Abstract
We consider the distributed setting of N autonomous mobile robots that operate in Look-Compute-Move (LCM) cycles and use colored lights (the robots with lights model). We assume obstructed visibility where a robot cannot see another robot if a third robot is positioned between them on the straight line segment connecting them. In this paper, we consider the problem of positioning N autonomous robots on a plane so that every robot is visible to all others (this is called the Complete Visibility problem). This problem is fundamental, as it provides a basis to solve many other problems under obstructed visibility. In this paper, we provide the first, asymptotically optimal, O(1) time, O(1) color algorithm for Complete Visibility in the asynchronous setting. This significantly improves on an O(N)-time translation of the existing O(1) time, O(1) color semi-synchronous algorithm to the asynchronous setting. The proposed algorithm is collision-free, i.e., robots do not share positions, and their paths do not cross. We also introduce a new technique for moving robots in an asynchronous setting that may be of independent interest, called Beacon-Directed Curve Positioning.
Highlights
The classical model of distributed computing by mobile robots models each robot as a point in the plane that is equipped with a local coordinate system and sensory capabilities to determine the positions of other robots [1]
Each robot proceeds in Look-Compute-Move (LCM) cycles: When a robot becomes active, it first gets a snapshot of its surroundings (Look), computes a destination based on the snapshot (Compute), and moves towards the destination (Move)
We present an algorithm for C OMPLETE V ISIBILITY that runs in O(1) time using O(1) colors even in the asynchronous setting
Summary
The classical model of distributed computing by mobile robots models each robot as a point in the plane that is equipped with a local coordinate system and sensory capabilities to determine the positions of other robots [1]. Solving C OMPLETE V ISIBILITY enables solutions to many other robot problems under obstructed visibility, including gathering, pattern formation, and leader election. We recently solved the problem of pattern formation in Reference [4], which uses the solution to C OMPLETE V ISIBILITY presented in this paper in the first step of its four-step algorithm. The result of Das et al [2] is as follows: Any algorithm (for any problem) in the robots with lights model that uses k > 1 colors in the semi-synchronous setting can be simulated in the asynchronous setting with, at most, 5 · k colors. We present an algorithm for C OMPLETE V ISIBILITY that runs in O(1) time using O(1) colors even in the asynchronous setting. Note that O(1) runtime is optimal for C OMPLETE V ISIBILITY, irrespective of the number of colors
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