Gathering over Meeting Nodes in Infinite Grid

The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived

Meeting in a Polygon by Anonymous Oblivious Robots

The Meeting problem for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of $P$, we minimize the number of searchers $k$ for which the Meeting problem is solvable. Specifically, if $P$ has a rotational symmetry of order $\sigma$ (where $\sigma=1$ corresponds to no rotational symmetry), we prove that $k=\sigma+1$ searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with $k=2$ searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations, and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.Comment: 37 pages, 9 figure

TuringMobile: A Turing Machine of Oblivious Mobile Robots with Limited Visibility and Its Applications

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. Each robot is punctiform and memoryless, it operates in R^m, it has a local reference system independent of the other robots\u27 ones, and is activated asynchronously by an adversarial scheduler. Moreover, the 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 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

Practical Considerations and Applications for Autonomous Robot Swarms

In recent years, the study of autonomous entities such as unmanned vehicles has begun to revolutionize both military and civilian devices. One important research focus of autonomous entities has been coordination problems for autonomous robot swarms. Traditionally, robot models are used for algorithms that account for the minimum specifications needed to operate the swarm. However, these theoretical models also gloss over important practical details. Some of these details, such as time, have been considered before (as epochs of execution). In this dissertation, we examine these details in the context of several problems and introduce new performance measures to capture practical details. Specifically, we introduce three new metrics: (1) the distance complexity (reflecting power usage and wear-and-tear of robots), (2) the spatial complexity (reflecting the space needed for the algorithm to work), and (3) local computational complexity (reflecting the computational requirements for each robot in the swarm). We apply these metrics in the study of some well-known and important problems, such as Complete Visibility and Arbitrary Pattern Formation. We also introduce and study a new problem, Doorway Egress, that captures the essence of a swarm’s navigation through restricted spaces. First, we examine the distance and spatial complexity used across a class of Complete Visibility algorithms. Second, we provide algorithms for Complete Visibility on an integer plane, including some that are asymptotically optimal in terms of time, distance complexity, and spatial complexity. Third, we introduce the problem of Doorway Egress and provide algorithms for a variety of robot swarm models with various optimalities. Finally, we provide an optimal algorithm for Arbitrary Pattern Formation on the grid

Position discovery for a system of bouncing robots

International audienceA collection of n anonymous mobile robots is deployed on a unit-perimeter ring or a unit-length line segment. Every robot starts moving at constant speed, and bounces each time it meets any other robot or segment endpoint, changing its walk direction. We study the problem of position discovery, in which the task of each robot is to detect the presence and the initial positions of all other robots. The robots cannot communicate or perceive information about the environment in any way other than by bouncing nor they have control over their walks which are determined by their initial positions and their starting directions. Each robot has a clock allowing it to observe the times of its bounces. We give complete characterizations of all initial configurations for both the ring and the segment in which no position detection algorithm exists and we design optimal position detection algorithms for all feasible configurations

"Semi-Asynchronous": A New Scheduler in Distributed Computing

The study of mobile entities that based on local information have to accomplish global tasks is of main interest for the scientific community. Classic models for the activation and synchronization of mobile entities are the fully-synchronous (FSync), semi-synchronous (SSync), and asynchronous (Async) models, where entities alternate between active and inactive states with different timing. According to the assumed synchronization model, very different results have been achieved in the field of distributed computing. One of the main outcomes is the big gap between the Async and the other models in terms of manageability and algorithm design. In fact, there are still many problems for which it is not known whether synchronicity is crucial for designing resolution algorithms or not. In order to better understand the Async case, here we propose a further model referred to as the semi-asynchronous (SAsync). This slightly deviates from SSync. In fact, like in SSync (and FSync), the duration of the activation of an entity is kept of fixed time whereas, like in Async, the starting instant of the activation is not fully synchronized with the possible activation of other entities. We show that for entities moving on graphs, the SSync model allows accomplishing more tasks than the SAsync that in turn allows accomplishing more tasks than the Async. Furthermore, our results show that, especially to tackle problems in the Euclidean plane, the SAsync model is already quite challenging, therefore there is no need to get involved with complications arising in the Async model

Navigation problems for autonomous robots in distributed environments

This thesis studies algorithms for Distributed Computing. More specifically however the project aimed to carry out research on the performance analysis of mobile robots in a variety of different settings. In a range of different network and geometric settings we investigate efficient algorithms for the robots to perform given tasks. We looked at a variety of different models when completing this work but focused mainly on cases where the robots have limited communication mechanisms. Within this framework we investigated cases where the robots were numerous to cases where they were few in number. Also we looked at scenarios where the robots involved had different limitations on the maximal speeds they could travel. When conducting this work we explored two main tasks carried out by the robots that became the primary theme of the study. These two main tasks are Robot Location Discovery and Robot Evacuation. To accomplish these tasks we constructed algorithms that made use of both randomised and deterministic approaches in their solutions