Vehicle-Based Trajectory Specification in Presence of Traffic Lights with Stochastic Switching Times

Abstract

Vehicle-based GLOSA (Green Light Optimal Speed Advisory) systems use information about the next switching time of the traffic lights to calculate fuel-efficient position and velocity profiles for connected vehicles, according to their current state (position and speed). A stochastic optimal control problem was recently proposed to address the GLOSA problem in cases where the next switching time is decided in real time and is therefore uncertain in advance. The corresponding numerical solution via SDP (Stochastic Dynamic Programming) calls for substantial computational time (few minutes), which excludes problem solution in the vehicle’s computer in real time. This work considers the same stochastic problem of optimal trajectory specification for vehicles approaching a signalized junction with traffic signals operated in real-time (adaptive) mode, due to which the next switching time is stochastic. However, a modified version of Dynamic Programming, known as Discrete Differential Dynamic Programming (DDDP), is used for numerical solution of the stochastic optimal control problem. It is demonstrated, based on a realistic example, that the DDDP algorithm achieves results equivalent to those obtained with the ordinary SDP algorithm, albeit with significantly better performance in terms of computational time. Specifically, the solution is typically obtained in around 1 CPUs, which is real-time feasible and would allow for the DDDP calculations to be executed in the vehicle’s on-board computer.