286 research outputs found
Parameterized Verification of Algorithms for Oblivious Robots on a Ring
We study verification problems for autonomous swarms of mobile robots that
self-organize and cooperate to solve global objectives. In particular, we focus
in this paper on the model proposed by Suzuki and Yamashita of anonymous robots
evolving in a discrete space with a finite number of locations (here, a ring).
A large number of algorithms have been proposed working for rings whose size is
not a priori fixed and can be hence considered as a parameter. Handmade
correctness proofs of these algorithms have been shown to be error-prone, and
recent attention had been given to the application of formal methods to
automatically prove those. Our work is the first to study the verification
problem of such algorithms in the parameter-ized case. We show that safety and
reachability problems are undecidable for robots evolving asynchronously. On
the positive side, we show that safety properties are decidable in the
synchronous case, as well as in the asynchronous case for a particular class of
algorithms. Several properties on the protocol can be decided as well. Decision
procedures rely on an encoding in Presburger arithmetics formulae that can be
verified by an SMT-solver. Feasibility of our approach is demonstrated by the
encoding of several case studies
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
A Certified Universal Gathering Algorithm for Oblivious Mobile Robots
We present a new algorithm for the problem of universal gathering mobile
oblivious robots (that is, starting from any initial configuration that is not
bivalent, using any number of robots, the robots reach in a finite number of
steps the same position, not known beforehand) without relying on a common
chirality. We give very strong guaranties on the correctness of our algorithm
by proving formally that it is correct, using the COQ proof assistant. To our
knowledge, this is the first certified positive (and constructive) result in
the context of oblivious mobile robots. It demonstrates both the effectiveness
of the approach to obtain new algorithms that are truly generic, and its
managability since the amount of developped code remains human readable
Circle Formation by Asynchronous Opaque Fat Robots on an Infinite Grid
This study addresses the problem of "Circle Formation on an Infinite Grid by
Fat Robots" (). Unlike prior work focused solely on point robots
in discrete domain, it introduces fat robots to circle formation on an infinite
grid, aligning with practicality as even small robots inherently possess
dimensions. The algorithm, named , resolves the
problem using a swarm of fat luminous robots. Operating under an asynchronous
scheduler, it achieves this with five distinct colors and by leveraging
one-axis agreement among the robots
On the Synthesis of Mobile Robots Algorithms: the Case of Ring Gathering
International audienceRecent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and correctness proofs.This paper is the first to propose a formal framework to automatically design distributed algorithms that are dedicated to autonomous mobile robots evolving in a discrete space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. Our contribution is threefold. First, we propose an encoding of the gathering problem as a reachability game. Then, we automatically generate an optimal distributed algorithm for three robots evolving on a fixed size uniform ring. Finally, we prove by induction that the generated algorithm is also correct for any ring size except when an impossibility result holds (that is, when the number of robots divides the ring size)
Pattern Formation for Fat Robots with Memory
Given a set of autonomous, anonymous, indistinguishable, silent,
and possibly disoriented mobile unit disk (i.e., fat) robots operating
following Look-Compute-Move cycles in the Euclidean plane, we consider the
Pattern Formation problem: from arbitrary starting positions, the robots must
reposition themselves to form a given target pattern. This problem arises under
obstructed visibility, where a robot cannot see another robot if there is a
third robot on the straight line segment between the two robots. We assume that
a robot's movement cannot be interrupted by an adversary and that robots have a
small -sized memory that they can use to store information, but that
cannot be communicated to the other robots. To solve this problem, we present
an algorithm that works in three steps. First it establishes mutual visibility,
then it elects one robot to be the leader, and finally it forms the required
pattern. The whole algorithm runs in rounds, where
is related to leader election, which takes rounds with
probability at least . The algorithms are collision-free and do not
require the knowledge of the number of robots.Comment: arXiv admin note: text overlap with arXiv:2306.1444
Terminating Exploration Of A Grid By An Optimal Number Of Asynchronous Oblivious Robots
International audienceWe consider swarms of asynchronous oblivious robots evolving into an anonymous grid-shaped network. In this context, we investigate optimal (w.r.t. the number of robots) deterministic solutions for the terminating exploration problem. We first show lower bounds in the semi-synchronous model. Precisely, we show that at least three robots are required to explore any grid of at least three nodes, even in the probabilistic case. Then, we show that at least four (resp. five) robots are necessary to deterministically explore a (2,2)-Grid (resp. a (3,3)-Grid). We then propose deterministic algorithms in the asynchronous model. This latter being strictly weakest than the semi-synchronous model, all the aforementioned bounds still hold in that context. Our algorithms actually exhibit the optimal number of robots that is necessary to explore a given grid. Overall, our results show that except in two particular cases, three robots are necessary and sufficient to deterministically explore a grid of at least three nodes and then terminate. The optimal number of robots for the two remaining cases is four for the (2,2)-Grid and five for the (3,3)-Grid, respectively
Distributed Systems and Mobile Computing
The book is about Distributed Systems and Mobile Computing. This is a branch of Computer Science devoted to the study of systems whose components are in different physical locations and have limited communication capabilities. Such components may be static, often organized in a network, or may be able to move in a discrete or continuous environment. The theoretical study of such systems has applications ranging from swarms of mobile robots (e.g., drones) to sensor networks, autonomous intelligent vehicles, the Internet of Things, and crawlers on the Web. The book includes five articles. Two of them are about networks: the first one studies the formation of networks by agents that interact randomly and have the ability to form connections; the second one is a study of clustering models and algorithms. The three remaining articles are concerned with autonomous mobile robots operating in continuous space. One article studies the classical gathering problem, where all robots have to reach a common location, and proposes a fast algorithm for robots that are endowed with a compass but have limited visibility. The last two articles deal with the evacuations problem, where two robots have to locate an exit point and evacuate a region in the shortest possible time
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