A Convex Optimization Framework for Minimum Lap Time Design and Control of Electric Race Cars

Lap time is the most important performance indicator in racing. In order to minimize it, the powertrain of the race car must be carefully designed and the energy carried on-board must be meticulously administered. In particular, to obtain the fastest possible lap time, it is important to select the components’ technology and sizing accounting for the energy available on-board and for the resulting mass of the car. In this paper, we present a convex optimization framework to rapidly compute the minimum-lap-time control strategies for a battery electric race car. We first identify a convex model of the electric powertrain, including the battery, the electric motor, and two transmission technologies: a fixed-gear transmission (FGT) and a continuously variable transmission (CVT). Second, assuming an expert driver, we formulate the time-optimal control problem in a convex fashion for a given driving path, and compute its globally optimal solution with second-order conic programming algorithms. Third, we showcase our framework on the Le Mans track by comparing the performance achievable with an FGT and a CVT, and validate it with nonlinear simulations. Our results show that for the given setup a CVT can balance its lower efficiency and higher weight with a higher-efficiency and more aggressive motor operation, significantly outperforming the lap time achievable with an FGT. Finally, we leverage the computational efficiency of our framework to carry out parameter studies on the components, revealing that optimizing the size of the battery and the motor for the specific scenario can considerably improve the achievable lap time, and that the best transmission strongly depends on the sizing decisions.