Analytical and numerical solutions for energy minimization of road vehicles with the existence of multiple traffic lights

In this paper, we seek an optimal speed trajectory to minimize fuel consumption of a conventional vehicle on a route consisting of multiple traffic lights. We propose to solve the problem in two stages. In the first stage a high level control algorithm determines the traffic light arrival times. In the second stage we calculate the optimal velocity profile by utilizing the vehicle models and traffic light arrival times. We present two solution methods for the second stage. The first method proposes a closed form (analytical) solution to the optimization problem using simplified vehicle longitudinal and fuel consumption models. In the second method we utilize non-linear vehicle dynamics and solve the problem numerically. The two methods solve an example optimization problem with the existence of several traffic lights. We have compared the investigated optimal trajectories and evaluated the performance of the solutions in terms of calculation time and consumed fuel amount. The results show that the closed form solution requires significantly shorter calculation time with less than 0.1 % degradation in fuel economy compared to the numerical method.