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We study the Gathering problem for n autonomous mobile robots insemi-synchronous settings with persistent memory called light. It is well knownthat Gathering is impossible in a basic model when robots have no lights, ifthe system is semi-synchronous or even centralized (only one robot is active ineach time). On the other hand, Rendezvous (Gathering when n = 2) is possible ifrobots have lights of various types with a constant number of colors. In thispaper, we extend the model of robots with lights so that Gathering algorithmscan be discussed properly. Then we show Gathering algorithms with three typesof lights in the semi-synchronous settings and reveal relationship between thepower of lights and other additional assumptions. The most algorithms shownhere are optimal in the number of colors they use.

Gathering Problems for Autonomous Mobile Robots with Lights