Optimal Racing of an Energy-Limited Vehicle

Abstract

We consider the problem of controlling a vehicle to arrive at a fixed destination while minimizing a combination of energy consumption and travel time. Our model includes vehicle speed and accelaration limits, aerodynamic drag, rolling resistance, nonlinear engine losses, and internal energy limits. The naive problem formulation is not convex; however, we show that a simple convex relaxation is tight. We provide a numerical example, and discuss extensions to vehicles with unconventional drivetrains, such as hybrid vehicles and solar cars.