-time maneuvers on two different tracks. A professional racer driving is then coached in following the OC strategy on the Ferrari driving simulator, and we objectively prove that the driver can outperform his previous lap times. In the third and last part of the thesis, we aim to prove that free-trajectory real-time optimal control is a valid alternative to hierarchical MPC frameworks based on high-level path planning and low-level path tracing. We first develop a novel kineto-dynamic vehicle model able to satisfy the trade-off between computational lightness and accuracy in representing the vehicle's pure and combined dynamics. Then, by solving a minimum-time OC in real-time, we are able to autonomously drive a real scaled vehicle around a track at the limits of tire adherence.