Download - Cooperative Control of Vehicle Formation
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Cooperative Control of Vehicle FormationSanghoon Kim CDSL2007-12-26
J. Alex Fax, Richard M. Murry, Information Flow and Cooperative Control of Vehicle Formations, IEEE A.C. 20041Introduction1)CooperationGiving consent to providing ones state and following a common protocol that serves the group objectiveConsensusMeans to reach an agreement regarding a certain quantity of interest that depends on the states of all agentsDecentralized ControlDepends on only neighbors of each vehicle21) Consensus and Cooperation in Networked Multi-Agent System, IEEE A.C. 2006 Recent Research in Cooperative Control of Multi-Vehicle Systems ,2006IntroductionDecentralized Cooperative Control3
Dynamics of i-th Vehicle Task in terms of Cost Function Additively Decoupled Task (or just Decoupled) Decentralized Control Cannot decoupled Cooperative TaskDepends on neighborsRole of vehicleApplications1/2 Military SystemsFormation Flight Alignment Reduction of a drag forceCooperative Classification and Surveillance agent , agent ()Cooperative Attack and Rendezvous, Mixed Initiative SystemsHuman operator + Autonomous vehicles 4Applications2/2Mobile Sensor NetworksEnvironmental SamplingDistributed Aperture ObservingEx) Collective of microsatellites Virtual big single satelliteTransportation SystemsIntelligent HighwaysSafety , Density Air traffic controlCollision warning, Congestion Control Free Flight
5Graph Theory Definitions Directed graph G Vertex / ArcUndirectedIn(Out)-degreeCompletePath / AccessStrongly ConnectedDisconnectedCommunication / ComponentInitial / Final vertexN-cycle / k-periodic Acycle / Primitive
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Adjacency matrixNormalized adjacency matrixLaplacian matrixStochastic matrix
Irreducible / Reducible MatrixReducible if permutation P exists such that
Positive (Nonnegative) MatrixGraph TheoryLaplacian Matrix7
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EquivalentGraph TheoryPerron-Frobenius TheoremSpectral Radius of A =
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Graph TheoryEigenvalues of Laplacians10
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Kronecker ProductDefinition
Properties12
13/23 AIn =? Collection of Dynamics In A=? Manipulating scalar data from N vehicles
Formation ControlStabilization with constant referencesLeader Follower approachSimple Reference by the leaderFormation stability individual vehicles stabilityPoor disturbance rejectionHeavily on the leader / over-reliance on a single vehicleVirtual Leader approachGood disturbance rejectionHigh communication and computation Communication Topology Robustness to changes in a topology
14/23Formation Equations15
Dynamics of i-th VehicleDecentralized ControllerAll Collective System Internal state measurement External relative state measurement V is internal state Consensus Algorithm
Set of vehicles which vehicle i can sense16
To representation of L17/23
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NOTE : block diagonal To Upper TriangularEquivalence Transformation To Decompose collective dynamics20
U is upper triangular with eigenvalues of L on diagonal T : Schur Transformation of L
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Decompose into pieces22
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Formation Stabilityver.124
Proof) Dynamics of each vehicle Eq. (13) is equivalent to eq.(11)NOTE) zero eigenvalue unobservability of absolute motion of the formation (states x)Formation Stabilityver.2via Nyquist CriterionAssumptionEach internal vehicle is stable (inner loop) PA has no eigenvalues in RHPDont use y PC1 =zero Stabilization of Relative formation dynamics25
Transfer function of x z for all iNyquist Criterionfor all i
Let
Formation Stabilityver.2 via Nyquist Criterion (2)26
Evaluating Formations via Laplacian Eigenvalues27
Complete
Acycle (Directed)Leader-Follower
Single Directed CycleNonzero
Nonzero
Perron DiskMagnitude of nonzero eigenvaluesBound on Real part of eigenvaluesPeriodicityBADExample28
K(s) = More arc not better performance Periodicity Bad 28DiscussionMeasures of Graph Periodicity to quantify stabilityWeighted GraphLatency on NetworkVehicles with Nonlinear Dynamics
Next Coming SeminarInformation FlowsRobustness to Graph TopologyAnalogous to Disturbance Observer
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