170 research outputs found
Dynamical maximum entropy approach to flocking
Peer reviewedPublisher PD
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
Fluctuation-Driven Flocking Movement in Three Dimensions and Scale-Free Correlation
Recent advances in the study of flocking behavior have permitted more sophisticated analyses than previously possible. The concepts of “topological distances” and “scale-free correlations” are important developments that have contributed to this improvement. These concepts require us to reconsider the notion of a neighborhood when applied to theoretical models. Previous work has assumed that individuals interact with neighbors within a certain radius (called the “metric distance”). However, other work has shown that, assuming topological interactions, starlings interact on average with the six or seven nearest neighbors within a flock. Accounting for this observation, we previously proposed a metric-topological interaction model in two dimensions. The goal of our model was to unite these two interaction components, the metric distance and the topological distance, into one rule. In our previous study, we demonstrated that the metric-topological interaction model could explain a real bird flocking phenomenon called scale-free correlation, which was first reported by Cavagna et al. In this study, we extended our model to three dimensions while also accounting for variations in speed. This three-dimensional metric-topological interaction model displayed scale-free correlation for velocity and orientation. Finally, we introduced an additional new feature of the model, namely, that a flock can store and release its fluctuations
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
Effects of anisotropic interactions on the structure of animal groups
This paper proposes an agent-based model which reproduces different
structures of animal groups. The shape and structure of the group is the effect
of simple interaction rules among individuals: each animal deploys itself
depending on the position of a limited number of close group mates. The
proposed model is shown to produce clustered formations, as well as lines and
V-like formations. The key factors which trigger the onset of different
patterns are argued to be the relative strength of attraction and repulsion
forces and, most important, the anisotropy in their application.Comment: 22 pages, 9 figures. Submitted. v1-v4: revised presentation; extended
simulations; included technical results. v5: added a few clarification
Online Flocking Control of UAVs with Mean-Field Approximation
We present a novel approach to the formation controlling of aerial robot
swarms that demonstrates the flocking behavior. The proposed method stems from
the Unmanned Aerial Vehicle (UAV) dynamics; thus, it prevents any unattainable
control inputs from being produced and subsequently leads to feasible
trajectories. By modeling the inter-agent relationships using a pairwise energy
function, we show that interacting robot swarms constitute a Markov Random
Field. Our algorithm builds on the Mean-Field Approximation and incorporates
the collective behavioral rules: cohesion, separation, and velocity alignment.
We follow a distributed control scheme and show that our method can control a
swarm of UAVs to a formation and velocity consensus with real-time collision
avoidance. We validate the proposed method with physical and high-fidelity
simulation experiments.Comment: To appear in the proceedings of IEEE International Conference on
Robotics and Automation (ICRA), 202
Modeling limited attention in opinion dynamics by topological interactions
This work explores models of opinion dynamics with opinion-dependent
connectivity. Our starting point is that individuals have limited capabilities
to engage in interactions with their peers. Motivated by this observation, we
propose a continuous-time opinion dynamics model such that interactions take
place with a limited number of peers: we refer to these interactions as
topological, as opposed to metric interactions that are postulated in classical
bounded-confidence models. We observe that topological interactions produce
equilibria that are very robust to perturbations.Comment: To be presented at NETGCOOP 2020; revised version including
simulation
Statistical mechanics for natural flocks of birds
Interactions among neighboring birds in a flock cause an alignment of their
flight directions. We show that the minimally structured (maximum entropy)
model consistent with these local correlations correctly predicts the
propagation of order throughout entire flocks of starlings, with no free
parameters. These models are mathematically equivalent to the Heisenberg model
of magnetism, and define an "energy" for each configuration of flight
directions in the flock. Comparing flocks of different densities, the range of
interactions that contribute to the energy involves a fixed number of
(topological) neighbors, rather than a fixed (metric) spatial range. Comparing
flocks of different sizes, the model correctly accounts for the observed scale
invariance of long ranged correlations among the fluctuations in flight
direction
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