323 research outputs found
Gathering Anonymous, Oblivious Robots on a Grid
We consider a swarm of autonomous mobile robots, distributed on a
2-dimensional grid. A basic task for such a swarm is the gathering process: All
robots have to gather at one (not predefined) place. A common local model for
extremely simple robots is the following: The robots do not have a common
compass, only have a constant viewing radius, are autonomous and
indistinguishable, can move at most a constant distance in each step, cannot
communicate, are oblivious and do not have flags or states. The only gathering
algorithm under this robot model, with known runtime bounds, needs
rounds and works in the Euclidean plane. The underlying time
model for the algorithm is the fully synchronous model. On
the other side, in the case of the 2-dimensional grid, the only known gathering
algorithms for the same time and a similar local model additionally require a
constant memory, states and "flags" to communicate these states to neighbors in
viewing range. They gather in time .
In this paper we contribute the (to the best of our knowledge) first
gathering algorithm on the grid that works under the same simple local model as
the above mentioned Euclidean plane strategy, i.e., without memory (oblivious),
"flags" and states. We prove its correctness and an time
bound in the fully synchronous time model. This time bound
matches the time bound of the best known algorithm for the Euclidean plane
mentioned above. We say gathering is done if all robots are located within a
square, because in such configurations cannot be
solved
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
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
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
Synchronous Robots vs Asynchronous Lights-Enhanced Robots on Graphs
AbstractIn this paper, we consider the distributed setting of computational mobile entities, called robots, that have to perform tasks without global coordination. Depending on the environment as well as on the robots' capabilities, tasks might be accomplished or not.In particular, we focus on the well-known scenario where the robots reside on the nodes of a graph and operate in Look-Compute-Move cycles. In one cycle, a robot perceives the current configuration in terms of robots positions (Look), decides whether to move toward some edge of the graph (Compute), and in the positive case it performs an instantaneous move along the computed edge (Move).We then compare two basic models: in the first model robots are fully synchronous, while in the second one robots are asynchronous and lights-enhanced, that is, each robot is equipped with a constant number of lights visible to all other robots. The question whether one model is more powerful than the other in terms of computable tasks has been considered in [Das et al., Int.'l Conf. on Distributed Computing Systems, 2012] but for robots moving on the Euclidean plane rather than on a graph.We provide two different tasks, and show that on graphs one task can be solved in the fully synchronous model but not in the asynchronous lights-enhanced model, while for the other task the converse holds. Hence we can assert that the fully synchronous model and the asynchronous lights-enhanced model are incomparable on graphs. This opens challenging directions in order to understand which peculiarities make the models so different
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