271 research outputs found
Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots
We consider a team of identical, oblivious, asynchronous mobile robots
that are able to sense (\emph{i.e.}, view) their environment, yet are unable to
communicate, and evolve on a constrained path. Previous results in this weak
scenario show that initial symmetry yields high lower bounds when problems are
to be solved by \emph{deterministic} robots. In this paper, we initiate
research on probabilistic bounds and solutions in this context, and focus on
the \emph{exploration} problem of anonymous unoriented rings of any size. It is
known that robots are necessary and sufficient to solve the
problem with deterministic robots, provided that and are coprime.
By contrast, we show that \emph{four} identical probabilistic robots are
necessary and sufficient to solve the same problem, also removing the coprime
constraint. Our positive results are constructive
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
Optimal deterministic ring exploration with oblivious asynchronous robots
We consider the problem of exploring an anonymous unoriented ring of size
by identical, oblivious, asynchronous mobile robots, that are unable to
communicate, yet have the ability to sense their environment and take decisions
based on their local view. Previous works in this weak scenario prove that
must not divide for a deterministic solution to exist. Also, it is known
that the minimum number of robots (either deterministic or probabilistic) to
explore a ring of size is 4. An upper bound of 17 robots holds in the
deterministic case while 4 probabilistic robots are sufficient. In this paper,
we close the complexity gap in the deterministic setting, by proving that no
deterministic exploration is feasible with less than five robots whenever the
size of the ring is even, and that five robots are sufficient for any that
is coprime with five. Our protocol completes exploration in O(n) robot moves,
which is also optimal
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 an even number of robots in an odd ring without global multiplicity detection
We propose a gathering protocol for an even number of robots in a ring-shaped
network that allows symmetric but not periodic configurations as initial
configurations, yet uses only local weak multiplicity detection. Robots are
assumed to be anonymous and oblivious, and the execution model is the non-
atomic CORDA model with asynchronous fair scheduling. In our scheme, the number
of robots k must be greater than 8, the number of nodes n on a network must be
odd and greater than k+3. The running time of our protocol is O(n2)
asynchronous rounds.Comment: arXiv admin note: text overlap with arXiv:1104.566
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
Certified Universal Gathering in for Oblivious Mobile Robots
We present a unified formal framework for expressing mobile robots models,
protocols, and proofs, and devise a protocol design/proof methodology dedicated
to mobile robots that takes advantage of this formal framework. As a case
study, we present the first formally certified protocol for oblivious mobile
robots evolving in a two-dimensional Euclidean space. In more details, we
provide 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 orientation
nor chirality. We give very strong guaranties on the correctness of our
algorithm by proving formally that it is correct, using the COQ proof
assistant. This result demonstrates both the effectiveness of the approach to
obtain new algorithms that use as few assumptions as necessary, and its
manageability since the amount of developed code remains human readable.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0160
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