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Under The Hood: Maneuver Planning With Astrogator

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Under The Hood:Maneuver Planning With Astrogator

Matt Berry

Kevin Ring

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?

- Astrogator is STK’s 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

- 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

Astrogator

Mission Control Sequence

Configuration

Ephemeris

Astrogator

Runs Mission Control

Sequence

Other Mission

Data

- 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

State

Segment 1

Ephemeris

State

Ephemeris

Segment 2

State

- 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

Specify spacecraft state at some epoch

Choose any coordinate system

Enter in Cartesian, Keplerian, etc.

Enter spacecraft properties: mass, fuel, etc.

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

Numerically integrates using chosen propagator

Propagator can be configured in Astrogator browser

Propagation continues until stopping conditions are met

- 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

- Can also specify constraints:
- Only stop if another calc object is =, <, >, 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”

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

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

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

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

State

Impulsive Maneuver

Add delta-V to state

State

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

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

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

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

while (keepGoing)

get leader’s 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

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

State

Update

Update state parameters

State

- 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

- 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

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

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

- 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

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

run sequence to get results

while (not converged and count < 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

- 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

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

- 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

- Coarse and fine targeting of a maneuver
- Example of “bad partials”

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

- Meet in the middle targeting problem

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

Segment 1

Segment 2

Final Ephemeris

0

5

10

15

time

Two points

at the same time

- 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

- Methods of Orbit Propagation Jim WoodburnWednesday 10:45 a.m.-12:15 p.m.
- Space SystemsJohn Carrico and Bob HallWednesday 10:45 a.m.-12:15 p.m.
- Astrogator Users’ Group breakfastThursday 7:15 a.m.
- STK Plug-ins using Compiled CodeVince CoppolaThursday 10:45 a.m.-12:15 p.m.

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