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This work deals with the problem of gathering $n$ oblivious mobile entities,called robots, at a point (not known beforehand) placed on an infinitetriangular grid. The robots are considered to be myopic, i.e., robots havelimited visibility. Earlier works of gathering mostly considered the robotseither on a plane or on a circle or on a rectangular grid under both full andlimited visibility. In the triangular grid, there are two works to the best ofour knowledge. The first one is by Cicerone et al. on arbitrary patternformation where full visibility is considered. The other one by Shibata et al.which considers seven robots with 2- hop visibility that form a hexagon withone robot in the center of the hexagon in a collision-less environment under afully synchronous scheduler .  In this work, we first show that gathering on a triangular grid with 1-hopvision of robots is not possible even under a fully synchronous scheduler ifthe robots do not agree on any axis. So one axis agreement has been consideredin this work (i.e., the robots agree on a direction and its orientation). Wehave also shown that the lower bound for time is $\Omega(n)$ epochs when $n$number of robots are gathering on an infinite triangular grid. An algorithm isthen presented where a swarm of $n$ number of robots with 1-hop visibility cangather within $O(n)$ epochs under a semi-synchronous scheduler. So thealgorithm presented here is time optimal.

Time Optimal Gathering of Myopic Robots on an Infinite Triangular Grid