Atmospheric Flight Dynamics

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Artificial Potential Field Methods for
Interacting Robotic AgentsColin
McInnesDepartment of Mechanical
EngineeringUniversity of StrathclydeICSS - 25
September 2007
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Engineering requirements

• Strong interest in swarms of interacting robotic
  agents for land, air and space
• How to assemble a cluster of spacecraft for a
  distributed science mission?
• How to build robust behaviours in a swarm of
  terrestrial mobile robots?

100 agent mobile robot swarm (MIT)
30 agent spacecraft swarm (EADS Astrium)
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Approaches to autonomy

• Decompose agent workspace into a graph - search
  graph for optimal path
• Define a constrained, optimal control problem -
  how to solve in real-time?
• Use nested rules (artificial life approach) -
  how to verify resulting behaviours?

Decomposition to a searchable graph
Optimal control algorithm (calculus of variations)
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Artificial potential fields

• Map workspace onto an artificial potential field
  (agent goals obstacles)
• Follow gradient of potential field (Laplace
  equation is free of local minima)
• Replace algorithm validation with mathematical
  proof - verifiable behaviour

Artificial potential field (single agent)
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Generating simple attractors

• Swarm of N interacting agents - final state is
  an attractor in phase space
• Define a goal G and use pair-wise interaction
  potential to avoid collisions
• Agent controls provided in closed analytic form
  - real-time implementation

Map
Controls
Negative semi-definite unless
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Ring of 40 spacecraft (long range attraction,
short range repulsion)
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More complex attractors

• Swarm with pair-wise attractive (cohesion)
  repulsive (avoidance) potentials
• Pair-wise dissipation L - minimise energy E ,
  conserve angular momentum H
• Constrained minimum-energy state of swarm is a
  vortex (relative equilibrium)

Align velocity vectors
Vortex state
Constrained minimisation
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McInnes Vortex Formation in Swarms of
Interacting Particles Phys. Rev. E, Vol. 75,
No. 3, 2007
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Pattern formation

• To generate a specific configuration of agents
  create a graph of the problem
• Form adjacency matrix of the graph and use to
  generate the potential field
• Being used as the basis of control for ESA
  Darwin formation-flying mission

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Ahmed Badawy
Translational
Rotational
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(No Transcript)
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Bifurcation in swarms

• Define potential field with a 1D bifurcation
  (e.g. modified pitchfork potential)
• Manipulate swarm behaviour through a single
  parameter (easy operations)
• Extension to bifurcations of higher co-dimension
  (exploit cusp catastrophe)

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Double ring
Cluster
Single ring
Derek Bennet
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Agent internal states

• Allow agents to modify their own coupling
  parameters in the potential field
• Can now escape from local minima which traps
  swarm with fixed coupling
• Attractive potential a function of speed of
  swarm centre-of-mass (solid-liquid)

Internal agent dynamics
Long range adhesion/short range repulsion
potentials
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Solid-liquid transition
Adaptive maze solver
Mohamed Abdelwahid
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Statistical mechanics of swarms

• Large swarm of agents - possibly driven by
  thermal noise for small devices
• If interaction potential can be defined, then
  determine partition function Z
• From partition function, predict global
  properties of swarm, entropy S etc ?

Stationary solution
MEMS 'micro-robot', Duke Univ.
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Swarm with directed random walk
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Conclusions

• Growing interest in "swarm engineering" for a
  range of applications
• Potential fields provide phase space attractors
  for swarm behaviour
• Bifurcations provide a means to manipulate
  number/type of attractors
• Can statistical mechanics provide a route to
  complex, provable behaviour?