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

翻译：本文研究在无限三角网格上收集距离为1的近视机器人问题。我们证明Goswami等人(SSS, 2022)提出的算法具有格点线性。这意味着该算法不需要假设分布式调度器：它能在异步环境下正确运行。同时表明，即使机器人配备单向摄像机（而非分布式调度器所需的全面摄像机）观察邻近机器人，该算法也能正确工作。由于格点线性，我们可以预先确定聚集点。我们还证明该算法在$2n$轮内收敛，低于Goswami等人所示的$2.5(n+1)$轮。