Given a set of $n\geq 1$ unit disk robots in the Euclidean plane, we consider the fundamental problem of providing mutual visibility to them: the robots must reposition themselves to reach a configuration where they all see each other. This problem arises under obstructed visibility, where a robot cannot see another robot if there is a third robot on the straight line segment between them. This problem was solved by Sharma et al. [ICDCN, 2018] in the luminous robots model, where each robot is equipped with an externally visible light that can assume colors from a fixed set of colors, using 9 colors and $O(n)$ rounds. In this work, we present an algorithm that requires only 2 colors and $O(n)$ rounds. The number of colors is optimal since at least two colors are required even for point robots [Di Luna et al., Information and Computation, 2017].

翻译：给定欧几里得平面上 $n\geq 1$ 个单位圆盘机器人，我们考虑为其提供互视性的基本问题：机器人必须重新定位自身，以达到所有机器人都能彼此看见的配置。该问题出现在受限可视性条件下，即若两个机器人之间的直线段上存在第三个机器人，则一个机器人无法看见另一个机器人。Sharma 等人 [ICDCN, 2018] 在发光机器人模型中解决了该问题，其中每个机器人配备一个外部可见光源，该光源可采用固定颜色集中的颜色，他们使用了 9 种颜色和 $O(n)$ 轮次。在本工作中，我们提出一种仅需 2 种颜色和 $O(n)$ 轮次的算法。颜色数量是最优的，因为即使对于点机器人，也至少需要两种颜色 [Di Luna 等人, Information and Computation, 2017]。