Path: FormationFlying/Analysis
% Formation flying maintenance simulation.
*** Notes on Usage ***
The input data for this function can be created automatically for
different test cases, using the "FFMaintenanceTests" function.
To generate a default data structure:
>> simOptions = FFMaintenanceTests;
Once this function has run and the outputs have been created, use the
"FFMaintenancePlotter" function to plot the data.
*** Inputs ***
Supply the initial state of the reference (el0) and the initial relative
state (dEl0), define the desired relative motion (goals), the maneuver
window (window), maneuver parameters (params), the error deadband (deadband),
the noise (noise), how many orbits to simulate (nOrbits), the number of
simulation points per orbit (nSPO), the disturbance options (distOpt), the
cross-sectional area, mass, and the control method to use.
*** Estimated Absolute and Relative States (ECI) ***
The estimated absolute and relative ECI position and velocity are provided
by adding noise to the true state. This emulates the data provided by a
relative navigation unit.
*** Estimated Relative State (Hills) ***
The estimated relative position and velocity in the Hill's frame is
computed via a transformation from the estimated absolute and relative
ECI position and velocity. This computation is performed in the
"AbsRelECI2Hills" function.
*** Estimated Orbital Elements ***
The estimated mean orbital elements and mean orbital element differences
are computed from the estimated absolute and relative ECI position and
velocity. This computation is performed in the "ECI2MeanElements" function.
*** Desired Orbital Elements ***
At each step in the simulation, the initial goals are used along with the
current estimate of the mean orbital elements to compute the desired
orbital element differences.
*** Desired Relative State (Hills) ***
The desired element differences are transformed to the Hill's frame,
defining the desired relative position and velocity.
*** Relative State Error (Hills) ***
The relative position errors and relative velocity errors are computed by
comparing the desired and estimated states.
*** Deadband ***
A constant position deadband is defined in the relative Hill's frame. It
is a parallelapiped, for each side may have different lengths. If the
relative state error exceeds 75%% of the deadband "box" in any axis, a
maintenance maneuver is planned.
*** Maneuver Planning ***
The "ImpulsiveManeuver" function is called when the deadband is exceeded, and
when no other maneuver is pending. It is supplied with the current estimate
of the orbital elements, the formation goals, and a set of parameters.
It solves for a burn sequence, consisting of the in-plane and out-of-plane
delta-v's required to eliminate the error in the mean element differences,
as well as the times at which to apply the delta-v's.
*** Delta-V ***
A delta-v is introduced by applying a constant thrust over a
finite amount of time. The times at which thrust is applied is determined
by the burn sequence, which is provided by the ImpulsiveManeuver function.
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Form:
simData = FFMaintenanceSim( simOptions );
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Inputs
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simOptions (.) Data structure with the following fields:
- el0 (1,6) Initial reference orbital elements (Alfriend format) [a,theta,i,q1,q2,W]
- dEl0 (1,6) Initial orbital element differences (Alfriend format)
- goals (.) Goals data structure defining desired relative motion
- window (.) Data structure defining the desired maneuver window
- params (.) Data structure defining several maneuver parameters
- deadband (1,3) x,y,z dimensions of the position error deadband "box"
- noise (1,4) Standard deviation of noise for the following sources:
noise(1) - absolute position [m]
noise(2) - absolute velocity [m/s]
noise(3) - relative position [m]
noise(4) - relative velocity [m/s]
- nOrbits (1) Number of orbits to simulate
- nSPO (1) Number of simulation points per orbit
- distOpt (1,3) Disturbance options (flags)
(1) solar: whether to simulate with solar pressure or not
(2) drag: whether to simulate with drag or not
(3) J2: whether to simulate with J2 or not
- mass (1,2) Mass of reference and relative [kg]
- aera (1,2) Cross-sectional area of reference and relative [m^2]
- controlMethod (1) Which control method to use:
- closed form solution (1)
- linear programming (2)
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Outputs
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simData (.) Simulation output data structure with the following fields
- time (1,:) Time vector [orbits]
- fH (3,:) Applied thrust in Hills frame [kN]
- rE (3,:) True ECI position of reference
- vE (3,:) True ECI velocity of reference
- rE_est (3,:) Estimated ECI position of reference
- vE_est (3,:) Estimated ECI velocity of reference
- rH (3,:) True Hills-frame relative position
- vH (3,:) True Hills-frame relative velocity
- rH_est (3,:) Estimated Hills-frame relative position
- vH_est (3,:) Estimated Hills-frame relative velocity
- rH_des (3,:) Desired Hills-frame relative position
- vH_des (3,:) Desired Hills-frame relative velocity
- dElMean (6,:) True mean element differences
- dElMean_est (6,:) Estimated mean element differences
- dElMean_des (6,:) Desired mean element differences
- elRefMean_est (6,:) Estimated mean elements of reference
- fDiffDragH (3,:) Hills-frame differential drag force
- fDiffDragE (3,:) ECI-frame differential drag force
- fDiffSolarH (3,:) Hills-frame differential solar force
- fDiffSolarE (3,:) ECI-frame differential solar force
- fDiffJ2H (3,:) Hills-frame differential J2 force (apparent)
- fDiffJ2E (3,:) ECI-frame differential J2 force (apparent)
- deadband (1,3) Size of the position error deadband "box" (same as input)
AC: ACData/ACTConstants AerospaceUtils: AtmosphericCalculations/AtmDens2 AerospaceUtils: Coord/ECIToEF AerospaceUtils: Coord/QHills FormationFlying: Analysis/FFMaintenancePlotter FormationFlying: Analysis/FFMaintenanceTests FormationFlying: Control/ImpulsiveLPManeuver FormationFlying: Control/ImpulsiveManeuver FormationFlying: Control/InPlane FormationFlying: Control/LinOrbLQG FormationFlying: Control/OptimalInPlaneDeltaV FormationFlying: Control/OutOfPlane FormationFlying: Coord/CirclePhase FormationFlying: Coord/EllipsePhase FormationFlying: Coord/GetHillsMats FormationFlying: Coord/InitializeFormation FormationFlying: Coord/IsCircGeom FormationFlying: Coord/IsEccGeom FormationFlying: Coord/RotateState FormationFlying: DataStructures/BurnData_Structure FormationFlying: DataStructures/EccGeometry_Structure FormationFlying: DataStructures/Geometry_Structure FormationFlying: DataStructures/Maneuver_Structure FormationFlying: DataStructures/PlanningParameters_Structure FormationFlying: DataStructures/Window_Structure FormationFlying: Dynamics/DiscreteHills FormationFlying: Dynamics/HillsEqns FormationFlying: EccDynamics/FFEccDH FormationFlying: EccDynamics/FFEccDiscreteHills FormationFlying: EccDynamics/FFEccGoals FormationFlying: EccDynamics/FFEccIntConst FormationFlying: EccDynamics/FFEccLawdensEqns FormationFlying: EccDynamics/FFEccLinOrb FormationFlying: EccDynamics/FFEccProp FormationFlying: EccDynamics/FFEccRMat FormationFlying: EccDynamics/FFEccYExt EccDynamics: Derivatives/FFEccDDY EccDynamics: Derivatives/FFEccDY FormationFlying: Guidance/PCGoals FormationFlying: LP/LPCircular FormationFlying: LP/LPCircularTimeWeight FormationFlying: LP/LPEccentric FormationFlying: LP/LPEccentricGVE FormationFlying: LP/LPEccentricTimeWeight FormationFlying: Transformation/AbsRelECI2Hills FormationFlying: Transformation/DeltaElem2Hills FormationFlying: Transformation/ECI2Hills FormationFlying: Transformation/ECI2MeanElements FormationFlying: Transformation/FFEccDeltaElem2Hills FormationFlying: Transformation/FFEccGoals2Hills FormationFlying: Transformation/FFEccHills2DeltaElem FormationFlying: Transformation/GeometryCirc2Ecc FormationFlying: Transformation/GeometryEcc2Circ FormationFlying: Transformation/Goals2DeltaElem FormationFlying: Transformation/Goals2Hills FormationFlying: Transformation/Hills2DeltaElem FormationFlying: Transformation/Hills2ECI FormationFlying: Transformation/Osc2Mean FormationFlying: Utility/AccelVector2ManeuverStruct FormationFlying: Utility/FFEccTargetTrueAnom FormationFlying: Utility/ManeuverStruct2AccelVector FormationFlying: Utility/MeanAnom2TrueLat FormationFlying: Utility/NOrbVector FormationFlying: Utility/Nu2TimeDomain FormationFlying: Utility/NuDot FormationFlying: Utility/Time2NuDomain FormationFlying: Utility/TimeUntilTheta FormationFlying: Visual/CostVis FormationFlying: Visual/FFEccAnalyzeShape FormationFlying: Visual/HillsFramePlot Orbit: GravityModels/LoadGEM Orbit: GravityModels/LoadGravityModel Orbit: GravityModels/NormalizationMatrix Orbit: GravityModels/UnnormalizeGravity Orbit: OrbitCoord/Alfriend2El Orbit: OrbitCoord/El2Alfriend Orbit: OrbitCoord/OrbElemDiff Orbit: OrbitCoord/SLR Orbit: OrbitMechanics/AGravity Orbit: OrbitMechanics/GVEDynamics Orbit: RHSOrbit/LinOrb Plotting: GUI/AnimationGUI Plotting: Help/HelpSystem Plotting: Utilities/InitializeAxes SC: BasicOrbit/CP2I SC: BasicOrbit/E2M SC: BasicOrbit/E2Nu SC: BasicOrbit/El2RV SC: BasicOrbit/M2E SC: BasicOrbit/M2EApp SC: BasicOrbit/M2EEl SC: BasicOrbit/M2EHy SC: BasicOrbit/M2Nu SC: BasicOrbit/M2NuAbs SC: BasicOrbit/M2NuPb SC: BasicOrbit/Nu2E SC: BasicOrbit/Nu2M SC: BasicOrbit/Nu2MAbs SC: BasicOrbit/OrbRate SC: BasicOrbit/Period SC: BasicOrbit/RV2El SC: Disturbances/SolarF SC: Ephem/EOfE SC: Ephem/EarthRot SC: Ephem/Eclipse SC: Ephem/GMSTime SC: Ephem/MSidDay SC: Ephem/NutDelta SC: Ephem/ObOfE SC: Ephem/SunV1 SC: SCData/sCTConstants SC: SCMat/GEMT1 Common: CommonData/Constants Common: CommonData/SwooshWatermark Common: CommonData/xSplashSmall Common: ComponentModels/Box Common: ComponentModels/Cone Common: ComponentModels/Frustrum Common: Control/C2DZOH Common: Control/QCE Common: Control/QCR Common: Control/Riccati Common: Database/Constant Common: General/CellToMat Common: General/CloseFigure Common: General/DeBlankLT Common: General/DeleteCell Common: General/DispWithTitle Common: General/GetNewTag Common: General/MatToCell Common: General/StringMatch Common: General/Watermark Common: Graphics/AddView Common: Graphics/AddZoom Common: Graphics/Axis3D Common: Graphics/CameraControls Common: Graphics/DrawVertices Common: Graphics/Ellipsd Common: Graphics/Map Common: Graphics/Mesh2 Common: Graphics/NPlot Common: Graphics/NewFig Common: Graphics/Plot2D Common: Graphics/PltStyle Common: Graphics/SliderBar Common: Graphics/TitleS Common: Graphics/XLabelS Common: Graphics/YLabelS Common: Graphics/ZLabelS Common: Quaternion/Mat2Q Common: Quaternion/QForm Common: Quaternion/QTForm Common: Quaternion/U2Q Common: Time/DTSToDTA Common: Time/Date2JD Common: Time/JD2000 Common: Time/JD2T Common: Time/JDToMidnight Common: Time/T2JD Common: Transform/Altitude Common: Transform/RPhiTheta2Cart Common: Transform/RotMat Math: Analysis/PDAL Math: Analysis/SCHarm Math: Analysis/Simplex Math: Analysis/Simplex2 Math: Geometry/Perpendicular Math: Integration/RK4 Math: Integration/RK4TI Math: Linear/Cross Math: Linear/Dot Math: Linear/DupVect Math: Linear/Factorl Math: Linear/InvP Math: Linear/Mag Math: Linear/Unit Math: MathUtils/Odd Math: MathUtils/R2P5 Math: Solvers/NewtRaph Math: Trigonometry/CosD Math: Trigonometry/SinD Math: Trigonometry/UnwrapPhase Math: Trigonometry/WrapPhase
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