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Cooperative Control of Vehicle Formation

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

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Cooperative Control of Vehicle Formation

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  1. Cooperative Control of Vehicle Formation 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. Introduction1) • 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 1) Consensus and Cooperation in Networked Multi-Agent System, IEEE A.C. 2006 Recent Research in Cooperative Control of Multi-Vehicle Systems ,2006

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

  4. Applications1/2 • Military Systems • Formation Flight • Alignment  Reduction of a drag force • Cooperative Classification and Surveillance • 여러 agent가 함께 특정 정보를 수집, 공유 하는 것 • 여러 agent가 어떤 정보를 함께 관리하고 유지하는 것 (감시) • Cooperative Attack and Rendezvous • 특정시간, 특정위치에 모이게 하는 것 • Mixed Initiative Systems • Human operator + Autonomous vehicles  조화

  5. Applications2/2 • 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

  6. Graph Theory Definitions • 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

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

  8. Equivalent

  9. Graph TheoryPerron-Frobenius Theorem • Spectral Radius of A =

  10. Graph TheoryEigenvalues of Laplacians

  11. Kronecker Product • Definition • Properties

  12. AⓧIn=?  Collection of Dynamics In ⓧ A =?  Manipulating scalar data from N vehicles

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

  15. To representation of L

  16.  To Upper Triangular  NOTE : block diagonal

  17. Equivalence Transformation To Decompose collective dynamics T : Schur Transformation of L U is upper triangular with eigenvalues of L on diagonal

  18. Decompose into pieces

  19. Formation Stabilityver.1 Proof) Dynamics of each vehicle Eq. (13) is equivalent to eq.(11) NOTE) zero eigenvalue unobservability of absolute motion of the formation (states x)

  20. Formation Stabilityver.2via Nyquist Criterion • Assumption • Each internal vehicle is stable (inner loop) PA has no eigenvalues in RHP • Don’t use y  PC1 =zero Stabilization of Relative formation dynamics Let Transfer function of x  z for all i Nyquist Criterionfor all i

  21. Formation Stabilityver.2 via Nyquist Criterion (2)

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

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

  24. Discussion • 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

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