On Doorway Egress by Autonomous Robots.

We consider the distributed setting of n autonomous mobile robots operating in Look-Compute-Move (LCM) cycles on the real plane. Robots may be without lights (the classic oblivious robots model) or equipped with lights (the robots with lights model). Under obstructed visibility, a robot cannot see another robot if a third robot is positioned between them on the straight line connecting them, but it is not the case under unobstructed visibility. Robots are said to collide if they share positions or their paths intersect within concurrent LCM cycles. In this paper, we introduce and study DOORWAY EGRESS, the problem of robots exiting through a doorway from one side of a wall to the other; initially, the robots are positioned at distinct positions on one side of a wall. We study time-efficient solutions where time is measured using a standard notion of epochs - an epoch is a duration in which each robot completes at least one LCM cycle. For solutions to DOORWAY EGRESS with only 1 epoch, we: design an asynchronous algorithm if collisions are allowed; prove that an asynchronous algorithm is impossible if collisions are not allowed; and design a semi-synchronous algorithm without collisions. To further investigate asynchronous algorithms without collisions, we present algorithms with different combinations of robot abilities: center dot O(1) epochs with lights under obstructed visibility; center dot O(1) epochs without lights under unobstructed visibility; and center dot O(n) epochs without lights under obstructed visibility. Our results reveal dependencies and trade-offs among obstructed/unobstructed visibility, lights/no lights, and semisynchronous/asynchronous settings.