Collision-Free Linear Time Mutual Visibility for Asynchronous Fat Robots

This paper studies the mutual visibility problem for a distributed system of n ≥ 3 asynchronous opaque fat robots under the obstructed visibility model. Robots are represented as unit discs in the Euclidean plane and they block both motions and visions of the other robots through them. The mutual visibility problem requires the robots to reposition themselves in such a way that all the robots in the system become mutually visible to each other. Collision-free movement is one of the desirable features that any algorithm for fat robots needs to satisfy. This paper proposes a distributed collision-free mutual visibility algorithm for asynchronous fat robots with externally visible lights. The proposed algorithm uses O(1) colors for the lights of the robots, assumes one-axis agreement, and runs in O(n) asynchronous rounds.