2,011 research outputs found
Dynamical maximum entropy approach to flocking
Peer reviewedPublisher PD
Starling flock networks manage uncertainty in consensus at low cost
Flocks of starlings exhibit a remarkable ability to maintain cohesion as a
group in highly uncertain environments and with limited, noisy information.
Recent work demonstrated that individual starlings within large flocks respond
to a fixed number of nearest neighbors, but until now it was not understood why
this number is seven. We analyze robustness to uncertainty of consensus in
empirical data from multiple starling flocks and show that the flock
interaction networks with six or seven neighbors optimize the trade-off between
group cohesion and individual effort. We can distinguish these numbers of
neighbors from fewer or greater numbers using our systems-theoretic approach to
measuring robustness of interaction networks as a function of the network
structure, i.e., who is sensing whom. The metric quantifies the disagreement
within the network due to disturbances and noise during consensus behavior and
can be evaluated over a parameterized family of hypothesized sensing strategies
(here the parameter is number of neighbors). We use this approach to further
show that for the range of flocks studied the optimal number of neighbors does
not depend on the number of birds within a flock; rather, it depends on the
shape, notably the thickness, of the flock. The results suggest that robustness
to uncertainty may have been a factor in the evolution of flocking for
starlings. More generally, our results elucidate the role of the interaction
network on uncertainty management in collective behavior, and motivate the
application of our approach to other biological networks.Comment: 19 pages, 3 figures, 9 supporting figure
Dynamical modeling of collective behavior from pigeon flight data: flock cohesion and dispersion
Several models of flocking have been promoted based on simulations with
qualitatively naturalistic behavior. In this paper we provide the first direct
application of computational modeling methods to infer flocking behavior from
experimental field data. We show that this approach is able to infer general
rules for interaction, or lack of interaction, among members of a flock or,
more generally, any community. Using experimental field measurements of homing
pigeons in flight we demonstrate the existence of a basic distance dependent
attraction/repulsion relationship and show that this rule is sufficient to
explain collective behavior observed in nature. Positional data of individuals
over time are used as input data to a computational algorithm capable of
building complex nonlinear functions that can represent the system behavior.
Topological nearest neighbor interactions are considered to characterize the
components within this model. The efficacy of this method is demonstrated with
simulated noisy data generated from the classical (two dimensional) Vicsek
model. When applied to experimental data from homing pigeon flights we show
that the more complex three dimensional models are capable of predicting and
simulating trajectories, as well as exhibiting realistic collective dynamics.
The simulations of the reconstructed models are used to extract properties of
the collective behavior in pigeons, and how it is affected by changing the
initial conditions of the system. Our results demonstrate that this approach
may be applied to construct models capable of simulating trajectories and
collective dynamics using experimental field measurements of herd movement.
From these models, the behavior of the individual agents (animals) may be
inferred
Consensus reaching in swarms ruled by a hybrid metric-topological distance
Recent empirical observations of three-dimensional bird flocks and human
crowds have challenged the long-prevailing assumption that a metric interaction
distance rules swarming behaviors. In some cases, individual agents are found
to be engaged in local information exchanges with a fixed number of neighbors,
i.e. a topological interaction. However, complex system dynamics based on pure
metric or pure topological distances both face physical inconsistencies in low
and high density situations. Here, we propose a hybrid metric-topological
interaction distance overcoming these issues and enabling a real-life
implementation in artificial robotic swarms. We use network- and
graph-theoretic approaches combined with a dynamical model of locally
interacting self-propelled particles to study the consensus reaching pro- cess
for a swarm ruled by this hybrid interaction distance. Specifically, we
establish exactly the probability of reaching consensus in the absence of
noise. In addition, simulations of swarms of self-propelled particles are
carried out to assess the influence of the hybrid distance and noise
A Tight Lower Bound on the Controllability of Networks with Multiple Leaders
In this paper we study the controllability of networked systems with static
network topologies using tools from algebraic graph theory. Each agent in the
network acts in a decentralized fashion by updating its state in accordance
with a nearest-neighbor averaging rule, known as the consensus dynamics. In
order to control the system, external control inputs are injected into the so
called leader nodes, and the influence is propagated throughout the network.
Our main result is a tight topological lower bound on the rank of the
controllability matrix for such systems with arbitrary network topologies and
possibly multiple leaders
Resilience and Controllability of Dynamic Collective Behaviors
The network paradigm is used to gain insight into the structural root causes
of the resilience of consensus in dynamic collective behaviors, and to analyze
the controllability of the swarm dynamics. Here we devise the dynamic signaling
network which is the information transfer channel underpinning the swarm
dynamics of the directed interagent connectivity based on a topological
neighborhood of interactions. The study of the connectedness of the swarm
signaling network reveals the profound relationship between group size and
number of interacting neighbors, which is found to be in good agreement with
field observations on flock of starlings [Ballerini et al. (2008) Proc. Natl.
Acad. Sci. USA, 105: 1232]. Using a dynamical model, we generate dynamic
collective behaviors enabling us to uncover that the swarm signaling network is
a homogeneous clustered small-world network, thus facilitating emergent
outcomes if connectedness is maintained. Resilience of the emergent consensus
is tested by introducing exogenous environmental noise, which ultimately
stresses how deeply intertwined are the swarm dynamics in the physical and
network spaces. The availability of the signaling network allows us to
analytically establish for the first time the number of driver agents necessary
to fully control the swarm dynamics
Declarative vs Rule-based Control for Flocking Dynamics
The popularity of rule-based flocking models, such as Reynolds' classic
flocking model, raises the question of whether more declarative flocking models
are possible. This question is motivated by the observation that declarative
models are generally simpler and easier to design, understand, and analyze than
operational models. We introduce a very simple control law for flocking based
on a cost function capturing cohesion (agents want to stay together) and
separation (agents do not want to get too close). We refer to it as {\textit
declarative flocking} (DF). We use model-predictive control (MPC) to define
controllers for DF in centralized and distributed settings. A thorough
performance comparison of our declarative flocking with Reynolds' model, and
with more recent flocking models that use MPC with a cost function based on
lattice structures, demonstrate that DF-MPC yields the best cohesion and least
fragmentation, and maintains a surprisingly good level of geometric regularity
while still producing natural flock shapes similar to those produced by
Reynolds' model. We also show that DF-MPC has high resilience to sensor noise.Comment: 7 Page
Jamming in a lattice model of stochastically interacting agents with a field of view
We study the collective dynamics of a lattice model of stochastically
interacting agents with a weighted field of vision. We assume that agents
preferentially interact with neighbours, depending on their relative location,
through velocity alignments and the additional constraint of exclusion. Unlike
in previous models of flocking, here the stochasticity arises intrinsically
from the interactions between agents, and its strength is dependent on the
local density of agents. We find that this system yields a first-order jamming
transition as a consequence of these interactions, even at a very low density.
Furthermore, the critical jamming density is found to strongly depend on the
nature of the field of view.Comment: 5 pages, 3 figures + 3 pages supplementary materia
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