Minimization of Fuel Consumption for Vehicle Trajectories

Eco-driving, a timely and well-known subject, aims at reducing fuel consumption by appropriately maneuvering a vehicle with a human or automated driver. In this work, the eco-driving problem is cast in an optimal control framework. State equations reflect the simple vehicle kinematics for position and speed, with the acceleration acting as a control input. Initial and final states (position and speed) are fixed. For the fuel consumption estimation, a number of alternatives are employed. To start with, a realistic, but nonlinear and non-smooth formula from the literature is considered. Simple smoothing procedures are then applied to enable the application of powerful numerical algorithms for the efficient solution of the resulting nonlinear optimal control problem. Furthermore, simpler quadratic approximations of the nonlinear formula are also considered, which enable analytical problem solutions. A comprehensive comparison on the basis of various driving scenarios demonstrates that the often utilized, but sometimes strongly questioned, square-of-acceleration term delivers excellent approximations for fuel minimizing trajectories in the present setting. A GLOSA (Green Light Optimal Speed Advisory) approach, based on the analytical solution of an optimal control problem is also presented.