Auction algorithm sensitivity for multi-robot task allocation

TL;DR

This paper analyzes how sensitive auction algorithms are for multi-robot task allocation in uncertain landscapes, providing bounds on cost fluctuations that do not change the optimal task assignment.

Contribution

It introduces a method to determine cost intervals within which the auction algorithm's solution remains stable, enhancing understanding of solution robustness.

Findings

Derived cost intervals ensuring solution stability

Demonstrated robustness of auction algorithms in uncertain environments

Provided theoretical bounds for solution sensitivity

Abstract

We consider the problem of finding a low-cost allocation and ordering of tasks between a team of robots in a d-dimensional, uncertain, landscape, and the sensitivity of this solution to changes in the cost function. Various algorithms have been shown to give a 2-approximation to the MinSum allocation problem. By analysing such an auction algorithm, we obtain intervals on each cost, such that any fluctuation of the costs within these intervals will result in the auction algorithm outputting the same solution.