Swarm Coordination Under Conflict

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Swarm Coordination Under Conflict 9/11/08
N. Olgac, D. A. Sierra, P. McCullough, E. Adams.
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• Outline
• Introduction
• Goals
• Analysis of the 1P-1E Scenario
• Multi-Agent Swarm Case
• Phase 1
• Phase 2
• Simulations

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Introduction

• 2 swarms of equal numbers and their hostile
  interactions are modeled and simulated.
• The two swarms (the pursuers and the evaders) are
  governed by attraction-repulsion momenta
  structures.
• The antagonistic scenario is split into two
  phases approach and prosecution.

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• Outline
• Introduction
• Goals
• Analysis of the 1P-1E Scenario
• Multi-Agent Swarm Case
• Phase 1
• Phase 2
• Simulations

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Goals

• Suggest basic behavioral models and control
  strategies of agent-to-agent interaction
• Assess the stability and performance
  characteristics of the ensuing dynamics.

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• Outline
• Introduction
• Goals
• Analysis of the 1P-1E Scenario
• Multi-Agent Swarm Case
• Phase 1
• Phase 2
• Simulations

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Analysis of the 1P-1E Scenario Momenta structure
(from Gazi and Passino 2003)

x pursuer z evader. gpe
momentum on the pursuer due to the evader. gep
momentum on the evader due to the pursuer.
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Four possible compositions of momenta
(B) Capture at dde (D) Capture at d0 A and C
---- no capture.
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Case study 1 Momentum profile (B)
The distances at which the momentum is greater
than 2 of its peak.
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Candidate Lyapunov function for 1P-1E scenario
would yield
yp
E

P
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• Outline
• Introduction
• Goals
• Analysis of the 1P-1E Scenario
• Multi-Agent Swarm Case
• Phase 1
• Phase 2
• Simulations

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Multi-Agent Swarm Case

• Two phase approach
• Phase 1 Approach phase. The two swarms are taken
  as single agents (making the ensemble act like
  the 1P-1E case)
• Phase 2 Prosecution phase. After the the centers
  of gravity of the swarms are within a certain
  proximity of each other, the individual pursuers
  target and capture its exclusive nearest evader
  ENE.
• Capture will take place when each pursuer has
  secured its ENE

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Momenta Structure for Multiple Swarms

Condition number for the transition from Phase 1
to Phase 2.
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• Outline
• Introduction
• Goals
• Analysis of the 1P-1E Scenario
• Multi-Agent Swarm Case
• Phase 1
• Phase 2
• Simulations

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Phase 1
Swarms act like the 1P-1E. The centers of P and E
will converge
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Lyapunov Candidate for Phase 1

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• Outline
• Introduction
• Goals
• Analysis of the 1P-1E Scenario
• Multi-Agent Swarm Case
• Phase 1
• Phase 2
• Simulations

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Phase 2

The dynamics become
Artificial damping control on the pursuer
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General Lyapunov Stability for Phase 1 and 2

The general Lyapunov function that accounts for
both phases is as follows
Phase 1
Normalizing
Phase 2
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Piecewise Enforcement of Lyapunov Function

• We monitor VG numerically and compute the two
  successive values for the current and previous
  step, VG(k-1) and VG(k).
• If , then
  . Thus no damping is applied
• If occurs following a
  change in ENE assignment, we ignore this increase
  and select . We
  continue to monitor the next time step for any
  increase
• If then the control
  inserts damping to discard enough energy in the
  following step to revert this increase.

Dart
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• Outline
• Introduction
• Goals
• Analysis of the 1P-1E Scenario
• Multi-Agent Swarm Case
• Phase 1
• Phase 2
• Simulations

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Animations Momenta profile (D) is taken.
Dart 0
Dart ? 0
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Simulation Results
violations
Dart 0
Dart ? 0
Traces
Total Momenta
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Lyapunov function with Dart ? 0
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Swarm Conclusions

• A control strategy for a dynamics involving two
  swarms in conflict is presented.
• It imposes the ultimate capture of the evaders.
• Phase 1 (approach of the swarms) and Phase 2
  (prosecution of the agents) are observed in
  sequence.

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Questions?