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In this paper, we study the problem of gathering distance-1 myopic robots onan infinite triangular grid. We show that the algorithm developed by Goswami etal. (SSS, 2022) is lattice-linear (cf. Gupta and Kulkarni, SRDS 2023). Thisimplies that a distributed scheduler, assumed therein, is not required for thisalgorithm: it runs correctly in asynchrony. It also implies that the algorithmworks correctly even if the robots are equipped with a unidirectional\textit{camera} to see the neighbouring robots (rather than an omnidirectionalone, which would be required under a distributed scheduler). Due tolattice-linearity, we can predetermine the point of gathering. We also showthat this algorithm converges in $2n$ rounds, which is lower than thecomplexity ($2.5(n+1)$ rounds) that was shown in Goswami et al.

Tolerance to Asynchrony of an Algorithm for Gathering Myopic Robots on an Infinite Triangular Grid