On Optimal Doorway Egress by Autonomous Robots

Abstract

We consider the distributed setting of n autonomous mobile robots operating in Look-Compute-Move (LCM) cycles in the Euclidean plane. In this paper, we introduce and study the problem of exiting n robots positioned initially on one side of a wall to its other side through a door (which we call the Doorway Egress problem). This problem is fundamental as it resembles evacuating robots from a working area after they are done with an assigned job. We consider both point (dimensionless) and fat (unit circle) robots. For each of these, we consider three abilities: visibility, lights, and synchronization. We show that without any of these abilities (i.e., obstructed visibility, no lights, and asynchronous setting), both point and fat robots can solve Doorway Egress in O(n) time. We then show that with any one of the three abilities (global visibility or lights or semi-synchronous setting) point robots can solve the problem in optimal $\varTheta (1)$ time. Finally, we show that with global visibility, grid-alignment, and any one of the two other abilities (lights or semi-synchronous setting), fat robots can solve the problem in optimal $\varTheta \!\left( \sqrt{n}+\frac{n}{s}\right)$ time, where 2s is the width of the door. Our results also point to possible dependencies and trade-offs between these abilities.

Keywords