Separation of Unconscious Robots with Obstructed Visibility

We study a recently introduced $\mathit{\text{unconscious}}$ mobile robot model, where each robot is associated with a $\mathit{\text{color}}$, which is visible to other robots but not to itself. The robots are autonomous, anonymous, oblivious and silent, operating in the Euclidean plane under the conventional $\mathit{\text{Look-Compute-Move}}$ cycle. A primary task in this model is the $\mathit{\text{separation}}\mathit{\text{problem}}$, where unconscious robots sharing the same color must separate from others, forming recognizable geometric shapes such as circles, points, or lines. All prior works model the robots as $\mathit{\text{transparent}}$, enabling each to know the positions and colors of all other robots. In contrast, we model the robots as $\mathit{\text{opaque}}$, where a robot can obstruct the visibility of two other robots, if it lies on the line segment between them. Under this obstructed visibility, we consider a variant of the separation problem in which robots, starting from any arbitrary initial configuration, are required to separate into concentric semicircles. We present a collision-free algorithm that solves the separation problem under a semi-synchronous scheduler in $O(n)$ epochs, where $n$ is the number of robots. The robots agree on one coordinate axis but have no knowledge of $n$.