florian klein fklein@upb.de flocking cooperation with limited communication in mobile networks

Florian Kleinfklein@upb.de

Flocking

Cooperation with Limited Communication in Mobile Networks

2 Florian Klein (fklein@upb.de)

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 (fklein@upb.de)

A flock‘s movement may look erratic…

4 Florian Klein (fklein@upb.de)

… but it may hide complex structures…

5 Florian Klein (fklein@upb.de)

… and it often knows where it‘s going.

6 Florian Klein (fklein@upb.de)

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 (fklein@upb.de)

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 (fklein@upb.de)

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

9 Florian Klein (fklein@upb.de)

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

10 Florian Klein (fklein@upb.de)

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

11 Florian Klein (fklein@upb.de)

Spatial adjacency matrix defines influence

Simple approach:

Refined approach:

ij

ijrqqqa iij

ij

0

/

otherwise

z

zz

qaij ]1,[

],0[

01

cos12

11

12 Florian Klein (fklein@upb.de)

Framenets express structural constraints

Agents form structural -net

Each -agent responsible for maintaining a distance d with respect to every neighbor

Different realizations possible

13 Florian Klein (fklein@upb.de)

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

14 Florian Klein (fklein@upb.de)

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 )(

15 Florian Klein (fklein@upb.de)

Sigmoid function controls behavior

-10 -5 5 10 15 20

-5

-4

-3

-2

-1

1

2)(12

ba2

ba

cz

cz

dz

zdz

16 Florian Klein (fklein@upb.de)

Protocol for nonsmooth adjacency matrices:

Protocol for smooth adjacency matrices:

with:

,-Protocol as a Rule of Flocking

iNjijl

ij

ijij

ji ppcqq

qqq

r

qq

rqqaiu

'2,, 1

dqqq ij

iNjijl

ij

iji ppc

qq

qqqu

1,,

17 Florian Klein (fklein@upb.de)

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

,,

18 Florian Klein (fklein@upb.de)

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

19 Florian Klein (fklein@upb.de)

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

20 Florian Klein (fklein@upb.de)

Obstacle avoidance using - and -agents

Introduction of virtual agents

21 Florian Klein (fklein@upb.de)

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

22 Florian Klein (fklein@upb.de)

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

23 Florian Klein (fklein@upb.de)

Potential Applications - Robotics

Autonomous vehicles Collision avoidance Navigation Optimization of throughput?

Military applications Reconnaissance Mine sweeping

Space exploration

24 Florian Klein (fklein@upb.de)

Demonstration