GP4: Gaussian Process Proactive Path Planning for the Stochastic on Time Arrival Problem

Abstract

This paper investigates the stochastic on time arrival (SOTA) problem in Gaussian process (GP) regulated environments. We presume that the travel times of the underlying transportation network follow a multi-variate Gaussian distribution, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> . <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</i> . Gaussian process, and propose a Gaussian process <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">proactive</i> path planner (GP4), which outputs a dynamic routing policy for maximizing the traveller's on-time-arrival probability. When given an instantiated travel time of a certain link, GP is able to analytically represent/predict the posterior travel time distribution over the entire transportation network. With that, we let the ego vehicle ‘proactively’ select the next traversal link, which maximizes the expected stochastic on time arrival probability based on the predicted posterior travel time distribution. Various extensions of GP4 to other forms of travel time distribution assumptions, such as Log-GP and Bi-GP, are proposed and extensive experimental results demonstrate the efficiency and applicability of GP4 to various transportation networks, including a real use case with real traffic data in Chengdu, China.