Florian Klein Flocking Cooperation with Limited Communication in Mobile Networks

2Florian Klein 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

3Florian Klein A flock‘s movement may look erratic…

4Florian Klein … but it may hide complex structures…

5Florian Klein … and it often knows where it‘s going.

6Florian Klein 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)

7Florian Klein 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

8Florian Klein 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

9Florian Klein 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

10Florian Klein 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

11Florian Klein Spatial adjacency matrix defines influence  Simple approach:  Refined approach:

12Florian Klein Framenets express structural constraints  Agents form structural  -net  Each  -agent responsible  for maintaining a distance d   with respect to every neighbor  Different realizations possible

13Florian Klein 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

14Florian Klein Potential function defines structural energy

15Florian Klein Sigmoid function controls behavior

16Florian Klein  Protocol for nonsmooth adjacency matrices:  Protocol for smooth adjacency matrices:  with: ,  -Protocol as a Rule of Flocking

17Florian Klein 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 c d

18Florian Klein 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

19Florian Klein 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:

20Florian Klein Obstacle avoidance using  - and  -agents  Introduction of virtual agents   

21Florian Klein 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

22Florian Klein 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

23Florian Klein Potential Applications - Robotics  Autonomous vehicles  Collision avoidance  Navigation  Optimization of throughput?  Military applications  Reconnaissance  Mine sweeping  Space exploration

24Florian Klein Demonstration