1,973 research outputs found
State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
We study a class of swarming problems wherein particles evolve dynamically
via pairwise interaction potentials and a velocity selection mechanism. We find
that the swarming system undergoes various changes of state as a function of
the self-propulsion and interaction potential parameters. In this paper, we
utilize a procedure which, in a definitive way, connects a class of
individual-based models to their continuum formulations and determine criteria
for the validity of the latter. H-stability of the interaction potential plays
a fundamental role in determining both the validity of the continuum
approximation and the nature of the aggregation state transitions. We perform a
linear stability analysis of the continuum model and compare the results to the
simulations of the individual-based one
Towards Swarm Calculus: Urn Models of Collective Decisions and Universal Properties of Swarm Performance
Methods of general applicability are searched for in swarm intelligence with
the aim of gaining new insights about natural swarms and to develop design
methodologies for artificial swarms. An ideal solution could be a `swarm
calculus' that allows to calculate key features of swarms such as expected
swarm performance and robustness based on only a few parameters. To work
towards this ideal, one needs to find methods and models with high degrees of
generality. In this paper, we report two models that might be examples of
exceptional generality. First, an abstract model is presented that describes
swarm performance depending on swarm density based on the dichotomy between
cooperation and interference. Typical swarm experiments are given as examples
to show how the model fits to several different results. Second, we give an
abstract model of collective decision making that is inspired by urn models.
The effects of positive feedback probability, that is increasing over time in a
decision making system, are understood by the help of a parameter that controls
the feedback based on the swarm's current consensus. Several applicable
methods, such as the description as Markov process, calculation of splitting
probabilities, mean first passage times, and measurements of positive feedback,
are discussed and applications to artificial and natural swarms are reported
A Model for Collective Dynamics in Ant Raids
Ant raiding, the process of identifying and returning food to the nest or
bivouac, is a fascinating example of collective motion in nature. During such
raids ants lay pheromones to form trails for others to find a food source. In
this work a coupled PDE/ODE model is introduced to study ant dynamics and
pheromone concentration. The key idea is the introduction of two forms of ant
dynamics: foraging and returning, each governed by different environmental and
social cues. The model accounts for all aspects of the raiding cycle including
local collisional interactions, the laying of pheromone along a trail, and the
transition from one class of ants to another. Through analysis of an order
parameter measuring the orientational order in the system, the model shows
self-organization into a collective state consisting of lanes of ants moving in
opposite directions as well as the transition back to the individual state once
the food source is depleted matching prior experimental results. This indicates
that in the absence of direct communication ants naturally form an efficient
method for transporting food to the nest/bivouac. The model exhibits a
continuous kinetic phase transition in the order parameter as a function of
certain system parameters. The associated critical exponents are found,
shedding light on the behavior of the system near the transition.Comment: Preprint Version, 30 pgs., 18 figures, complete version with
supplementary movies to appear in Journal of Mathematical Biology (Springer
COORDINATION OF LEADER-FOLLOWER MULTI-AGENT SYSTEM WITH TIME-VARYING OBJECTIVE FUNCTION
This thesis aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the system in the case of complete information exchange. Using Lyapunov methods, the stability and boundedness of the agents\u27 trajectories under single order and higher order dynamics are analyzed. Illustrative numerical simulations are presented to demonstrate the validity of our results. Then, we extend these results for multi-agent systems with limited information exchange and switching communication topology. The first steps of the realization of an experimental framework have been made with the ultimate goal of verifying the simulation results in practice
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