Astrogator Automation: Inside

1
Astrogator AutomationInside Out
2
Agenda

• Background
• Automation Inside Astrogator
• Automation Outside Astrogator
• Full Analysis Example
• Conclusions
• Questions

3
What is Astrogator?

• Missions analysis and operations often include
  orbit maneuvers
• Fuel use
• Maneuver strategies
• Station-keeping
• Need to calculate initial conditions to achieve
  desired orbits
• Maneuver planning
• Reconstruction
• Calibration

4
Inside Automation

• The Targeter and Plugins

5
Targeting

• Mission design
• Operational orbit selection
• Launch and transfer
• Operational support
• Orbit maintenance
• Performance assessment
• Determine control parameters that meet specific
  constraints

6
Formulation

• Linearization of a Taylor series expansion about
  a known state
• Singular Value Decomposition of sensitivity
  matrix to calculate inverse
• Have to solve for scaled parameters in cases of
  an ill-conditioned matrix
• Iterate on equations to converge to solution

7
Derivative Computation

• Finite differencing
• Forward
• Backward
• Central
• Signed

8
Solution Types

• Over determined (more constraints than control
  parameters) least squares
• Under determined (more control parameters than
  constraints) minimum norm
• Exactly determined (same number of controls and
  constraints) unique solution

There is no notion of optimality
9
Iteration And Convergence

• Require mechanism to end our search
• Give up (maximum iterations)
• Equality constraints are met (to within
  tolerance)
• Control parameter solution is stationary (to
  within tolerance)

10
A Simple Sample Problem

• Initial orbit
• Circular
• Equatorial
• 90 minute period
• Determine the velocity increment required to
  achieve a semimajor axis of 50,000 km
• Initial guess
• DV 2000 m/sec

11
Step Control

• Setup
• Forward differencing 0.1 km/sec
• Step control 0.2 km/sec
• Results
• 12 Iterations
• 24 function evaluations

12
Central Differencing

• Setup
• Central differencing 0.1 km/sec
• Step control 0.2 km/sec
• Results
• 8 Iterations
• 24 function evaluations

13
Line Search

• Setup
• Forward differencing 0.1 km/sec
• Step control None
• Results
• 3 Iterations
• 33 function evaluations

14
Change Of Variables

• Setup
• Forward differencing 0.1 km/sec
• Step control None
• Results
• 4 Iterations
• 8 function evaluations

15
Multi-Sequence Automation

• A means of configuring control parameters in
  different combinations over same trajectory
• Allows both independent analysis and sequential
  analysis

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Multi-sequence Automation

• Required for certain maneuvers
• Multiple levels of control over same path
• Allows collection of maneuvers into common block
• Do multiple sequential burns within same sequence
• Trial and error target selection
• Experiment but retain various control/constraint
  permutations

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Configurable Parameters

• Control Parameters
• Active
• Perturbation controls
• Scaling mechanism
• Equality Constraints
• Active
• Tolerance
• Scaling

18
Configurable Parameters

• Convergence Criteria
• Max Number of Iterations
• Stop at equality or equality and static
  control updates
• Step Control
• Line search mechanism
• Homotopy
• Derivative method
• Run logging

19
Multi-Sequence Automation

• Lunar Example
• Determine profile to get to target lunar orbit
• Sequence of controls
• Target on DRa, DDec to synchronize controlling
  launch time and mid-course burn time
• Target on B-plane to gets close to final orbit
  controlling mid-course burn magnitude in addition
  to above
• Target on Lunar Altitude Inclination for final
  orbit controlling same as above

20
Auxiliary Sequence Automation

• Repeatable events
• Subroutine-like capability
• Queued off specific orbital event
• Apoapsis
• Epoch
• Custom stopping condition
• Activated at given stopping condition

21
Constraint parameters

• Applied to stopping condition
• Equivalent to AND logic
• If Duration Constraints
• Do STOP
• Else if Apoapsis Constraints
• Do Coast-Burn-Coast-Burn
• Else if MaxPropTime !MinPropTime
• Do STOP
• Else
• Next Step
• End If

22
Example-NGST Halos

• Given Initial orbit insertion parameters
• Determine Nominal ten halo orbit maneuver
  sequences into future

23
Manual Way

• For each orbit, add a new target sequence
• Useful if each halo a requires different sequence
• Negatives
• Redundant segments
• Introduction of errors
• Changes difficult

24
Auxiliary Sequence Way

• Maneuver Sequence Encapsulated in Auxiliary
  Sequence
• Positives
• Remove redundancy
• Central point for changes
• Negatives
• Difficult to tailor individual maneuvers

25
Plug-in Basics

• Extensible Architecture in STK
• Astrogator Plug-in points
• Propagator
• Custom engine models
• Calc objects
• Inline functions
• Languages
• Matlab
• Matlab DLLs
• Perl
• VBS

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Propagator Plugins

• Acceleration computation
• Two-body motion plus perturbations
• Indirect Plugin Influence
• Thrust
• Drag
• Solar
• Plugin

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Propagator Update Values

• Between integration steps adjust satellite
  properties
• Drag Area
• SRP Area
• Dry Mass
• Fuel Mass
• CD
• CR

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Propagator Force Model Eval Plugin

• Similar to Propagator update plugins
• Evaluated at each propagation sampling
  stepseveral times more than update plugin
• Has more returns
• Atmospheric Density
• Solar Intensity
• Acceleration (in CBI, CBF, CbiVNC, CbiLVLH)

29
Engine Modeling

• At each propagation evalution
• Thrust
• Isp
• Mass flow rate

30
Calculation Objects

• Provides full flexibility in types of
  calculations available in Astrogator
• Calc Objects used in
• Stopping Conditions
• Stopping Constraints
• Plug-in inputs
• STK Reports/Graphs
• Direct plugin inline versions

31
Inline Example

• In-house DT function
• Requires geodetic position and current time
• Needed for
• Stopping condition
• Solar panel efficiency for ion engine operation

32
AerobrakingAeroAstros SPORT

• Problem
• High Cost of Small Launch Vehicles Limits Market
• Solution Small Payload Orbit Transfer Vehicle
  (SPORT)
• Launch as Auxiliary Payload on Large Launch
  Vehicle
• Cheapest and Most Frequent Excess Capacity on GTO
  Launches
• Aerobrake Down to More Desirable LEO Destination
• Aerobraking Enables 90 Propellant Reduction
• Other Aerobraking Applications
• Enter Orbit Around Other Planets (Venus, Mars)
• Aero-Assisted Swing-by
• Return from Libration Point or Helio for
  Maintenance

33
AeroAstro Atmosphere Modeling

• STK/Astrogator usage
• Constrained Stopping Conditions
• Multiply-Nested Control Sequences with Internal
  Targeters
• Matlab Plug-In-Script for Propagator
• Drag Coefficient Varies Depending on Aerodynamic
  Flow Regime Free Molecular ? Transition ?
  Continuum
• Plug-In-Script Computes Flow Regime Based on STK
  Atmospheric Model ? Continuously Adjusts Drag
  Coefficient Based on NASA LaRC DSMC Results
• Also Extract Atmospheric Properties for
  Aeroheating Analysis

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Internal Automation Summary

• Targeter provides direct automation for root
  finding solutions
• Multi-Profile analysis provides flexibility in
  problem solving
• Auxiliary sequence provides subroutine-like
  automation
• Plug-ins open up internal system to user
  customizable functions and system integration

35
Outside Automation

• Connect Attributes

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Connect

• Basics
• Commands
• Pushing data in
• Getting data out
• Invoking action

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Connect Basics

• Text message commands
• Text return data
• ltCommandgt ltObjectgt ltDatagt
• Connections
• TCP/IP
• MS COM Layer

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Pushing Astrogator data into STK

• ASTROGATOR ltSatellite Object Pathgt ltactiongt
  ltAstrogator Object Pathgt ltValuegt ltUnitsgt
• Examples
• Set Propagate segment stopping conditions
• Set reference coordinate system
• Set type and direction

39
Getting Astrogator data out of STK

• ASTROGATOR_RM ltSatellite Object Pathgt ltactiongt
  ltAstrogator Object Pathgt
• Examples
• Pull Inclination at end of propagation segment
• Pull final burn direction and magnitude at end of
  targeting
• Pull custom computation at end of finite maneuver

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Attributes

• Description
• Methodology
• Examples

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What are Attributes ?

• A generic means of accessing data throughout STK
  products (STK, Astrogator, STK/OD,NTK)
• Means of accessing data symbolically.
• Symbolically means associating a piece of data
  with a name.
• So,you could say things like
• gimme Scenario1.hubble.Swath.Type
• And youd actually get it !

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Attribute Example 1

• MainSEQUENCE.SegmentList.TargetHOI.Profiles

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Attribute Example 2

• MainSEQUENCE.SegmentList.TargetSk1.SegmentList.To1
  stCross.Propagator

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Pushing Data

• General usage for setting parameters throughout
  MCS Sequences
• Build List of values
• SegmentList at various levels
• MainSEQUENCE
• Target_Sequence
• Stopping conditions
• Apoapsis
• Duration
• Constraints
• Altitude
• Change direct values
• Stopping condition Trip Values
• Duration 200 sec
• Constraint tolerances
• Altitude gt 50 km

46
Targeter Control

• AddMCSSegmentControl
• SetMCSControlValue
• RemoveMCSSegmentControl
• ClearMCSSegmentControls

47
Setting up targeting

• Use SetValue to define segment results
• Segment results become targeting constraints
• Set desired values, tolerances et cetera with
  SetValue
• Activate necessary targeting parameters for
  constraint with SetMCSConstraintValue

48
Extracting DataGetValue

• Generic command for extracting data throughout
  the MCS Sequences
• Pull list of values
• Segments in SegmentList
• Stopping conditions
• Pull groups of values
• Initial state in Cartesian coordinates
• Final thrust vector
• Pull individual values
• Final state inclination
• Targeter control status

49
Extracting DataSegment Results

• GetMCSSegmentResults return results at end of
  segment
• ASTROGATOR_RM /Satellite/Satellite1
  GetMCSSegmentResults MainSEQUENCE.SegmentList.Targ
  et_Sequence.SegmentList.Impulsive_Maneuver
• GetValue gives option of pulling results at
  beginning and end of segment
• ASTROGATOR_RM /Satellite/Satellite1 GETVALUE
  MainSEQUENCE.SegmentList.Target_Sequence.SegmentLi
  st.Impulsive_Maneuver.InitialResultValues
• ASTROGATOR_RM /Satellite/Satellite1 GETVALUE
  MainSEQUENCE.SegmentList.Target_Sequence.SegmentLi
  st.Impulsive_Maneuver.FinalResultValues

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STK Settings

• Setup satellite for Astrogator propagator
• SetPropagator ltObjectPathgt ltPathgt
• Propagating
• Propagate ltObjectPathgt Time1 Time2
• Time is ignored but required for Connect syntax
  reasons

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Integration

• Jaqar Swing-by Calculator
• MaNE
• Phoenix Integration Systems
• Custom Apps

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Outside Automation Summary

• Attributes provides flexible mechanism for
  accessing low level data symbolically
• Connect used as driver interface for
  reading/writing Astrogator Attributes
• Allows full configuration of satellite parameters

53
Full-up Example
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Problem Statement

• Given New Horizons mission profile
• Determine burn configuration with full force
  modeling
• Determine optimum burn configuration
• Determine burn profile sensitivity

55
Solution-Initial Design

• Jaqar Swing-by Calculator (SBC) designs initial
  New Horizon orbit
• SBC exports solution as Astrogator satellite
• Astrogator satellite loaded and targeted for
  final solution

56
Maneuver Modeling

• Convert all burns from impulsive to finite
• Burn centering
• Initial values from impulsive maneuver case
• Conversion step by step
• Set defaults

57
Burn Optimization

• Determine minimum fuel usage requirement
• Matlab parametric optimization
• Vary time of each burn
• Re-target Astrogator sequence
• Pull final fuel mass to determine fuel used

58
Determine Stability

• Script similar to burn optimization but using
  Monte Carlo analysis
• Vary each parameter and attempt to retarget in
  future maneuvers
• Initial state parameters
• Engine out during burns
• Bad pointing during burn
• Engine efficiency issues

59
Conclusions

• Automation in Astrogator provides convenient
  mechanism for solving common engineering problems
• Automation allows for full range of analyses of
  orbit design in all regimes
• Automation allows for integration with existing
  tools or vendor specific functions

60
Questions?
61
Homotopy Continuation

• Setup
• Forward differencing 0.1 km/sec
• Step control 0.2 km/sec
• Results
• 17 Iterations (98)
• 34 function evaluations

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Connect Basics

• General command structure
• ltCommandgt ltObjectPathgt ltCommand Datagt
• Command is a one word key
• New
• GetReport
• ObjectPath is string naming an object
• /Satellite/Satellite1
• Command Data is any information necessary to
  execute command
• Object type and name for New
• Report style name and interval for GetReport

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SetValue Examples

• Setting stopping condition value
• ASTROGATOR /Satellite/Satellite1 SETVALUE
  MainSEQUENCE.SegmentList.Propagate.StoppingConditi
  ons.Duration.TripValue 4 hours
• Setting Initial state sma
• ASTROGATOR /Satellite/Satellite1 SETVALUE
  MainSEQUENCE.SegmentList.Initial_State.InitialStat
  e.Keplerian.sma 8000 km

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Pushing DataSetMCSControlValue

• ASTROGATOR ltSatellite Object Pathgt
  SetMCSControlValue ltAstrogator Object Pathgt
  ltOwning Segmentgt ltControl Namegt Active ltValuegt
• Example
• ASTROGATOR /Satellite/Satellite1
  SetMCSControlValue MainSEQUENCE.SegmentList.Target
  _Sequence.Profiles.profile1 Impulsive_Maneuver
  Cartesian.X Active True
• Targeter Control commands
• AddMCSSegmentControl
• RemoveMCSSegmentControl
• ClearMCSSegmentControls

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Pushing DataAddMCSSegmentControl

• ASTROGATOR ltSatellite Object Pathgt
  AddMCSSegmentControl ltAstrogator Object Pathgt
  ltCalculation Objectgt
• Example
• ASTROGATOR /Satellite/Satellite1
  AddMCSSegmentControl MainSEQUENCE.SegmentList.Targ
  et_Sequence.SegmentList.Impulsive_Maneuver
  Cartesian.Y Active True

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GetValue Examples

• Get SegmentList
• ASTROGATOR_RM /Satellite/Satellite1 GetValue
  MainSEQUENCE.SegmentList
• Get Initial state in Keplerian Elements
• ASTROGATOR_RM /Satellite/Satellite1 GETVALUE
  MainSEQUENCE.SegmentList.Initial_State.InitialStat
  e.Keplerian
• Get X-component of initial position in Cartesian
• ASTROGATOR_RM /Satellite/Satellite1 GETVALUE
  MainSEQUENCE.SegmentList.Initial_State.InitialStat
  e.Cartesian.X

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Extracting DataGetMCSConstraintValue

• Pull results from targeting procedure
• ASTROGATOR_RM ltSatellite Object Pathgt
  GetMCSConstraintValue ltAstrogator Profile Pathgt
  ltOwning Segmentgt ltControl Namegt ltAttributegt
• ASTROGATOR_RM /Satellite/Satellite1
  GetMCSConstraintValue MainSEQUENCE.SegmentList.Tar
  get_Sequence.Profiles.Differential_Corrector
  Impulsive_Maneuver Semimajor_Axis Achieved