Continuous time gathering of agents with limited visibility and bearing-only sensing

A group of mobile agents, identical, anonymous, and oblivious (memoryless), able to sense only the direction (bearing) to neighboring agents within a finite visibility range, are shown to gather to a meeting point, in finite time, by applying a very simple rule of motion. The agents act in continuous time, and their rule of motion is as follows: they determine the smallest visibility disk sector in which all their visible neighbors reside. If this disk sector spans an angle smaller than $$\pi $$π, then they set the velocity vector to be the sum of the two unit vectors in $${\mathbb {R}}^2$$R2 pointing to the extremal neighbors. Otherwise, they do not move. If the initial constellation of agents has a visibility graph that is connected, we prove that the agents gather to a common meeting point in finite time.