Optimal control of Formula 1 race cars in a VDrift based virtual environment

Abstract Control of autonomous vehicles and providing recommendations to drivers in real time are challenging tasks from an algorithmic point of view. To include realistic effects, such as nonlinear tire dynamics, at least medium-sized mathematical models need to be considered. Yet, fast feedback is of utmost importance. Existing Nonlinear Model Predictive Control (NMPC) algorithms need to be enhanced to comply with these two contradictory requirements. As the testing of algorithms in an automatic driving context is cumbersome and expensive, we propose a virtual testbed for NMPC of driving cars. We use the open source race simulator VDrift as virtual real world, in which algorithms need to cope with the mismatch between the detailed physical model in the simulator and a coarser approximative model used for NMPC. We present the general framework of this virtual environment and an optimal control problem based on a medium-sized ordinary differential equation model and a generic and flexible parameterization of the track constraint. We discuss one possible algorithmic approach to the task of minimum time driving including gear shifts and give preliminary open loop numerical results for a Porsche on Germany's Formula One racing circuit Hockenheimring. This can be used as a reference against which other (closed loop) solutions can be compared in the future.