1. Sanghoon Kim CDSL 2007-12-26 J. Alex Fax, Richard M. Murry, Information Flow and Cooperative Control of Vehicle Formations, IEEE A.C. 2004

2. Cooperation Giving consent to providing one’s state and following a common protocol that serves the group objective Consensus Means to reach an agreement regarding a certain quantity of interest that depends on the states of all agents Decentralized Control Depends on only neighbors of each vehicle 2 1) Consensus and Cooperation in Networked Multi-Agent System, IEEE A.C. 2006 Recent Research in Cooperative Control of Multi-Vehicle Systems,2006

3. 3 Dynamics of i-th Vehicle Task in terms of Cost Function Additively Decoupled Task (or just Decoupled) Decentralized Control  Cannot decoupled  Cooperative Task Depends on neighbors Role of vehicle

4. Military Systems Formation Flight Alignment  Reduction of a drag force Cooperative Classification and Surveillance 여러 agent 가 함께 특정 정보를 수집, 공유 하는 것 여러 agent 가 어떤 정보를 함께 관리하고 유지하는 것 ( 감시 ) Cooperative Attack and Rendezvous 특정시간, 특정위치에 모이게 하는 것 Mixed Initiative Systems Human operator + Autonomous vehicles  조화 4

5. Mobile Sensor Networks Environmental Sampling Distributed Aperture Observing Ex) Collective of microsatellites  Virtual big single satellite Transportation Systems Intelligent Highways Safety, Density ↑ Air traffic control Collision warning, Congestion Control  Free Flight 5

6. Directed graph G Vertex / Arc Undirected In(Out)-degree Complete Path / Access Strongly Connected Disconnected Communication / Component Initial / Final vertex N-cycle / k-periodic Acycle / Primitive 6

7. Adjacency matrix Normalized adjacency matrix Laplacian matrix Stochastic matrix Irreducible / Reducible Matrix Reducible if permutation P exists such that Positive (Nonnegative) Matrix 7

8. 8/23 Equivalent

9. Spectral Radius of A = 9

10. 10

11. 11/24

12. Definition Properties 12

13. 13/23 A ⓧ I n =?  Collection of Dynamics I n ⓧ A=?  Manipulating scalar data from N vehicles

14. Stabilization with constant references Leader Follower approach Simple Reference by the leader Formation stability  individual vehicles’ stability Poor disturbance rejection Heavily on the leader / over-reliance on a single vehicle Virtual Leader approach Good disturbance rejection High communication and computation  Communication Topology Robustness to changes in a topology 14/23

15. 15 Dynamics of i-th Vehicle Decentralized Controller All Collective System  Internal state measurement ↑ External relative state measurement  V is internal state  Consensus Algorithm Set of vehicles which vehicle i can sense

16. 16  To representation of L

17. 17/23

18. 18

19. 19  NOTE : block diagonal  To Upper Triangular

20. 20 U is upper triangular with eigenvalues of L on diagonal T : Schur Transformation of L

21. 21/23

22. 22

23. 23/23

24. 24 Proof) Dynamics of each vehicle Eq. (13) is equivalent to eq.(11) NOTE) zero eigenvalue  unobservability of absolute motion of the formation (states x)

25. Assumption Each internal vehicle is stable (inner loop)  P A has no eigenvalues in RHP Don’t use y  P C1 =zero  Stabilization of Relative formation dynamics 25 Transfer function of x  z for all i Nyquist Criterion for all i Let

26. 26

27. 27 Complete  Acycle  (Directed) Leader-Follower  Single Directed Cycle Nonzero Perron Disk Magnitude of nonzero eigenvalues Bound on Real part of eigenvalues Periodicity  BAD

28. 28 K(s) = More arc  not better performance ∵ Periodicity  Bad

29. Measures of Graph Periodicity to quantify stability Weighted Graph Latency on Network Vehicles with Nonlinear Dynamics Next Coming Seminar Information Flows Robustness to Graph Topology Analogous to Disturbance Observer 29