Redundant Robot Assignment on Graphs with Uncertain Edge Costs

TL;DR

This paper introduces a polynomial-time framework for assigning redundant robots to goal locations on graphs with uncertain edge travel times, effectively reducing waiting times despite the NP-hardness of the problem.

Contribution

It presents a novel, efficient method leveraging structural properties and distributive functions to solve the redundant robot assignment problem with provable bounds.

Findings

Redundant robot deployment reduces waiting times under uncertainty.

The proposed method is computationally efficient and scalable.

Experimental results validate the effectiveness of the approach.

Abstract

We provide a framework for the assignment of multiple robots to goal locations, when robot travel times are uncertain. Our premise is that time is the most valuable asset in the system. Hence, we make use of redundant robots to counter the effect of uncertainty and minimize the average waiting time at destinations. We apply our framework to transport networks represented as graphs, and consider uncertainty in the edge costs (i.e., travel time). Since solving the redundant assignment problem is strongly NP-hard, we exploit structural properties of our problem to propose a polynomial-time solution with provable sub-optimality bounds. Our method uses distributive aggregate functions, which allow us to efficiently (i.e., incrementally) compute the effective cost of assigning redundant robots. Experimental results on random graphs show that the deployment of redundant robots through our method reduces waiting times at goal locations, when edge traversals are uncertain.