On-Board Orbit Determination for a Deep-Space Cubesat

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

(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 ?

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 =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

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

accuracy measurement σin = 15 arcsec

Segret @ iCubeSat 2016, Oxford, #11 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Elementary dynamic model “Y+1kY”

“Y+1kY” U A 3 3 ng alo /s m 0k t 3 a actual trajectory at S s” be ie u od reference trajectory f C B o d ry un cto ro je eg ra or r t “f a al ne n tili tio ec fic R 4 /s ith km w 0 3 2 2 AU 4 1000 km 0.1 AU 1 AU 1 1 AU Z

Y X

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 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat

Realistic model “E2M” with small σin “E2M”

18 20 n s i ar M to th ar σ = 0.1 arcsec E in om fr and at s ” S on T 0 be ti t “ σin = 1 arcsec u ga wr f C pa g o ro nin ” ise y p n es ru or ” iso di C ct 0 tt o ) je “T je B ve ra ry at nd ur t to s u c tic ec xi ro ck lis aj -a eg la a Tr Y or (b re f. on “f 2 Re s ar ● / n ✔ m 1 pla + co ✔ n- no 4 ●

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) .. 500 m (Y)

better results in the middle of the cruise?

Segret @ iCubeSat 2016, Oxford, #21 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat

“E2M”: <δx,δy,δz> at small σin

σin = 1 arcsec => σout > 2km (Y) .. 4km (X,Z) !!!

Mean value could be acceptable but it cannot be trusted due to σout

Segret @ iCubeSat 2016, Oxford, #22 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat

“E2M”: <δr>foreground bodies at small σin

σin = 0.1 arcsec => σout ~500 m distance shifts are moderate, then increase

σout few 100s of km

Segret @ iCubeSat 2016, Oxford, #23 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat

“E2M”: <δr>foreground bodies at small σin

σin = 1 arcsec => σout ~500 m distance shifts are moderate, then increase

nd σout ~250 km (3000 km / 2 body)

Segret @ iCubeSat 2016, Oxford, #24 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat

“E2M”: <δVx,δVy> at small σin

σin = 0.1 arcsec => σout > 2 .. 5 m/s Velocities vary during On-board OD: at least 1° in direction and +/- 0.1 m/s in intensities

σin = 1 arcsec => σout > 20 .. 50 m/s (!!)

Segret @ iCubeSat 2016, Oxford, #25 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Temporary assessments ● Lessons from “Y+1kY” fictional model

➢ Some dispersion with 0 σin → Numeric degeneracy (INV function)

➢ st σout vs. σin is very sensitive, optical accuracy is the 1 driver ➢ “close” foreground bodies is the 2nd driver for the overall accuracy ➢ Shifts 102..103km vs. 10-5..10-6km/s → dimensionless approach

● Lessons from “E2M” realistic model ➢ The sensitivity seems to be well explained through “Y+1kY” ➢ Periods in the cruise seem more favorable to run the on-board OD ➢ Uniform velocity during OD is not any realistic assumption ➢ (direction of the Sun was not considered)

Segret @ iCubeSat 2016, Oxford, #26 / 27 Birdy Technology On-board Orbit Determination for a Deep-Space CubeSat Conclusion: We've got a roadmap!

● Study about On-board Orbit Determination is still in BIRDY Technology is also a student project: More than 54 students have participated from 2014 in progress : need to improve by 2-3 orders of magnitude France and in Taiwan ➢ on-board “Steepest descent” algorithm Involved Institutions: 1.Association Planete Mars, 2.Mars Society Switzerland, 3.Observatoire de Paris, 4.Laboratoire d’Etudes Spatiales et d’Instrumentation en ➢ Astrophysique, 5.Laboratoire Atmospheres, Milieux, Observations Spatiales, non-uniform velocity, N=5 measurements needed 6.Centre National de la Recherche Scientifique, 7.Institut de Mecanique Celeste et de Calcul des Ephemerides, 8.National Cheng Kung University, 9.LabEx ➢ Exploration Spatiale des Environnements Planetaires, 10.Centre d'Etudiant pour select the N “best” observables la Recherche et l’Exploration Spatiale, 11.Research University Paris Sciences Lettres, 12.Pierre and Marie Curie University, 13.Universite Lille 1 Sciences et Technologies, 14.Institut Polytechnique des Sciences Avancees, 15.Ecole d'Ingenierie des Sciences Aerospatiales, 16.Consortium Liquid Micro Pulsed Plasma Thruster, 17.KopooS Consulting Ind., 18.Ecole Centrale Lille, 19.Joint ● The required accuracy depends on the “TCM” potential Institute for VLBI in Europe , 20.Ecole Centrale-Supelec Involved actors (chronological order, number in brackets = institution)

Students to date (05/2016) : J.Vannitsen(8), A.Ansart(15,8), Q.Tahan(15,8), M.Agnan(10,8), J.Velardo(10,3), A.Deligny(10,3), G.Quinsac(11,10,3), ● A software-bench is functional to quantify the error A.Porquet(10,3,7), A.Lassissi(10,3), N.Gerbal(15), O.Sleimi(14,8), S.Durand(10,3,4), R.Klajzyngier(18), J.Diby(18,10,3), T.Mallet(18,8), propagation J.Foissaud(18), L.Orsatto(18), E.Colin(18), N.Heim(18), J.Lin(8,10,3), A.Tsai(8), A.Chen(8), J.Tsai(8), T.Chang(8), D.Boisseau(15,8), A.Sibué(11), J.Evens(11), A.Schnitzer(10,3), S.Thibault(10,3), H.Poincelin(10.3), S.Delaire(20), I.Berber(20), T.Charoy(20), A.Nirello(20), A.Sabir(20), M.Bougadouha(20), F.Le-coz(20), M.Gonzalez(20), M.Romero-Lopez(20), D.Gonzalez(20), I.Ouattara(8), K.Chun(8), ● F.Rizzitelli(8), E.Fournier-Bidoz(20), S.Wohlgemuth(20), F.Orstadius(20), Need to adapt and assess in the “asteroid” context C.Shen(18), J.Franel(18), T.Guidez(18), S.Sueur(18), A.v.Wesemael(18), B.Kalidas(18), R.Sabrekov(18), N.Traore(10,3,4).

Supervisors, experts and sponsors : B.Segret (4,9,3,1), B.Mosser (4,10,11), K.Wang (8), J.C.Juang (8), J.J.Miau (8), C.Koppel (16,17), J.Daniel (1), ● Anticipate an Extended Kalman Filter: Y.Desplanques (18), D.LePicart (18), P.Boutin (20), F.Deleflie (7,3,6,12,13), M.Cabane (5,12), M.Dudeck (12), K.L.Klein (4), N.Vilmer (4), R.Heidmann (1), P.Brisson (1,2), D.Coscia (5), G.Cimò (19). Ⱶ The right physical model? (sampled, analytical,...)

Ⱶ Set-up of the noise co-variance matrices? (process noise, measurement noise)

Segret @ iCubeSat 2016, Oxford, #27 / 27