276,147 research outputs found
Distributed computing by mobile robots: uniform circle formation
Consider a set of n finite set of simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct locations, moving freely in the plane and able to sense the positions of the other robots. We study the primitive task of the robots arranging themselves on the vertices of a regular n-gon not fixed in advance (Uniform Circle Formation). In the literature, the existing algorithmic contributions are limited to conveniently restricted sets of initial configurations of the robots and to more powerful robots. The question of whether such simple robots could deterministically form a uniform circle has remained open. In this paper, we constructively prove that indeed the Uniform Circle Formation problem is solvable for any initial configuration in which the robots are in distinct locations, without any additional assumption (if two robots are in the same location, the problem is easily seen to be unsolvable). In addition to closing a long-standing problem, the result of this paper also implies that, for pattern formation, asynchrony is not a computational handicap, and that additional powers such as chirality and rigidity are computationally irrelevant
Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity
AbstractThis paper presents a distributed algorithm whereby a group of mobile robots self-organize and position themselves into forming a circle in a loosely synchronized environment. In spite of its apparent simplicity, the difficulty of the problem comes from the weak assumptions made on the system. In particular, robots are anonymous, oblivious (i.e., stateless), unable to communicate directly, and disoriented in the sense that they share no knowledge of a common coordinate system. Furthermore, robots’ activations are not synchronized. More specifically, the proposed algorithm ensures that robots deterministically form a non-uniform circle in a finite number of steps and converges to a situation in which all robots are located evenly on the boundary of the circle
The Rotating Vicsek Model: Pattern Formation and Enhanced Flocking in Chiral Active Matter
We generalize the Vicsek model to describe the collective behaviour of polar
circle swimmers with local alignment interactions. While the phase transition
leading to collective motion in 2D (flocking) occurs at the same interaction to
noise ratio as for linear swimmers, as we show, circular motion enhances the
polarization in the ordered phase (enhanced flocking) and induces secondary
instabilities leading to structure formation. Slow rotations result in phase
separation whereas fast rotations generate patterns which consist of phase
synchronized microflocks of controllable self-limited size. Our results defy
the viewpoint that monofrequent rotations form a rather trivial extension of
the Vicsek model and establish a generic route to pattern formation in chiral
active matter with possible applications to control coarsening and to design
rotating microflocks.Comment: Contains a Supplementary Materia
Simultaneous Phase Separation and Pattern Formation in Chiral Active Mixtures
Chiral active particles, or self-propelled circle swimmers, from sperm cells
to asymmetric Janus colloids, form a rich set of patterns, which are different
from those seen in linear swimmers. Such patterns have mainly been explored for
identical circle swimmers, while real-world circle swimmers, typically possess
a frequency distribution. Here we show that even the simplest mixture of
(velocity-aligning) circle swimmers with two different frequencies, hosts a
complex world of superstructures: The most remarkable example comprises a
microflock pattern, formed in one species, while the other species phase
separates and forms a macrocluster, coexisting with a gas phase. Here, one
species microphase-separates and selects a characteristic length scale, whereas
the other one macrophase separates and selects a density. A second notable
example, here occurring in an isotropic system, are patterns comprising two
different characteristic length scales, which are controllable via frequency
and swimming speed of the individual particles
COOPERATIVE TARGET TRACKING IN CONCENTRIC FORMATIONS
This paper considers the problem of coordinating multiple unmanned aerial vehicles (UAVs) in a circular formation around a moving target. The main contribution is allowing for versatile formation patterns on the basis of the following components. Firstly, new uniform spacing control laws are proposed that spread the agents not necessarily over a full circle, but over a circular arc. Uniform spacing formation controllers are proposed, regulating either the separation distances or the separation angles between agents. Secondly, the use of virtual agents is proposed to allow for different radii in agents’ orbits. Thirdly, a hierarchical combination of formation patterns is described. A Lyapunov analysis is conducted to study the stability characteristics. This paper also addresses the practical issue of collision avoidance that arises while UAVs are developing formations. An additional control component is added that repels agents to steer away from each other once they get too close. All UAVs have constant linear velocities. Control of the UAV is via its yaw rate. The proposed extensions to formation on a portion of a circle, circling on different radii for different agents, formation in local geometric shapes, and inter-vehicle collision avoidance, provide more complete solution to cooperative target tracking in concentric formations
Emergent velocity agreement in robot networks
In this paper we propose and prove correct a new self-stabilizing velocity
agreement (flocking) algorithm for oblivious and asynchronous robot networks.
Our algorithm allows a flock of uniform robots to follow a flock head emergent
during the computation whatever its direction in plane. Robots are
asynchronous, oblivious and do not share a common coordinate system. Our
solution includes three modules architectured as follows: creation of a common
coordinate system that also allows the emergence of a flock-head, setting up
the flock pattern and moving the flock. The novelty of our approach steams in
identifying the necessary conditions on the flock pattern placement and the
velocity of the flock-head (rotation, translation or speed) that allow the
flock to both follow the exact same head and to preserve the flock pattern.
Additionally, our system is self-healing and self-stabilizing. In the event of
the head leave (the leading robot disappears or is damaged and cannot be
recognized by the other robots) the flock agrees on another head and follows
the trajectory of the new head. Also, robots are oblivious (they do not recall
the result of their previous computations) and we make no assumption on their
initial position. The step complexity of our solution is O(n)
On localized vegetation patterns, fairy circles and localized patches in arid landscapes
We investigate the formation of localized structures with a varying width in
one and two-dimensional systems. The mechanism of stabilization is attributed
to strong nonlocal coupling mediated by a Lorentzian type of Kernel. We show
that, in addition to stable dips found recently [see, e.g., C. Fernandez-Oto,
M. G. Clerc, D. Escaff, and M. Tlidi, Phys. Rev. Lett. {\bf{110}}, 174101
(2013)], exist stable localized peaks which appear as a result of strong
nonlocal coupling, i.e. mediated by a coupling that decays with the distance
slower than an exponential. We applied this mechanism to arid ecosystems by
considering a prototype model of a Nagumo type. In one-dimension, we study the
front that connects the stable uniformly vegetated state with the bare one
under the effect of strong nonlocal coupling. We show that strong nonlocal
coupling stabilizes both---dip and peak---localized structures. We show
analytically and numerically that the width of localized dip, which we
interpret as fairy circle, increases strongly with the aridity parameter. This
prediction is in agreement with filed observations. In addition, we predict
that the width of localized patch decreases with the degree of aridity.
Numerical results are in close agreement with analytical predictions
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