Under The Hood: Maneuver Planning With Astrogator

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Under The HoodManeuver Planning With Astrogator

• Matt Berry
• Kevin Ring

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Agenda

• Introduction to Astrogator
• The components of Astrogator
• Segments
• Stopping Conditions
• Engine Models
• Targeter Profiles
• Examples

• What are they?
• What do they do?
• How do they work?

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Whats Astrogator?

• Astrogator is STKs mission planning module
• Used for
• Trajectory design
• Maneuver planning
• Station keeping
• Launch window analysis
• Fuel use studies
• Derived from code used by NASA contractors
• Embedded into STK

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Astrogator in STK

• Astrogator is one of 11 satellite propagators
• Propagator generates ephemeris
• Astrogator satellite acts like other STK
  satellites
• Can run STK reports (including Access)
• Can animate in 3D and 2D windows
• Generates ephemeris by running Mission Control
  Sequence (MCS)
• Components used in MCS configured in Astrogator
  Browser

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Astrogator
Astrogator
Mission Control Sequence Configuration
Ephemeris
Astrogator
Runs Mission Control Sequence
Other Mission Data
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The Mission Control Sequence

• A series of segments that define the problem
• A graphical programming language
• Two types of segments
• Segments that produce ephemeris
• Segments that change the run flow of the MCS
• Segments pass their final state as the initial
  state to the next segment
• Some segments create their own initial state

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The Mission Control Sequence
State
Segment 1
Ephemeris
State
Ephemeris
Segment 2
State
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Segments that produce ephemeris

• Initial State specifies initial conditions
• Launch simulates launching
• Propagate integrate numerically until some
  event
• Maneuver impulsive or finite
• Follow follows leader vehicle until some event
• Update updates spacecraft parameters

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Initial state segment

• Specify spacecraft state at some epoch
• Choose any coordinate system
• Enter in Cartesian, Keplerian, etc.
• Enter spacecraft properties mass, fuel, etc.

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Launch segment

• Specify launch and burnout location
• Specify time of flight
• Use any central body
• Connects launch and burnout points with an
  ellipse
• Creates its own initial state

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Propagate segment

• Numerically integrates using chosen propagator
• Propagator can be configured in Astrogator
  browser
• Propagation continues until stopping conditions
  are met

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Stopping conditions

• Define events on which to stop a segment
• Stop when some calc object reaches a desired
  value
• A calc object is any calculated value, such as an
  orbital element
• Calc objects can be user-defined

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Stopping conditions

• Can also specify constraints
• Only stop if another calc object is , lt, gt, some
  value
• Determines if exact point stopping condition is
  met, then checks if constraints are satisfied
• Multiple constraints behave as logical And
• Segments can have multiple stopping conditions
• Stops when the first one is met
• Behaves as a logical Or

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Event detection

• Exact time of event found with Regula-Falsi
• f(t) found by integrating to time t

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Propagate segment pseudo-code

• while (keepGoing)
• take integration step
• if (stopping condition tripped over step)
• find exact point of stopping condition
• if (constraints met at that point)
• keepGoing false
• end if
• end if
• end while

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Maneuver segment

• Maneuver segment owns two distinct segments
• Finite maneuver
• Impulsive maneuver
• Combo box controls which one is run
• Finite maneuver created from impulsive maneuver
  with Seed button

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Impulsive maneuver

• Adds delta-V to the current state
• Can specify magnitude and direction of delta-V
• Computes estimated burn duration and fuel usage,
  based on chosen engine
• Can configure engine model in Astrogator browser

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Impulsive maneuver
State
Impulsive Maneuver Add delta-V to state
State
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Finite maneuver

• Works like propagate segment, thrust added to
  force model
• Can specify the direction of the thrust vector
• Can be specified in plug-in
• Magnitude of thrust comes from engine model
• Can center the burn about current state

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Engine models

• Compute thrust, Isp, and/or mass flow rate (two
  of three)
• Four Kinds
• Constant Thrust and Isp
• Polynomial Engine T and Isp functions of
  pressure, temperature
• Ion Isp and mass flow functions of power
• Plugin you decide
• Thrust and mass flow rate sent back to force model

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Finite burn seeding

• Creates finite maneuver from impulsive
• Duration stopping condition set to estimated burn
  duration of impulsive maneuver
• Copies all settings from impulsive maneuver to
  finite maneuver

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Follow segment

• Choose leader to follow
• Specify offset from the leader
• Follow leader between joining conditions and
  separation conditions
• Behave just like stopping conditions
• Creates its own initial state

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Follow segment pseudo-code

• while (keepGoing)
• get leaders next ephemeris point
• add offset
• if (not adding points yet)
• if (joining conditions are met)
• find exact point of joining condition
• start adding points
• end if
• end if
• if (adding points)
• add point to ephemeris
• if (separation conditions met over step)
• find exact point of separation conditions
• keepGoing false
• end if
• end if
• end while

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Update segment

• Used to update spacecraft properties
• Useful to simulate stage separation, docking, etc
  
• Set properties to a new value, or add or subtract
  from their current value

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Update segment
State
Update Update state parameters
State
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Segments that change run flow

• Auto-Sequences called by propagate segments
• Target Sequence loops over segments, changing
  values until goals are met
• Backwards Sequence changes direction of
  propagation
• Return exits a sequence
• Stop stops computation

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Auto-sequences

• Instead of stopping a segment, stopping
  conditions can trigger an auto-sequence
• An auto-sequence is another sequence of segments
• Behaves like a subroutine
• After the auto-sequence is finished, control
  returns to the calling segment
• Auto-sequences can inherit stopping conditions
  from the calling segment

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Auto-sequences example
Initial State
Propagate
Apoapsis
Periapsis
Duration 1 day
Burn In Plane Sequence
Burn Out Of Plane Sequence
Finite Maneuver In Plane
Finite Maneuver Out of Plane
Duration 100 sec
Duration 100 sec
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Target sequence

• Runs through a series of targeter profiles
• Behaves like a while loop
• Profile manipulates the segments in target
  sequence
• Two types of profiles
• Differential corrector
• Profiles that change segments properties

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Differential corrector

• Controls chosen from segments in target sequence
• Results are calc objects computed at the end of
  segments in the sequence
• Determine controls, x, to meet results, y
• Evaluated by running targeter sequence

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Differential corrector

• Correction to controls found from linearized
  Taylor series
• A found from finite differencing, perturbation
  added to each control
• Inverse found from singular value decomposition

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Differential corrector pseudo-code

• run sequence to get results
• while (not converged and count lt max iterations)
• for each control
• adjust control by perturbation
• run sequence to get results
• end for
• compute partial matrix
• compute inverse of partials
• compute new control values
• run sequence to get results
• increment count
• end while

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Profiles that alter segment properties

• Change maneuver type toggles finite / impulsive
  
• Seed finite maneuver creates finite from
  impulsive maneuver
• Change stopping conditions toggles stopping
  conditions
• Change return enables / disables return segment

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Target sequence pseudo-code

• execute each profile
• run sequence final time
• clean up after profiles
• After targeter finished running, segments left in
  original state
• Changes to controls / segment properties not
  applied until Apply Corrections button is used

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Using the targeter effectively

• Multiple targeting profiles divide problem into
  parts
• Coarse and fine targeting
• U.S. Patent No. 6,937,968
• Target sequence can be changed between DC
  profiles with segment property profiles
• Differential corrector relies on good partials
• Set perturbation and max step appropriately
• Best to have equal number of controls and results

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Targeting examples

• Coarse and fine targeting of a maneuver
• Example of bad partials

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Backward sequence

• Segments in backward sequences propagated
  backwards
• Propagate finite maneuvers integrated with
  negative time step
• Impulsive maneuvers delta-Vs are subtracted
• Can pass initial or final state of sequence to
  next segment

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Backwards prop example

• Meet in the middle targeting problem

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Putting the ephemeris together

• Segment ephemeris merged after MCS is run
• When overlaps occur later segment in MCS wins
• Only overlapped portion of earlier segments
  ephemeris removed
• Possible to have discontinuous ephemeris
• Sequences have option not to generate ephemeris

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Ephemeris merging
Segment 1
Segment 2
Final Ephemeris
5
10
15
0
time
Two points at the same time
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Ephemeris merging example
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Summary

• Astrogator is a tool in STK for mission planning
• Astrogator is not complicated it just does what
  you tell it to do
• Some math in Astrogator
• Event detection
• Differential corrector
• Engine model
• Orbit propagation
• Configuring Astrogator is the key

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Other related events

• Methods of Orbit Propagation Jim
  WoodburnWednesday 1045 a.m.-1215 p.m.
• Space SystemsJohn Carrico and Bob HallWednesday
  1045 a.m.-1215 p.m.
• Astrogator Users Group breakfastThursday 715
  a.m.
• STK Plug-ins using Compiled CodeVince
  CoppolaThursday 1045 a.m.-1215 p.m.

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Questions

• ?