Distributed and Adaptive Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment

TL;DR

This paper introduces distributed, adaptive algorithms for vehicle routing in stochastic, dynamic environments, improving robustness and scalability over centralized methods for the m-vehicle Dynamic Traveling Repairman Problem.

Contribution

It presents a new class of optimal, adaptive policies for the 1-DTRP and combines them with partitioning strategies to solve the m-DTRP in a distributed, scalable, and robust manner.

Findings

Algorithms are provably optimal in certain load conditions.

Distributed algorithms are within a constant factor of optimal.

System stabilizes under any load condition.

Abstract

In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival, location and on-site service are stochastic; the objective is to minimize the expected system time (wait plus service) of the demands. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized a-priori task assignment and are not robust against changes in the environment, e.g. changes in load conditions; therefore, they are of limited applicability in scenarios involving ad-hoc networks of autonomous vehicles operating in a time-varying environment. First, we present a new class of policies for the 1-DTRP problem that: (i) are provably optimal both in light- and heavy-load condition, and (ii) are adaptive, in particular, they are robust against changes in load conditions. Second, we show that partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules in its own region, are optimal in heavy-load conditions. Finally, by combining the new class of algorithms for the 1-DTRP with suitable partitioning policies, we design distributed algorithms for the m-DTRP problem that (i) are spatially distributed, scalable to large networks, and adaptive to network changes, (ii) are within a constant-factor of optimal in heavy-load conditions and stabilize the system in any load condition. Simulation results are presented and discussed.