Abstract
In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward its destination. Robots are punctiform and memoryless, they operate in \(\mathbb {R}^m\), they have local reference systems independent of each other, and are activated asynchronously by an adversarial scheduler. Moreover, robots are non-rigid, in that they may be stopped by the scheduler at each move before reaching their destination (but are guaranteed to travel at least a fixed unknown distance before being stopped). We show that despite these strong limitations, it is possible to arrange \(3m+3k\) of these weak entities in \(\mathbb {R}^m\) to simulate the behavior of a stronger robot that is rigid (i.e., it always reaches its destination) and is endowed with k registers of persistent memory, each of which can store a real number. We call this arrangement a TuringMobile. In its simplest form, a TuringMobile consisting of only three robots can travel in the plane and store and update a single real number. We also prove that this task is impossible with fewer than three robots. Among the applications of the TuringMobile, we focused on Near-Gathering (all robots have to gather in a small-enough disk) and Pattern Formation (of which Gathering is a special case) with limited visibility. Interestingly, our investigation implies that both problems are solvable in Euclidean spaces of any dimension, even if the visibility graph of the robots is initially disconnected, provided that a small amount of these robots are arranged to form a TuringMobile. In the special case of the plane, a basic TuringMobile of only three robots is sufficient.
Highlights
1.1 Framework and BackgroundThe investigations of systems of autonomous mobile robots have long moved outside the boundaries of the engineering, control, and AI communities
Among the applications of the TuringMobile, we focused on Near-Gathering and Pattern Formation with limited visibility
We have introduced the TuringMobile as a special configuration of oblivious non-rigid robots that can simulate a rigid robot with memory
Summary
The investigations of systems of autonomous mobile robots have long moved outside the boundaries of the engineering, control, and AI communities. The computational and complexity issues arising in such systems are important research topics within theoretical computer science, especially in distributed computing In these theoretical investigations, the robots are usually viewed as punctiform computational entities that live in a metric space, typically R2 or R3, in which they can move. From a computational point of view, there is another crucial factor: the visibility range of the robots, that is, how much of the surrounding space they are able to observe in a Look operation. In this regard, two basic settings are considered: unlimited visibility, where the robots can see the entire space (and all other robots), and limited visibility, when the robots have a fixed visibility radius.
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