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Team-Triggered Coordination of Robotic Networks for Optimal Deployment Cameron Nowzari 1 , Jorge Cort es 2 , and George J. Pappas 1 Electrical and Systems Engineering 1 University of Pennsylvania Mechanical and Aerospace Engineering 2

  1. Team-Triggered Coordination of Robotic Networks for Optimal Deployment Cameron Nowzari 1 , Jorge Cort´ es 2 , and George J. Pappas 1 Electrical and Systems Engineering 1 University of Pennsylvania Mechanical and Aerospace Engineering 2 University of California, San Diego American Control Conference Chicago, Illinois July 3, 2015

  2. -Coordination of robotic networks- Each individual senses immediate environment communicates with others processes information gathered takes action in response Multiple agents provide inherent robustness adaptive behavior enable tasks beyond individuals’ capabilities C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 2 / 22

  3. -Optimal deployment- of robotic sensor networks Objective: optimal task allocation and space partitioning optimal placement and tuning of sensors Why? servicing resource allocation environmental monitoring data collection force protection surveillance search and rescue C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 3 / 22

  4. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  5. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T Eve, where are you?! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  6. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T Eve, where are you?! I’m here! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  7. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T Now where are you? C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  8. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T Now where are you? Still here! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  9. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T How about now? C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  10. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T How about now? Still here... C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  11. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T And now?? C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  12. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T And now?? Leave me alone. C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  13. Real-time implementations of -optimal deployment- Time-triggered (periodic) coordination Agents take actions at some fixed period T And now?? Leave me alone. Simple , but Wasteful C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 4 / 22

  14. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  15. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information Eve, where are you?! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  16. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information Eve, where are you?! I’m here! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  17. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information (She probably hasn’t moved too far...) C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  18. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information (She probably hasn’t moved too far...) C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  19. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information (I’ll ask her again in a few seconds) C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  20. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information (I’ll ask her again in a few seconds) C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  21. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information Now where are you? C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  22. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information Now where are you? Still here! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  23. Real-time implementations of -optimal deployment- Self-triggered coordination Agents decide when to take actions based on available information Now where are you? Still here! Actions taken only when necessary , but potentially still conservative! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 5 / 22

  24. Real-time implementations of -optimal deployment- -Team-triggered coordination- Cooperative agents share more information with each other C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 6 / 22

  25. Real-time implementations of -optimal deployment- -Team-triggered coordination- Cooperative agents share more information with each other Eve, where are you?! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 6 / 22

  26. Real-time implementations of -optimal deployment- -Team-triggered coordination- Cooperative agents share more information with each other Eve, where are you?! I’m here! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 6 / 22

  27. Real-time implementations of -optimal deployment- -Team-triggered coordination- Cooperative agents share more information with each other But I’m going this way! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 6 / 22

  28. Real-time implementations of -optimal deployment- -Team-triggered coordination- Cooperative agents share more information with each other C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 6 / 22

  29. Real-time implementations of -optimal deployment- -Team-triggered coordination- Cooperative agents share more information with each other C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 6 / 22

  30. Real-time implementations of -optimal deployment- -Team-triggered coordination- Cooperative agents share more information with each other C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 6 / 22

  31. Real-time implementations of -optimal deployment- -Team-triggered coordination- Cooperative agents share more information with each other Higher quality information allows for less communication! C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 6 / 22

  32. -Team-triggered- control Objective: Combine best properties of event- and self-triggered strategies into a unified, implementable approach How? C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 7 / 22

  33. -Team-triggered- control Objective: Combine best properties of event- and self-triggered strategies into a unified, implementable approach How? Agents make promises to neighbors about their future states Agents warn each other when promises need to be broken C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 7 / 22

  34. Outline 1 Motivation 2 Problem Formulation aggregate objective optimization Voronoi partition 3 Triggered Deployment Algorithms self-triggered deployment algorithm team-triggered deployment algorithm simulations 4 Conclusions C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 8 / 22

  35. Expected-value multicenter function Objective: Given sensors/nodes/robots/sites ( p 1 , . . . , p n ) moving in environment S achieve optimal coverage φ : R d → R ≥ 0 density agent performance decreases with distance � � i ∈{ 1 ,...,n } � q − p i � 2 minimize H ( p 1 , . . . , p n ) = E φ min C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 9 / 22

  36. Voronoi partitions Let ( p 1 , . . . , p n ) ∈ S n denote the positions of n points The Voronoi partition V ( P ) = { V 1 , . . . , V n } generated by ( p 1 , . . . , p n ) V i = { q ∈ S | � q − p i � ≤ � q − p j � , ∀ j � = i } = S ∩ j HP ( p i , p j ) where HP ( p i , p j ) is half plane ( p i , p j ) 3 generators 5 generators 50 generators C. Nowzari (Penn) Team-triggered deployment Fri. July 3rd 10 / 22

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