Randomized Gathering of Asynchronous Mobile Robots

TL;DR

This paper investigates the gathering problem for two asynchronous, randomized mobile robots under adversarial scheduling, identifying conditions for possibility and impossibility of gathering based on adversary capabilities.

Contribution

It classifies the feasibility of robot gathering under different adversarial models and extends algorithms to multiple robots with merging capabilities.

Findings

Gathering possible against oblivious adversaries with zero computation delay.

Gathering possible when wait time plus computation delay exceeds a positive threshold.

Gathering impossible against adaptive adversaries with non-negative wait and computation delays.

Abstract

This paper revisits the widely researched \textit{gathering} problem for two robots in a scenario which allows randomization in the asynchronous scheduling model. The scheduler is considered to be the adversary which determines the activation schedule of the robots. The adversary comes in two flavors, namely, oblivious and adaptive, based on the knowledge of the outcome of random bits. The robots follow \textit{wait-look-compute-move} cycle. In this paper, we classify the problems based on the capability of the adversary to control the parameters such as wait time, computation delay and the speed of robots and check the feasibility of gathering in terms of adversarial knowledge and capabilities. The main contributions include the possibility of gathering for an oblivious adversary with (i) zero computation delay; (ii) the sum of wait time and computation delay is more than a positive value. We complement the possibilities with an impossibility. We show that it is impossible for the robots to gather against an adaptive adversary with non-negative wait time and non-negative computation delay. Finally, we also extend our algorithm for multiple robots with merging.