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We study a Rendezvous problem for 2 autonomous mobile robots in asynchronoussettings with persistent memory called light. It is well known that Rendezvousis impossible when robots have no lights in basic common models, even if thesystem is semi-synchronous. On the other hand, Rendezvous is possible if robotshave lights with a constant number of colors in several types lights. Inasynchronous settings, Rendezvous can be solved by robots with 4 colors oflights in non-rigid movement, if robots can use not only own light but alsoother robot's light (full-light), where non-rigid movement means robots may bestopped before reaching the computed destination but can move a minimumdistance \delta > 0 and rigid movement means robots can reach the computeddestination. In semi-synchronous settings, Rendezvous can be solved with 2colors of full-lights in non-rigid movement.  In this paper, we show that in asynchronous settings, Rendezvous can besolved with 2 colors of full-lights in rigid movement and in non-rigid movementif robots know the value of the minimum distance \delta. We also show thatRendezvous can be solved with 2 colors of full-lights in general non-rigidmovement if we consider some reasonable restricted class of asynchronoussettings.

Optimal Asynchronous Rendezvous for Mobile Robots with Lights