1. Pg 1 of 44 AGI www agiuc com Under The Hood: Maneuver Planning With Astrogator Matt Berry Kevin Ring

2. Pg 2 of 44 AGI www agiuc com 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?

3. Pg 3 of 44 AGI www agiuc com What’s Astrogator? 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

4. Pg 4 of 44 AGI www agiuc com 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

5. Pg 5 of 44 AGI www agiuc com Astrogator Mission Control Sequence Configuration Mission Control Sequence Configuration Astrogator Runs Mission Control Sequence Ephemeris Other Mission Data Other Mission Data

6. Pg 6 of 44 AGI www agiuc com 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

7. Pg 7 of 44 AGI www agiuc com The Mission Control Sequence State Segment 1 State Segment 2 State Ephemeri s

8. Pg 8 of 44 AGI www agiuc com 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

9. Pg 9 of 44 AGI www agiuc com Initial state segment Specify spacecraft state at some epoch Choose any coordinate system Enter in Cartesian, Keplerian, etc. Enter spacecraft properties: mass, fuel, etc.

10. Pg 10 of 44 AGI www agiuc com 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

11. Pg 11 of 44 AGI www agiuc com Propagate segment Numerically integrates using chosen propagator Propagator can be configured in Astrogator browser Propagation continues until stopping conditions are met

12. Pg 12 of 44 AGI www agiuc com 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

13. Pg 13 of 44 AGI www agiuc com Stopping conditions 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”

14. Pg 14 of 44 AGI www agiuc com Event detection Exact time of event found with Regula-Falsi f(t) found by integrating to time t

15. Pg 15 of 44 AGI www agiuc com 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 while

16. Pg 16 of 44 AGI www agiuc com 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

17. Pg 17 of 44 AGI www agiuc com 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

18. Pg 18 of 44 AGI www agiuc com Impulsive maneuver State Impulsive Maneuver Add delta-V to state State

19. Pg 19 of 44 AGI www agiuc com 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

20. Pg 20 of 44 AGI www agiuc com 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

21. Pg 21 of 44 AGI www agiuc com 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

22. Pg 22 of 44 AGI www agiuc com 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

23. Pg 23 of 44 AGI www agiuc com Follow segment: pseudo-code 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 if (adding points) add point to ephemeris if (separation conditions met over step) find exact point of separation conditions keepGoing = false end if end while

24. Pg 24 of 44 AGI www agiuc com 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

25. Pg 25 of 44 AGI www agiuc com Update segment State Update Update state parameters State

26. Pg 26 of 44 AGI www agiuc com 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

27. Pg 27 of 44 AGI www agiuc com 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

28. Pg 28 of 44 AGI www agiuc com Auto-sequences example Initial State Propagate Burn In Plane Sequence Burn Out Of Plane Sequence Duration = 1 day Periapsis Apoapsis Finite Maneuver In Plane Finite Maneuver Out of Plane Duration = 100 sec

29. Pg 29 of 44 AGI www agiuc com 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

30. Pg 30 of 44 AGI www agiuc com 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

31. Pg 31 of 44 AGI www agiuc com 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

32. Pg 32 of 44 AGI www agiuc com Differential corrector: pseudo-code 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

33. Pg 33 of 44 AGI www agiuc com 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

34. Pg 34 of 44 AGI www agiuc com 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

35. Pg 35 of 44 AGI www agiuc com 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

36. Pg 36 of 44 AGI www agiuc com Targeting examples Coarse and fine targeting of a maneuver Example of “bad partials”

37. Pg 37 of 44 AGI www agiuc com 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

38. Pg 38 of 44 AGI www agiuc com Backwards prop example Meet in the middle targeting problem

39. Pg 39 of 44 AGI www agiuc com Putting the ephemeris together 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

40. Pg 40 of 44 AGI www agiuc com Ephemeris merging Segment 1 Segment 2 Final Ephemeris time 510150 Two points at the same time Two points at the same time

41. Pg 41 of 44 AGI www agiuc com Ephemeris merging example

42. Pg 42 of 44 AGI www agiuc com 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

43. Pg 43 of 44 AGI www agiuc com Other related events Methods of Orbit Propagation Jim Woodburn Wednesday 10:45 a.m.-12:15 p.m. Space Systems John Carrico and Bob Hall Wednesday 10:45 a.m.-12:15 p.m. Astrogator Users’ Group breakfast Thursday 7:15 a.m. STK Plug-ins using Compiled Code Vince Coppola Thursday 10:45 a.m.-12:15 p.m.

44. Pg 44 of 44 AGI www agiuc com Questions ?