27,699 research outputs found
Getting Close Without Touching: Near-Gathering for Autonomous Mobile Robots
In this paper we study the Near-Gathering problem for a finite set of
dimensionless, deterministic, asynchronous, anonymous, oblivious and autonomous
mobile robots with limited visibility moving in the Euclidean plane in
Look-Compute-Move (LCM) cycles. In this problem, the robots have to get close
enough to each other, so that every robot can see all the others, without
touching (i.e., colliding with) any other robot. The importance of solving the
Near-Gathering problem is that it makes it possible to overcome the restriction
of having robots with limited visibility. Hence it allows to exploit all the
studies (the majority, actually) done on this topic in the unlimited visibility
setting. Indeed, after the robots get close enough to each other, they are able
to see all the robots in the system, a scenario that is similar to the one
where the robots have unlimited visibility.
We present the first (deterministic) algorithm for the Near-Gathering
problem, to the best of our knowledge, which allows a set of autonomous mobile
robots to nearly gather within finite time without ever colliding. Our
algorithm assumes some reasonable conditions on the input configuration (the
Near-Gathering problem is easily seen to be unsolvable in general). Further,
all the robots are assumed to have a compass (hence they agree on the "North"
direction), but they do not necessarily have the same handedness (hence they
may disagree on the clockwise direction).
We also show how the robots can detect termination, i.e., detect when the
Near-Gathering problem has been solved. This is crucial when the robots have to
perform a generic task after having nearly gathered. We show that termination
detection can be obtained even if the total number of robots is unknown to the
robots themselves (i.e., it is not a parameter of the algorithm), and robots
have no way to explicitly communicate.Comment: 25 pages, 8 fiugre
Meeting in a Polygon by Anonymous Oblivious Robots
The Meeting problem for searchers in a polygon (possibly with
holes) consists in making the searchers move within , 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 , we minimize the number of searchers
for which the Meeting problem is solvable. Specifically, if has a
rotational symmetry of order (where corresponds to no
rotational symmetry), we prove that searchers are sufficient, and
the bound is tight. Furthermore, we give an improved algorithm that optimally
solves the Meeting problem with 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
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
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