Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat On-board Orbit Determination for a Deep-Space CubeSat Boris Segret LESIA-ESEP, PSL / Paris Observatory, France D.A.A, N.C.K.U., Taiwan : Tristan Mallet, Jordan Vannitsen, Jiun-Jih Miau LESIA, PSL / Paris Observatory : Gary Quinsac IMCCE, PSL / Paris Observatory : Daniel Hestroffer, Florent Deleflie Segret @ iCubeSat 2016, Oxford, #1 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Orbit Determination in Birdy Technology (trajectory inspired by Dennis Tito for 2018) (Quinsac et al., 2016) (courtesy LPPT, European consortium for Liquid micro- (ESA's AIM mission to Didymos in 2022) Pulsed Plasma Thruster, FP7 funded, TRL 3 in 2015) Segret @ iCubeSat 2016, Oxford, #2 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat 1st Context: Birdy in Deep-Space Cruise Study Case = Earth-Mars-Earth free return trajectory 0● Mission Preparation 0 1 1● Deployment after IOI 2● Earth-to-Mars 3● Mars Flyby : First Datalink 4● Mars-to-Earth = Earth-to-Mars 5● End of Mission : Final Datalink 4 2 5 Science mode: for instance autonomous Space Weather Probe 3 (trajectory inspired by Dennis Tito for 2018) Segret @ iCubeSat 2016, Oxford, #3 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat 2nd Context: Birdy in “Flying-legs” Study case = released in situ by Mothercraft 0 0 Ground Segment: – Propagator with Models-in-the-loop 1 – Next Flying-legs to Mothercraft Models © ESA (Galvez/Carnelli) Flight Segment 1 2 2 – TCM: set new V~1m/s (1 day) 3 – Science mode (1 day ~80km) • Echo/Doppler (multiple S/C) 3 • Imaging surface features • Optical astrometry 4 – Navigation mode (OD+OC) 5 – S-band TT&C to Mothercraft 4 5 2 Segret @ iCubeSat 2016, Oxford, #4 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Orbit Determination: Accuracy ? Trajectory Solver / Ground Segment : – Reference Trajectory stored on-board – Expected directions of “foreground objects” Location determination / Flight Segment – Star Tracker (ADS) + Object Tracker (ODS) – Accuracy needed ? Accuracy reached ? Models-in-the-loop – gravitational – non-gravitational – expected (A.Porquet, IMCCE, 2014) Segret @ iCubeSat 2016, Oxford, #5 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Orbit Determination: Accuracy ? Trajectory Solver / Ground Segment : – Reference Trajectory stored on-board – Expected directions of “foreground objects” Location determination / Flight Segment – Star Tracker (ADS) + Object Tracker (ODS) – Accuracy needed ? Accuracy reached ? Models-in-the-loop – gravitational – non-gravitational – expected (A.Porquet, IMCCE, 2014) Segret @ iCubeSat 2016, Oxford, #6 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Simplified Approach M∗⃗X −C⃗ = 0⃗ χ 2 (⃗X ) = ‖ M∗⃗X −C⃗ ‖ 2 ⇒ min (⃗X | χ 2 (X⃗) ) ? 1 0 0 0 0 0 0 0 0 0 0 0 CC 0 0 0 0 0 0 i ,1 CSCS 0 1 0 0 0 0 0 0 0 0 0 0 CS 0 0 0 0 0 0 δ x i,1 i,1 1 CCSS 0 0 1 0 0 0 0 0 0 0 0 0 S 0 0 0 0 0 0 δ y i,1 i ,1 1 C 0 0 0 1 0 0 0 0 0 0 0 0 0 CC 0 0 0 0 0 δ z i ,1 i ,2 1 CSCS 0 0 0 0 1 0 0 0 0 0 0 0 0 CS 0 0 0 0 0 δ x i,2 i ,2 2 CCSS 0 0 0 0 0 1 0 0 0 0 0 0 0 S 0 0 0 0 0 δ y i,2 i ,2 2 C 0 0 0 0 0 0 1 0 0 0 0 0 0 0 CC 0 0 0 0 δ z i ,2 i ,3 2 CSCS 0 0 0 0 0 0 0 1 0 0 0 0 0 0 CS 0 0 0 0 δ x i,3 i ,3 3 CCSS 0 0 0 0 0 0 0 0 1 0 0 0 0 0 S 0 0 0 0 δ y i,3 i ,3 3 C 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 CC 0 0 0 δ z i ,3 i ,4 3 CSCS 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 CS 0 0 0 ∗ δ x − i,4 = 0⃗ i,4 4 CCSS 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 S 0 0 0 δ y i,4 i ,4 4 C 1 0 0 −1 0 0 0 0 0 0 0 0 0 0 0 0 dt 0 0 δ z i ,4 2 4 0 − 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 dt 2 0 dri,1 0 0 0 1 0 0 −1 0 0 0 0 0 0 0 0 0 0 0 0 dt 2 dri,2 0 0 0 0 1 0 0 −1 0 0 0 0 0 0 0 0 0 dt 0 0 dr Assumption: 3 i,3 0 0 0 0 0 1 0 0 −1 0 0 0 0 0 0 0 0 0 dt 3 0 dri,4 0 0 0 0 0 0 1 0 0 −1 0 0 0 0 0 0 0 0 0 dt j 3 V x 0 0 0 0 0 0 0 0 1 0 0 −1 0 0 0 0 0 0 dt 4 0 0 V y Constant Velocity 0 0 0 0 0 0 0 1 0 0 −1 0 0 0 0 0 0 dt 0 V 0 4 z 0 0 0 0 0 0 0 0 0 1 0 0 −1 0 0 0 0 0 0 dt 4 [ ] during N=4 measurements [ ] [ ] => 19 unknowns => 21 equations 1st simulation on Earth-Mars in 10/2015 without optical errors, validations in 03/2016 (T.Mallet, DAA/NCKU, 2015) Segret @ iCubeSat 2016, Oxford, #7 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Method for Monte-Carlo simulations Multidimensional Minimizing: M∗⃗X −C⃗ = 0⃗ 2 ⃗ ⃗ ⃗ 2 (a) “Steepest Descent” algorithm χ (X ) = ‖ M∗X −C ‖ preferred for on-board software ⇒ min (⃗X | χ 2 (X⃗) ) ? not implemented yet (b) or “Random search on a grid” (a) steepest descent along ⃗∇ χ 2(⃗X ) may be an alternative, not implemented yet (b) random search while evaluating ⃗∇ χ 2(⃗X ) (c) or MATLAB / OCTAVE “INV([C])” likely not for on-board software (c) new 19x19 linear system ⃗ 2 ⃗ ⃗ ⃗ ⃗ −1 ⃗ implemented here for MC simulations ∇ χ ( X ) = 0⇔ [C ]. X =Y ⇔ X =[C ] .Y x δ y “i” measurements ( z)i=1. .4 i=1..4 for 19 unknowns X⃗ = δ r j=1..4 “j” foreground bodies V x 4 from N foreground bodies V y V ( ( z ) ) Segret @ iCubeSat 2016, Oxford, #8 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Earth-to-Mars “E2M”: initial results... If +1m/s is applied on Y-axis at jettisoning wrt Reference Trajectory “T0” ➔ do we correctly reconstruct the expected shift wrt T0? Monte-Carlo series to estimate the mean reconstructed value <X>=f(σin) accuracy measurement σin << 1 arcsec Segret @ iCubeSat 2016, Oxford, #9 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Earth-to-Mars “E2M”: … and limits If +1m/s is applied on Y-axis at jettisoning wrt Reference Trajectory “T0” ➔ do we correctly reconstruct the expected shift wrt T0? Monte-Carlo series to estimate the mean reconstructed value <X>=f(σin) accuracy measurement σin = 1 arcsec Segret @ iCubeSat 2016, Oxford, #10 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Earth-to-Mars “E2M”: … and limits If +1m/s is applied on Y-axis at jettisoning wrt Reference Trajectory “T0” ➔ do we correctly reconstruct the expected shift wrt T0? Monte-Carlo series to estimate the mean reconstructed value <X>=f(σin) accuracy measurement σin = 15 arcsec Segret @ iCubeSat 2016, Oxford, #11 / 27 Elementary dynamic model “Y+1kY” On-board Orbit Determination for a Deep-Space CubeSat “Y+1kY” actual trajectory reference trajectory Birdy Technology 30 km/s 3 1 AU 1000 km Rectilinear trajectory of CubeSat at 30km/s along 3 AU with 4 fictional “foreground Bodies” Z 0.1 AU 4 Y 1 2 X 1 AU 2 AU Segret @ iCubeSat 2016, Oxford , # 12 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Elementary dynamic model “Y+1kY” Rectilinear trajectory of CubeSat at 30km/s along 3 AU with 4 fictional “foreground Bodies” 3 actual trajectory reference trajectory /s km 0 3 2 2 AU 4 1000 km 0.1 AU 1 AU 1 1 AU Z Y X Segret @ iCubeSat 2016, Oxford, #13 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat “Y+1kY” dispersions even at small σin The actual shift is small and constant (1000km) => assumption of “small shift” is not involved (Taylor dev.at 1 st order) Numeric degeneracy is likely involved, due to small angular variations with large distances (begin & end). σin = 0 (!) Y X Segret @ iCubeSat 2016, Oxford, #14 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat “Y+1kY” dispersions even at small σin -5 σin = 10 arcsec (!) Y X σout on dY *and* dVy, dVx! σout larger at large distances, on dV as well Segret @ iCubeSat 2016, Oxford, #15 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat “Y+1kY” dispersions even at small σin -3 σin = 10 arcsec (!) Y X σout on dY *and* dVy, dVx! σout larger at large distances, on dV as well Segret @ iCubeSat 2016, Oxford, #16 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat “Y+1kY” dispersions even at small σin σin = 0.1 arcsec Y X σout on dY and dVy, dVx! σout larger at large distances, on dV as well Segret @ iCubeSat 2016, Oxford, #17 / 27 Realistic model “E2M” with small On-board Orbit Determination for a Deep-Space CubeSat σ in = 0.1 arcsec σ and “ in = 1 arcsec E2M” Birdy Technology σ in (black curve) Cruise of CubeSat from Earth to Mars in 2018 ● 2 realistic trajectory propagations ✔ Ref.Trajectory “T0” ✔ +1m/s on Y-axis at jettisonning wrt “T0” ● 4 non-coplanar “foreground Bodies” Segret @ iCubeSat 2016, Oxford , # 18 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat “E2M” dispersions at small σin +1m/s on Y: the actual shift wrt T0 is larger over time => assumption of “small shift” not valid in late scenario @ σin = 0.1 arcsec => Mean value ~10km accurate (wrt a few 1000s km expected) in transverse or longitudinal directions σin = 0.1 arcsec Segret @ iCubeSat 2016, Oxford, #19 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat “E2M” dispersions at small σin +1m/s on Y: the actual shift wrt T0 is larger over time => assumption of “small shift” not valid in late scenario @ σin = 1 arcsec => Mean value ~100km accurate (wrt a few 1000s km expected) in transverse or longitudinal directions σin = 1 arcsec Segret @ iCubeSat 2016, Oxford, #20 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat “E2M”: <δx,δy,δz> at small σin σin = 0.1 arcsec => σout ~300 m (X,Z) .