florian klein [email protected] flocking cooperation with limited communication in mobile networks
TRANSCRIPT
2 Florian Klein ([email protected])
Overview
Introduction – what is flocking? Boids - Reynolds‘ three rules Mathematical Analysis Flocks as nets Coordination as minimization of structural
energy Protocols for flocking and obstacle avoidance
Potential Applications Practical Demonstration
3 Florian Klein ([email protected])
A flock‘s movement may look erratic…
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… but it may hide complex structures…
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… and it often knows where it‘s going.
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Introduction - Flocking
Natural phenomenon Flocks of birds Schools of fish Swarms of insects
Coordination based on local information Collision avoidance Joint navigation
Complex interdependencies (chaos theory)
7 Florian Klein ([email protected])
Boids – pioneers in the field of artificial flocking Developed by Craig Reynolds in 1986
Used for animation of birds‘ flight Stanley and Stella in: Breaking the Ice Big screen debut in „Batman Returns“
Became poster child of artificial life research
Simple rules lead to unpredictable behavior
8 Florian Klein ([email protected])
Boids – The Three Rules of Reynolds
Alignment Copy average alignment of
flockmates
Cohesion Steer towards center of
mass of flockmates
Separation Steer away from center of
mass of flockmates getting to close
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Boids – auxiliary rules
Local Neighborhood defined by conical shape
Versions used for animation tend to employ Preemptive obstacle avoidance Low priority targets as waypoints
No formal model published
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Saber / Murray - A mathematical framework
Graph theoretical approach Agents as nodes with point-mass dynamics Interaction between agents as edges
Agents interact with their immediate neighbors Defined by spatial adjacency matrix
Flocks as nets with specific configurations Strongly connected for spherical neighborhood Weakly connected for conic neighborhood
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Spatial adjacency matrix defines influence
Simple approach:
Refined approach:
ij
ijrqqqa iij
ij
0
/
otherwise
z
zz
qaij ]1,[
],0[
01
cos12
11
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Framenets express structural constraints
Agents form structural -net
Each -agent responsible for maintaining a distance d with respect to every neighbor
Different realizations possible
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Flocking as an optimization problem
Analogy to molecules: Stable state is energetically optimal
System state measured by Hamiltonian Molecule: Kinetic energy + positional energy Flock: Kinetic energy (p) + structural energy
C
H
CC
C
CC
H
H
H
H
H
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Potential function defines structural energy
-10 -5 5 10 15 20
5
10
15
20
z
bacczz
21)(1
2
ba 22
iNj
ijij dqqqaqV )(
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Sigmoid function controls behavior
-10 -5 5 10 15 20
-5
-4
-3
-2
-1
1
2)(12
ba2
ba
cz
cz
dz
zdz
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Protocol for nonsmooth adjacency matrices:
Protocol for smooth adjacency matrices:
with:
,-Protocol as a Rule of Flocking
iNjijl
ij
ijij
ji ppcqq
qqq
r
rqqaiu
'2,, 1
dqqq ij
iNjijl
ij
iji ppc
qqqu
1,,
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Using the ,-Protocol
Stress indicates deviation from energy optimum
Control input is yielded by
Overall impetus is sum of individual adjustments For every neighbor:
Correct position q to reduce stress Converge on neighbors velocity p, using dampening
factor cd
ij
ij
ij
ji qqqq
dqqqs
,,
ijdijNj
jii ppcqqqsu
,,
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The ,-Protocol and the rules of Reynold
Stress weights Transmit neighbors‘ vote on desired course Emulate first and third rule of Reynold Additionally covers special case when negative
and positive votes cancel out
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Quality of the ,-Protocol
Larger networks do not necessarily converge Especially when subjected to external influences
Generally achieves a rather close approximization of framework
Normalized Defect Factor:
2
)(
1))(( qVwqV
drqG
qG
nn
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Obstacle avoidance using - and -agents
Introduction of virtual agents
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Obstacle avoidance using - and -Agents
- agents Help agents to avoid obstacles
Placed on the obstacle‘s border Actively repelling -agents
-agents Help agents to resume their former course
Placed inside obstacle, parallel to the agent‘s velocity
Attracting -agents
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Applicability
Framework for flocking Formalizes flocking Enables goal-directed tweaking Allows verification
Obstacle avoidance still pending Split, rejoin and squeeze maneuvers not fully
understood Formal model yet incomplete
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Potential Applications - Robotics
Autonomous vehicles Collision avoidance Navigation Optimization of throughput?
Military applications Reconnaissance Mine sweeping
Space exploration
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Demonstration