Dear Guillermo, Dear Guillermo,

Trajectory Design and Maneuver PlanningTrajectory Design and Maneuver Planningwithwith

STK / AstrogatorSTK / Astrogator John Carrico

Analytical Graphics, Inc.

Dear Guillermo, Dear Guillermo,

www.stk.com

1-800.220.4STK

Tech Support: support@stk.com;

1-888.785.9973 (8 am to 8 pm Eastern, or leave message)

Analytical Graphics, Inc.

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Agenda

• What is Astrogator?

• History

• Examples & Exercises

• Installation

• File Configuration

• Sharing Your Scenarios

Analytical Graphics, Inc.

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Astrogator: What is it?

• “Astrogator” appears in Science Fiction; Follow-on to Navigator module.

• Interactive orbit maneuver and space mission planning tool

• For use by spacecraft operations and mission analysis staff

• Fully integrated within STK

For Earth-orbiting, formation-flying, constellation, For Earth-orbiting, formation-flying, constellation, Geostationary, Lunar, Lagrange-point, and interplanetary Geostationary, Lunar, Lagrange-point, and interplanetary missionsmissions

Analytical Graphics, Inc.

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History: Swingby->Navigator->Astrogator

• Swingby developed at Goddard Space Flight Center/Flight Dynamics Division by Computer Sciences Corp. (CSC) in 1989

• Swingby commercialized to become Navigator (CSC; 1994); purchased by AGI

• Astrogator developed to meet GSFC/Flight Dynamics Analysis Branch request for a COTS solution (Jan 1997)

• Requirements from Swingby, and other institutional software

• Swingby/Navigator algorithms, and some code, in Astrogator

Analytical Graphics, Inc.

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Example: GTO to Mars

• From a Geostationary transfer orbit to Mars

• Arrive on 17 Dec, 2003

• Lunar Swingby changes plane (look in VO)

• Mission Control Sequence (MCS)

• Colored Segments

• Trajectory draws while calculating

• Segment summary report

• Quick view of segment times

Analytical Graphics, Inc.

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Exercise 1: The Mission Control Sequence

• Initial Modified Keplerian: Rp = 7000 km; inc = 28.5º; e = .01; Epoch = 4 July ‘00

• Propagate orbit to 3rd perigee

• Generate Segment Summary Report

• Create new 2-D window– ECI Orthographic

• Graphics– Animation start time

– Show ‘All’ orbit pass

• Set scenario “as default”

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Exercise 1 (Cont’d)

• Name and save scenario!– Good rules of thumb:

• Create new folder for each scenario• Name folder the same as the scenario

• AutoSave– Will save work every 5 minutes (by default)

– User can change save interval: Application Basic Properties

Analytical Graphics, Inc.

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Example: Double Lunar Swingby (DLS)

• Two Gravity Assists (used for Wind and Geotail missions)

• Note MCS; Relationship of colors to trajectory

• Uses launch model (Simple Ascent)– Use burnout information from launch vehicle

• Note use of maneuver segments

• Target on B-Plane for gravity assist

• Copy (with Ctrl-C) time of maneuver or of gravity assist off of MCS panel; Paste (Ctrl-V) into 2-D window and hit enter for visualization

Analytical Graphics, Inc.

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Background: “Delta-V”

• Unique velocity at every point in orbit

• If you change the velocity at a given point on an orbit, you are on a new orbit

• A simple change in velocity is an impulsive “Delta-V”

• Firing an engine for a finite duration changes the velocity

Analytical Graphics, Inc.

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Exercise 2: Maneuvers

• 1 km/s impulsive maneuver at perigee– Local axes: VNC

• Propagate to 2nd apogee– Change segment

color

• Draw trajectory as calculated

• Turn off propagate on apply

• Adjust 2-D view with mouse

Analytical Graphics, Inc.

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Exercise 2 (Cont’d)

• Graph Altitude and True Anomaly

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Example: To The Moon

• Transfer from low-Earth orbit to the Lunar orbit

• Earth-centered trajectory– Propagator Selection

– Definition in Astrogator Component Browser

• Moon-centered trajectory– Segments may have different force models and even different central

bodies

• Segment summary coordinate system choice

• Compare Blue Moon scenario– Air Force Academy project

– Low Delta-V transfer to the Moon via “Weak Stability Boundary” (WSB)

Analytical Graphics, Inc.

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Exercise 3: Propagators and Force Models

• Add 2nd maneuver at apogee– Velocity = 1.0 km/s

– Normal = -2.0 km/s

• Propagate 1 day– Type “1 day”;

converted to units

– Use CisLunar Propagator

• Astrogator Component Browser– Create & use new

12x12 gravity force model for last segment

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Exercise 3 (cont’d)

• Graph semi-major axis and inclination

• Look at Initial State Segment Summary in Earth-Fixed coordinates

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Example: 2-Maneuver Transfer

• Orbit transfer

• Propagate segments

• Type in Delta-Vs

• Repeat count for stopping conditions

• Let the targeter search for answer (Shows on 2-D window)

• Station contact: “Access”

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Example: 2-Maneuver Transfer (cont’d)

• Help System:– Uses HTML Browser

– “Explore STK”

– Main Page

– Module Help

– Context-Sensitive Help

– Math

– Exercises

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Exercise 4: Targeting maneuvers

• Use ‘V’ component as control

• Select Radius of Apogee (Ra) as a result; observe value in Segment Summary

• Select Ra as a constraint (42165 km)

• Action = Run Targeter

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Exercise 4 (Cont’d)

• Look at radius value at apogee– These are not two-

body orbits

– Lunar and Solar perturbations

• Move propagate into target sequence

• Target on Radius Magnitude (R Mag) at the real apogee

• Apply corrections

Analytical Graphics, Inc.

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Exercise 5

• Target second maneuver (2 x 2)– Use Velocity and

Normal components as controls

– Ecc = 0; Inc = 5º

• Reasons for non-convergence– Max num iterations

– Max step on control

– No correlation

• Most problems are “square”; n controls and n constraints (n x n)

Analytical Graphics, Inc.

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Example: Ground Track Control

• LandSat-7– Repeating Ground Track (233)– World Reference System

(WRS)– Reference Longitude (295.4°)

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Example: Ground Track Control (cont’d)

• Drift to ground track error near 1.0 km

• Perform maneuver so turn-around within –1.0 km error

• Ground Track Error at Descending Node

• 1st Guess and Actual maneuvers plotted

Analytical Graphics, Inc.

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Example: Formation Flying

• Model and Control Multiple Satellites

• Reference Satellite:– Real

– Virtual

• Target on values relative to reference satellite(s)

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Example: Ascent to Formation

• Plan maneuvers to obtain formation

• Plan maneuvers to maintain formation

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Example: Constellation

• Multiple Satellites spread around a planet

• Control to reference satellite:– In-plane reference

– Other-orbit-plane reference

• Phased ascent from single launch vehicle

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Example: AutoBurn

• Capability to model repetitive sequences

• “Event Loop” philosophy

• Auto-burn capability using multiple stopping conditions

• Repeat count for stopping conditions

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Example: Mars Climate Observer

• Uses auto-burn to simulate aero- braking

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Exercise 6: AutoBurn

• Initial State: Modified Keplerian Elements:– Radius of Periapsis = 7000

– Eccentricity = 0.01

• Create auxiliary sequence in Control Sequence Browser– New Sequence: “Small Burn”

– Insert 1 segment: Impulsive Delta-V; 0.1 km/s along velocity

• In Main Sequence, add 2nd stopping condition– Stop on periapsis.

– Run new sequence “Small Burn”

• Run and look at propagate summary for list

Analytical Graphics, Inc.

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Example: Scripting

• Useful for parametric studies, Monte-Carlo analysis, automation, etc.

• Support for Perl, MATLAB®, and user programs (e.g., C, C++)

• Uses STK/Connect with TCP/IP socket

• Script can be run on same or separate computer

• User can write custom user interface

Analytical Graphics, Inc.

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Example: Monte-Carlo Error Analysis

• Perl script to repeat same sequence with random perturbations of initial launch burnout values

• Script set control parameters

• Script retrieves STK calculated results

• Script calculates statisticsValue Nominal Average Stdn Deviation

sma: 8376.1877 8376.3863 3.462ecc: 0.0004 0.0004 3.83E-05inc: 49.9937 50.0036 0.0194raan: 329.3873 329.4042 0.0331w: 315.4401 311.2355 6.0665ta: 253.1021 257.3001 5.9799

alat: 568.5422 568.5355 0.0878

• Maneuvers can beautomatically planned

• Results include all output data: Elements; Fuel-used; Delta-V; Access times and durations…

Analytical Graphics, Inc.

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Example: Engine Modeling

• Integrate accelerations due to engine thrust model; Integrate mass loss based on Specific Impulse (Isp)

• Finite maneuver modeling setup

• Engine model setup: thrust and Isp

• Polynomial test utility

• Out of fuel message

• Blow-Down or Pressure-Regulated

• Effect of changing thrust

• Thrust efficiency

• Multiple thrusters

• Attitude input/output

Analytical Graphics, Inc.

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Exercise 7: Engine Modeling

• MCS:– Initial state

– Propagate to perigee

– Finite Maneuver: 2000 second duration along velocity

– Propagate to perigee

• Create new polynomial engine model– Thrust: 400 (N) + 0.0001(N/Pa) x Pressure

– Isp: 150 (s) + 0.0001 (s/Pa) x Pressure

• Polynomial test utility: P = 1000 kPa; T = 293º K

• Run in Blow-Down mode

• Multiple thrusters: Use 2 Engines, half duration.

• Attitude input

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Example: Low Thrust

• Super-synchronous transfer to geo-synchronous

• Multiple stopping conditions: stops on first satisfied

• Multiple stopping conditions is the “Logical OR”– Stop propagation if ‘A = x’ OR ‘B = y’

• Constraint on stopping conditions– Finds stopping conditions and then checks constraints

– Multiple constraints allowed

• Constraints is the “Logical AND”– Stop propagation if ‘A = x’ AND ‘B = y’ (within a tolerance)

– Stop propagation if ‘A = x’ AND ‘B < y’

– Stop propagation if ‘A = x’ AND ‘B > y’

Analytical Graphics, Inc.

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Example: Maneuver Calibration

• Calculate thruster efficiency based on orbit determination (OD)

• Use calibration factor to improve subsequent maneuvers

• Baseline trajectory

• Simulate OD

• Calibrate

• User must decide on mass flow rate

Analytical Graphics, Inc.

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Example: Lagrange Point - MAP

• Microwave Anisotropy Probe

• Launch in spring 2001

• Small-amplitude Lagrange point orbit

• Display in rotating coordinates

• Phasing loops before Lunar gravity assist

• Create Sun-Earth-SC angle graph

• Astrogator Browser

Analytical Graphics, Inc.

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Example: NGST

• Next Generation Space Telescope

• Large Amplitude Libration Point

• Self-targeting for launch window calculations (+ 10 min)

• Can override trajectory segment colors (Turn off “Use Trajectory Segment Colors)

Analytical Graphics, Inc.

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Installation

• Astrogator is part of regular STK

• Activated with license

• Full STK installation on each PC– C:\Program Files\AGI\stk\…

• User Install– Each user has own data area on each machine

– D:\stk\jcarrico

Analytical Graphics, Inc.

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File Configuration

• Scenarios in a subdirectory share objects

• Rule of Thumb: One scenario per subdirectory– (or very similar scenarios)

– Helps when zipping files for someone else

• Astrogator subdirectory holds user-defined objects– Flag as Read-Only for configuration control

• User “config” subdirectory– Styles

– Read-Only Astrogator components

Analytical Graphics, Inc.

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Sharing Your Scenarios

• Using Winzip

• Recurse subfolders– Make sure to include the “Astrogator” subfolder