Flocking

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Flocking

• Cooperation with Limited Communication in Mobile
  Networks

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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

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A flocks movement may look erratic
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but it may hide complex structures
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and it often knows where its 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)

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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

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Boids The Three Rules of Reynolds
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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

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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

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Potential function defines structural energy
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Sigmoid function controls behavior
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?,?-Protocol as a Rule of Flocking

• Protocol for nonsmooth adjacency matrices
• Protocol for smooth adjacency matrices
• with

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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

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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

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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 obstacles border
• Actively repelling ?-agents
• ?-agents
• Help agents to resume their former course
• Placed inside obstacle, parallel to the agents
  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