Fast Two-Robot Disk Evacuation with Wireless Communication

TL;DR

This paper investigates optimal evacuation strategies for two robots with different speeds on a disk, providing bounds and strategies that improve upon previous methods, especially for higher speed disparities.

Contribution

It introduces new optimal evacuation strategies for robots with unequal speeds, extending previous work and establishing bounds for various speed ratios.

Findings

Optimal strategies for s ≥ 2.75 with matching bounds.

Non-matching bounds with ratio less than 1.22 for 1 ≤ s < 2.75.

Proposed strategies outperform previous methods for s ≥ 1.71.

Abstract

In the fast evacuation problem, we study the path planning problem for two robots who want to minimize the worst-case evacuation time on the unit disk. The robots are initially placed at the center of the disk. In order to evacuate, they need to reach an unknown point, the exit, on the boundary of the disk. Once one of the robots finds the exit, it will instantaneously notify the other agent, who will make a beeline to it. The problem has been studied for robots with the same speed~\cite{s1}. We study a more general case where one robot has speed $1$ and the other has speed $s \geq 1$. We provide optimal evacuation strategies in the case that $s \geq c_{2.75} \approx 2.75$ by showing matching upper and lower bounds on the worst-case evacuation time. For $1\leq s < c_{2.75}$, we show (non-matching) upper and lower bounds on the evacuation time with a ratio less than $1.22$. Moreover, we demonstrate that a generalization of the two-robot search strategy from~\cite{s1} is outperformed by our proposed strategies for any $s \geq c_{1.71} \approx 1.71$.