2,241 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
A Distributed Algorithm for Gathering Many Fat Mobile Robots in the Plane
In this work we consider the problem of gathering autonomous robots in the
plane. In particular, we consider non-transparent unit-disc robots (i.e., fat)
in an asynchronous setting. Vision is the only mean of coordination. Using a
state-machine representation we formulate the gathering problem and develop a
distributed algorithm that solves the problem for any number of robots.
The main idea behind our algorithm is for the robots to reach a configuration
in which all the following hold: (a) The robots' centers form a convex hull in
which all robots are on the convex, (b) Each robot can see all other robots,
and (c) The configuration is connected, that is, every robot touches another
robot and all robots together form a connected formation. We show that starting
from any initial configuration, the robots, making only local decisions and
coordinate by vision, eventually reach such a configuration and terminate,
yielding a solution to the gathering problem.Comment: 39 pages, 5 figure
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
Robots with Lights: Overcoming Obstructed Visibility Without Colliding
Robots with lights is a model of autonomous mobile computational entities
operating in the plane in Look-Compute-Move cycles: each agent has an
externally visible light which can assume colors from a fixed set; the lights
are persistent (i.e., the color is not erased at the end of a cycle), but
otherwise the agents are oblivious. The investigation of computability in this
model, initially suggested by Peleg, is under way, and several results have
been recently established. In these investigations, however, an agent is
assumed to be capable to see through another agent. In this paper we start the
study of computing when visibility is obstructable, and investigate the most
basic problem for this setting, Complete Visibility: The agents must reach
within finite time a configuration where they can all see each other and
terminate. We do not make any assumption on a-priori knowledge of the number of
agents, on rigidity of movements nor on chirality. The local coordinate system
of an agent may change at each activation. Also, by definition of lights, an
agent can communicate and remember only a constant number of bits in each
cycle. In spite of these weak conditions, we prove that Complete Visibility is
always solvable, even in the asynchronous setting, without collisions and using
a small constant number of colors. The proof is constructive. We also show how
to extend our protocol for Complete Visibility so that, with the same number of
colors, the agents solve the (non-uniform) Circle Formation problem with
obstructed visibility
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