1. SWARM COORDINATION UNDER CONFLICT
Nejat Olgac
Department of Mechanical Engineering
University of Connecticut
Eldridge S. Adams
Department of Ecology and Evolutionary Biology
We thank the ARO for funding.
We thank Mark Bacon, Rudy Cepeda, Paul McCullough, and Daniel Sierra for their participation. 1

2. Swarm conflicts in nature
Territorial battles
e.g., ants, termites, chimpanzees
Cooperative hunting of social prey
e.g., wolves/bison, tuna/herring 2

3. Redrawn from : Schmitt & Strand (1982) Cooperative hunting by yellowtail,
Seriola lalandei (Carangidae), on two species of fish prey. Copeia 1982: 3

4. Distance between agents
Force
Repulsion
Attraction
Distance between agents 4

5. Four potential functions
Between members of the same group
gPP : pursuer-to-pursuer forces or momenta
gEE : evader-to-evader forces or momenta
Between members of opposing groups
gEP : pursuer-to-evader forces or momenta
gPE : evader-to-pursuer forces or momenta
Read out g(PP); forces or momenta 5 5

6. Two-phase process Trans(PE) Phase 2: individual pursuit
Phase 1: approach
Trans(PE) ï þ ý ü î í ì + - ÷ ø ö ç è æ = d 1 2 PE
(PE) = Distance between swarm centroids 6

7. 7

8. Evolutionary computing used to optimize potential function parameters for the pursuer group, or for both groups simultaneously (game theory)
Pursuers are selected to maximize capture rate
Evaders are selected to minimize capture rate 8

9. Simple case : 2 Pursuers, 1 Evader
The evader is more agile than the pursuers (can turn more sharply)
Pursuers are attracted to the evader, and can repel or attract one another (social behavior) 9

10. Evaders are repelled by the pursuers10

11. The closest pursuer exerts a lateral force on the evader, causing the evader to turn out of the path of the pursuer 11

12. Evolving pursuers; evader behavior fixed
With social
behavior
Average catch rate
Without
social behavior
Parameters evolve to a steady state
600
Generation 12 12

13. However, if the evaders also evolve, pursuit and evasion strategies typically cycle.
Average catch rate
100
Generation 13

14. Forces acting on each pursuer:
Attraction or
repulsion by
other pursuer
Attraction to
evader
Drag
Feedback control
(PD control case)
Position vectors of pursuer and evader
Vector from pursuer to evader 14

15. Feedback control evolved jointly with the potential functions improves the capture rate
Average catch rate
Without
social behavior
With social
behavior
Generation
600
With feedback
control added
Parameters evolve to a steady state 15 15

16. Feedback control evolved jointly with the potential functions reduces the cycling of strategies during coevolution
Generation
Average catch rate
May1
100 16 16

17. CONTROL OF SWARMS UNDER CONFLICT (overview of three articles – IJC – JDSMC – IEEE SMC)
Use optimized/evolved model for capture rate
Control objectives
a) Increase capture rate,
b) Improve stability (Lyapunov)
c) Robustize against uncertainties
d) Time delays and delay scheduling
1st order dynamics: Momenta and Potential function --- (dissipative control simple damping + windowing procedures)
2nd order dynamics: PD control , Sliding Mode Control (SMC)

18. 1st order: Momenta Structure

19. Simple damping: Piecewise deployment of Lyapunov
Monitor VG --- store two successive values, VG(k-1) and VG(k).
If then no damping is applied
If discard enough energy in the following step
Undesirable chatter

20. Damping with Windowing.

21. Comparison of simple damping v. windowing
Damping Momenta for Pursuer # 2
Lyapunov function and violations for simple, 6-step, and no damping.

22. Simulation results of windowed damping.
No damping
Simple damping
Window damping

23. 2nd order: Force Structure - PD control

24. 2nd order: Force Structure - Sliding Mode Control - against uncertainties

25. Sliding Mode Control – SMC Uncertain – evader forcing + turning
Delays in feedback!! CTCR paradigm to schedule delays.

26. Thank you !!

27. Assignment Strategy
The Relative Exclusive Nearest Evader (RENE) Assignment strategy
The Exclusive Nearest Evader (ENE) Assignment strategy
Shift Centers
then ENE

28. Herding – parametric influences..