Gathering Semi-Synchronously Scheduled Two-State Robots

TL;DR

This paper investigates the Gathering problem for autonomous robots with limited communication and memory, showing impossibility results for certain models and improving existing algorithms in semi-synchronous settings.

Contribution

It proves that 2-color FSTA and FCOM robots cannot gather in SSYNCH without extra conditions and enhances previous algorithms for FSTA robots with 2-colors.

Findings

2-color FSTA and FCOM robots cannot solve Gathering in SSYNCH without additional assumptions.

Improved conditions for existing Gathering algorithms for FSTA robots with 2-colors in SSYNCH.

Gathering remains impossible under certain constraints even with rigid movement and chirality agreement.

Abstract

We study the problem \emph{Gathering} for $n$ autonomous mobile robots in synchronous settings with a persistent memory called \emph{light}. It is well known that Gathering is impossible in the basic model ($OBLOT$) where robots have no lights, even if the system is semi-synchronous (called SSYNCH). Gathering becomes possible, however, if each robot has a light of some type that can be set to a constant number of colors. In the $FCOM$ model, the robots can only see the lights of other robots. In the $FSTA$ model, each robot can only observe its own light. In the $LUMI$ model, all robots can see all lights. This paper focuses on $FSTA$ robots with 2-colored lights in synchronous settings. We show that 2-color $FSTA$ and $FCOM$ robots cannot solve Gathering in SSYNCH without additional conditions, even with rigid movement and agreement of chirality and the minimum moving distance. We also improve the condition of the previous gathering algorithm for $FSTA$ robots with 2-color working in SSYNCH.