Gathering on Rings for Myopic Asynchronous Robots With Lights

We investigate gathering algorithms for asynchronous autonomous mobile robots moving in uniform ring-shaped networks. Different from most work using the Look-Compute-Move (LCM) model, we assume that robots have limited visibility and lights. That is, robots can observe nodes only within a certain fixed distance, and emit a color from a set of constant number of colors. We consider gathering algorithms depending on two parameters related to the initial configuration: M_{init}, which denotes the number of nodes between two border nodes, and O_{init}, which denotes the number of nodes hosting robots between two border nodes. In both cases, a border node is a node hosting one or more robots that cannot see other robots on at least one side. Our main contribution is to prove that, if M_{init} or O_{init} is odd, gathering is always feasible with three or four colors. The proposed algorithms do not require additional assumptions, such as knowledge of the number of robots, multiplicity detection capabilities, or the assumption of towerless initial configurations. These results demonstrate the power of lights to achieve gathering of robots with limited visibility

Ring Exploration with Oblivious Myopic Robots

The exploration problem in the discrete universe, using identical oblivious asynchronous robots without direct communication, has been well investigated. These robots have sensors that allow them to see their environment and move accordingly. However, the previous work on this problem assume that robots have an unlimited visibility, that is, they can see the position of all the other robots. In this paper, we consider deterministic exploration in an anonymous, unoriented ring using asynchronous, oblivious, and myopic robots. By myopic, we mean that the robots have only a limited visibility. We study the computational limits imposed by such robots and we show that under some conditions the exploration problem can still be solved. We study the cases where the robots visibility is limited to 1, 2, and 3 neighboring nodes, respectively.Comment: (2012

Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the COQ higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results forconvergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalization, the corresponding COQ developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks

Asynchronous Gathering in a Torus

We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other but are endowed with visibility sensors that allow them to see the positions of the other robots. Most investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configurations. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local weak multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robot unless it is their current node. Consequently, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network

Gathering of Mobile Robots in Anonymous Trees

Gathering problem of mobile robots is a class of graph problem that has a lot of relevance in everyday life. The problem requires a set of mobile robots, initially located at different nodes of a graph, to gather at the same location in the graph, which is not decided before. This report considers the gathering problem of mobile robots in anonymous trees. The robots considered here are identical, do not communicate directly with other robots and also, all the robots execute the same algorithm to achieve gathering. Robots are assumed to have minimal capabilities with respect to the memory associated with them as well as their visibility capability. In this report, three models have been proposed for solving gathering problem under three different scenarios. Possible solutions in each of these models have been described. The current work that has already happened and the future work that can be done in each model have also been mentioned

Self-Stabilizing Robots in Highly Dynamic Environments

International audienceThis paper deals with the classical problem of exploring a ring by a cohort of synchronous robots. We focus on the perpetual version of this problem in which it is required that each node of the ring is visited by a robot infinitely often.The challenge in this paper is twofold. First, we assume that the robots evolve in a highly dynamic ring, i.e., edges may appear and disappear unpredictably without any recurrence nor periodicity assumption. The only assumption we made is that each node is infinitely often reachable from any other node. Second, we aim at providing a self-stabilizing algorithm to the robots, i.e., the algorithm must guarantee an eventual correct behavior regardless of the initial state and positions of the robots. Our main contribution is to show that this problem is deterministically solvable in this harsh environment by providing a self-stabilizing algorithm for three robots