Brief Announcement: Distinct Gathering Under Round Robin

We resolve one of the longest-standing questions about autonomous mobile robots in a surprising way. Distinct Gathering is the fundamental cooperation task of letting robots, initially scattered across the plane in distinct locations, gather in an arbitrary single point. The scheduler Round Robin cyclically activates the robots one by one in a fixed order. When activated, a robot perceives all robot locations and moves wherever it wants based only on this information. For n = 2 robots, the task is trivial. What happens for n ≥ 3 has remained an open problem for decades by now. The established conjecture declares the task to be impossible in this case. We prove that it is indeed impossible for n = 3 but, to great surprise, possible again for any n ≥ 4. We go beyond the standard requirements by providing a very robust algorithm that does not require any consistency or self-consistency for the local Cartesian maps perceived by the robots and works even for non-rigid movement, that is, if robots may be unpredictably stopped and deactivated during a movement.