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ORBIT DETERMINATION AND CONTROL FOR THE EUROPEAN STUDENT MOON ORBITER

ORBIT DETERMINATION AND CONTROL FOR THE EUROPEAN STUDENT MOON ORBITER. Federico Zuiani Alison Gibbings , Daniel Novak, Cesar Martinez, Francesco Rizzi Space Advanced Research Team Dept. of Aerospace Engineering University of Glasgow, UK. IAC-2010 – 40 th Student Conference. Agenda.

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ORBIT DETERMINATION AND CONTROL FOR THE EUROPEAN STUDENT MOON ORBITER

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  1. ORBIT DETERMINATION AND CONTROL FOR THE EUROPEAN STUDENT MOON ORBITER Federico Zuiani Alison Gibbings, Daniel Novak, Cesar Martinez, Francesco Rizzi Space Advanced Research Team Dept. of Aerospace Engineering University of Glasgow, UK IAC-2010 – 40th Student Conference

  2. Agenda ESMO NAVIGATION ANALYSIS & MANOEUVRES DESIGN Orbit Determination Background on ESMO Baseline Option Navigation Analysis Remarks

  3. European Student Moon Orbiter (ESMO) • Fourth mission within ESA’s Education Office Satellite Programme • Over 200 UG/PG students from 19 universities in 10 countries are currently participating in the ESMO mission • First student-designed microsatellite mission to the moon • SpaceART is the lead team for both Mission Analysis, Flight Dynamics subsystems • Successfully completed Phase A Feasibility Study, proceeding with preliminary design activities in Phase B BACKGROUND

  4. 2009 Baseline for Mission Analysis • Launch window anytime between 2011-2012 • ESMO would be injected into a GTO • All-day-launch requirement • Final operational orbit: • Highly elliptical, inclined lunar polar orbitrperi = 250 km, rapo = 3600 km • Uncontrolled stability requirement of minimum 6 months • Low ∆v WSB transfer with multi-revolutions departure from Earth • Requirement on max ∆v ≤ 1.35 km/s • 4x bi-propellant engines with thrust of 22 N and Isp of 285 s BACKGROUND Multi-revolution WSB transfer in Earth centred, equatorial reference frame

  5. New Baseline Requirements Problem • Cut down the nominal Dv budget to below 1 km/s • Estimate the required OD accuracy to reach the Moon and be captured into an orbit with a lifetime of 6 months • Devise a navigation and trajectory control strategy to reach the Moon and be captured into an orbit with a lifetime of 6 months. • Extended 1 month parking orbit before Trans Lunar Injection (TLI) Proposed Solution • Dv savings at the Earth is not possible without making operations more complicated (e.g. with a swing-by of the Moon) • We started the analysis from the Moon, going backward • OD analysis first, because if we do not know where we are, we do not know where we are going BACKGROUND

  6. Sensitivity of Lunar Orbit to LOI errors • Random errors were introduced into the Keplerian orbital elements after the injection manoeuvre • Error values ranged from 1%-5% of nominal value • Orbit was propagated forward for a maximum of 6 months using STK ORBIT DETERMINATION • Plot showing effect of errors for 10 sample orbits • For 1% error, max lifetime reduction of lunar orbit of 20 days • For 5% error, max lifetime reduction of lunar orbit of 90 days • Error of 1% is an acceptable compromise between mission objectives and orbit determination requirements Perilune lifetime with 1% error on initial orbital elements

  7. Sensitivity of Lunar Orbit to LOI errors • Random errors were introduced into the Keplerian orbital elements after the injection manoeuvre • Error values ranged from 1%-5% of nominal value • Orbit was propagated forward for a maximum of 6 months using STK ORBIT DETERMINATION • Plot showing effect of errors for 10 sample orbits • For 1% error, max lifetime reduction of lunar orbit of 20 days • For 5% error, max lifetime reduction of lunar orbit of 90 days • Error of 1% is an acceptable compromise between mission objectives and orbit determination requirements Perilune lifetime with 5% error on initial orbital elements

  8. Sensitivity of Lunar Orbit to LOI errors • Random errors were introduced into the Keplerian orbital elements after the injection manoeuvre • Error values ranged from 1%-5% of nominal value • Orbit was propagated forward for a maximum of 6 months using STK ORBIT DETERMINATION • For 1% error case: • Relative error in position and velocity projected along radial, transversal and out-of-plane reference frame • Origin represents the nominal solution • Relative to Earth to show the required OD capabilities of ground stations position velocity

  9. Capture Corridor • Data from 1% error case was used to define a region in the state space (position and velocity) at different times prior to lunar orbit insertion • The region, or corridor, defines the set of positions and velocities that ESMO must have at Δt prior to LOI to be correctly captured at the Moon • Displacements in position δr and velocity δv were randomly generated within a given range • The perturbed state vector [r, v] was then propagated backward for Δt ORBIT DETERMINATION h d v h Nominal trajectory r Corridor at tinsertion--Dt dr r Nominal trajectory r dr dv v r t v r-h plane r-h plane t

  10. Position and Velocity Dispersion • 10000 perturbed state vectors were propagated backwards for: one week, two weeks and up to the WSB point (farthest point from the Earth) • Max error of magnitude: δr ± 5 km and δv ± 10 m/s ORBIT DETERMINATION

  11. Position and Velocity Dispersion • 10000 perturbed state vectors were propagated backwards for: one week, two weeks and up to the WSB point (farthest point from the Earth) • Max error of magnitude: δr ± 5 km and δv ± 10 m/s ORBIT DETERMINATION

  12. OD Accuracy Requirements • Trajectories corresponding to the curl will not reach the WSB region and do not represent feasible transfers • Corridor tends to be thinner in the normal and transversal directions while it seems to stretch along the radial direction • Note, listed accuracies in position are particularly conservative compared to generated results • 100% margin was applied to account for current state of maturity of the project. • Orbit determination accuracy requirements ORBIT DETERMINATION

  13. Trajectory Correction Manoeuvres • Based on corridor analysis, a series of Trajectory Correction Manoeuvres (TCM) can be inserted along the transfer after each orbit determination segment • TCMs ensure ESMO’s position and velocity remain within the trajectory corridor, with the action of each TCM to reach the nominal reference trajectory • The orbit determination process was initially simulated using the ODTK package • Now we are testing an in-house Uncented Kalman Filter • Sources of errors used in analysis: • Trans-lunar injection burn • Typical dispersion errors of the launcher • Error in each major Δv manoeuvres of 1 m/s (3s) in every direction • Error in each TCM of 0.1 m/s (3s) in every direction • First OD segment assumed to occur at +1 week from TLI, and lasts for 3 days NAVIATION STRATEGY

  14. Example of OD+TCM Strategy NAVIATION STRATEGY WSB Trajectory in Earth-centred, Earth equatorial system Total nominal Δv = 1.1257 km/s

  15. Example of OD+TCM Strategy NAVIATION STRATEGY • 8 TCM’s strategy: situation at 1w from LOI

  16. Methods to Reduce Δv • Changes to the lunar orbit were first made by increasing the apolune altitude • All other orbital elements were kept to the existing baseline, with the altitude of perigee constrained to 100 km to comply with initial NAC requirement • The higher the apolune altitude, the quicker the orbit decayed: • 10000 km orbit decayed in 4 months • 20000 km orbit decayed after 55 days • 56000 km orbit decayed under 30 days NEW BASELINE OPTION

  17. Frozen ‘Ely’ Orbits • High eccentric frozen orbits offer substantial savings in Dv with long term uncontrolled orbit lifetime [Ely T, Lieb E, Constellations of Elliptical Inclined Lunar Orbits Providing Polar and Global Coverage, The Journal of the Astronautical Sciences 54(1), 2006] • High eccentric frozen orbits only occur under fixed conditions of argument of periapsis (ω = 90º or 270º) and inclination (i ≥ 39.2º) • The argument of perilune ω = 270º was selected to comply with the mission payload requirements offering perilune over the South Pole • Three test cases were propagated forward for 6 months, accounting for: • 3rd body effects from Earth and Sun • Moon’s gravitational force, using 20th degree, 20th order gravitational model (LP165P) NEW BASELINE OPTION

  18. Frozen Orbit Propagation • Mission Δv considered more important than NAC resolution requirement (zp ≤ 100 km) • Good compromise between ∆v and image resolution can be obtained based on Case 2 with a slightly lower perilune altitude • Frozen orbits are sensitive to orbital injection RAAN and injection date • New frozen orbit with adapted WSB transfer and LOI gives a total mission Δv of 0.869 km/s • Total savings of 0.247 km/s over previous baseline NEW BASELINE OPTION Case 2:Δv = 0.849 km/s, min(zp) > 100 km Case 3:Δv = 0.948 km/s, zp≤ 100km NEW Baseline Case 1:Δv = 0.947 km/s, zp≤ 100km only after day 145 OLD Baseline with nominal RAAN 100°

  19. Frozen Orbit Stability Assessment • Objective: describe stability behaviour of arrival orbit according to RAAN and arrival date to derive constraint on arrival condition for WSB trajectory optimization. • Orbit propagated for 6 months for multiple values of RAAN and TLOI . • Example: Stability assessment for a nominally unstable arrival orbit. • RAAN range: [0, 180°] • TLOI range: [Tnominal-16days, Tnominal+16days] • Result: constraints could be introduced in the trajectory optimization process. NEW BASELINE OPTION

  20. Frozen Orbit Stability NEW BASELINE OPTION

  21. Extended 1 month parking before TLI • Using a MBS offers higher launch date flexibility, a reduction of the gravity losses per manoeuvre and an expected reduction of the navigation ∆v • But for 1 month MBS adds 47.2 m/s to the total cost of the transfer compared to a single direct injection burn from GTO into the WSB transfer • Due to increase in perturbing effects of atmospheric drag, J2 and 3rd body effects NEW BASELINE OPTION Earth spirals occurring during the multi-burn strategy Direct: [1xGTO, 1xWSB, 1xLOI] ∆vtot = 869 m/s, mission length: 100 days MBS: [4xGTO, 1xWSB, 2xLOI] ∆vtot = 916 m/s, mission length: 133 days

  22. NEW BASELINE OPTION 11/18/2014 • Direct transfer versus multi-burn strategy

  23. Direct transfer versus multi-burn strategy • Total cost of the new nominal solution is 916.9 m/s, against the nominal 1116.29 m/s of the previous baseline, leading to a savings of 199.4 m/s NEW BASELINE OPTION

  24. NEW BASELINE OPTION 11/18/2014 • Ground Station Access • 3 different ESA Ground stations have been considered: Malindi, Perth, Villafranca.

  25. NEW BASELINE OPTION 11/18/2014 • Ground Station Access • The combination of the three Ground Stations guarantees sufficient adequate time.

  26. NEW BASELINE OPTION 11/18/2014 • Multiburn Strategy: errors on manoeuvres Objective: determine error on final state due to errors on thrust level and attitude. First manoeuvre was analysed: • Largest, ∆V~400 m/s • First to be performed, thruster calibration errors possible. • Methodology: • Nominal thrust profile is perturbed with a Gaussian error. • Manoeuvre is numerically propagated and error on final state is calculated.

  27. NEW BASELINE OPTION 11/18/2014 • Multiburn Strategy: errors on manoeuvres

  28. NEW LAUNCH WINDOW 11/18/2014 • 2014-2015 Launch Window • Previous launch window for 2011-2012 has been shifted to 2014-2015. • SpaceART’s database is currently being updated to meet new requirement. • Given the periodicity of Earth-Sun-Moon system the basic structure of the WSB transfer remains unchanged. • Work is in progress on refining and adding solutions.

  29. NEW LAUNCH WINDOW 11/18/2014 • 2014-2015 Launch Window

  30. Conclusions • First analysis of the orbit determination requirements and a possible navigation strategy for the European Student Moon Orbiter • Proposed corridor-targeting approach yields good results at a relatively low Dv cost and with mild orbit determination accuracy • Ideal for a small satellite missions with low ∆v budget • Navigation cost can be further optimised if the size of major manoeuvres is reduced. • MBS will fraction the TLI manouvre into several revolutions leading to a reduction of the magnitude of the TCM’s • Future work will address the optimisation of the TCM’s and an orbit determination process tailored to ESMO • This research is partially supported by Surrey Satellite Technology Ltd (SSTL), with thanks to: • Mark Taylor at SSTL • Dr. Paolo De Pascale at the European Space Operation Centre • The Space.ART MIAS/FD team, which has involved over 20 students since 2006 ESMO NAVIGATION ANALYSIS & MANOEUVRES DESIGN

  31. Recommendations • Do not put the task of writing formal documentation on us (the Universities) • It requires a lot of supervision time, the students are unhappy, you are unhappy, the students learn that space/ESA/Industry is only a matter of bureaucracy • It is impossible to achieve the goals of this type of mission only with undergrad students • They are discontinuous, unreliable and require a lot of supervision work beyond the normal supervision time of an academic • However, the cost of a PhD is ½ of the cost of a YGT and 1/n of a ESA/SSTL staff, therefore consider PhD students as an asset to complete ESMO successfully • Do not trust anyone who says that student time comes for free • Either he/she supports slavery or he/she is lying • When we ask for technical support, please do not charge us at the same rate you would charge ESA. ESMO NAVIGATION ANALYSIS & MANOEUVRES DESIGN

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