On-board Orbit Determination for a Deep-Space CubeSat

Transcription

1 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 icubesat 26, Oxford, # / 27

2 Orbit Determination in (trajectory inspired by Dennis Tito for 28) (Quinsac et al., 26) (courtesy LPPT, European consortium for Liquid micropulsed Plasma Thruster, FP7 funded, TRL 3 in 25) (ESA's AIM mission to Didymos in 222) icubesat 26, Oxford, #2 / 27

3 st Context: Birdy in Deep-Space Cruise Study Case = Earth-Mars-Earth free return trajectory Mission Preparation 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 Science mode: for instance autonomous Space Weather Probe 3 (trajectory inspired by Dennis Tito for 28) icubesat 26, Oxford, #3 / 27

4 2nd Context: Birdy in Flying-legs Study case = released in situ by Mothercraft Ground Segment: Propagator with Models-in-the-loop Next Flying-legs to Mothercraft Models ESA (Galvez/Carnelli) Flight Segment 2 TCM: set new V~m/s ( day) 3 Science mode ( day ~8km) Echo/Doppler (multiple S/C) 2 3 Imaging surface features Optical astrometry 4 Navigation mode (OD+OC) 5 S-band TT&C to Mothercraft icubesat 26, Oxford, #4 / 27

5 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, 24) icubesat 26, Oxford, #5 / 27

6 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, 24) icubesat 26, Oxford, #6 / 27

7 Simplified Approach = M X C χ ( X ) = M X C 2 2 min ( X χ 2 ( X))? Assumption: Constant Velocity during N=4 measurements [ CC i, CS i, S i, CC i,2 CS i,2 S i,2 CC i,3 CS i,3 S i,3 CC i,4 CS i,4 S i,4 dt 2 dt 2 dt 3 dt 3 dt 4 dt 4 ][][ ] δ x δ y δ z δ x2 δ y2 δ z2 δ x3 δ y3 δ z3 δ x4 δ y4 δ z4 dr i, dt 2 dr i,2 dr i,3 dr i,4 dt j 3 Vx Vy Vz dt 4 CSCS i, CCSS i, C i, CSCS i,2 CCSS i,2 C i,2 CSCS i,3 CCSS i,3 C i,3 CSCS i,4 = CCSS i,4 C i,4 => 9 unknowns => 2 equations st simulation on Earth-Mars in /25 without optical errors, validations in 3/26 (T.Mallet, DAA/NCKU, 25) icubesat 26, Oxford, #7 / 27

8 Method for Monte-Carlo simulations Multidimensional Minimizing: = M X C χ ( X ) = M X C 2 (a) Steepest Descent algorithm preferred for on-board software not implemented yet 2 min ( X χ 2 ( X))? (b) or Random search on a grid (a) steepest descent along χ 2 ( X) may be an alternative, not implemented yet (c) or MATLAB / OCTAVE INV([C]) (b) random search while evaluating χ 2 ( X) (c) new 9x9 linear system χ 2( X ) = [C ]. X = Y X =[C ]. Y likely not for on-board software implemented here for MC simulations (( )) () x δ y z i=..4 = δ r j=..4 X Vx Vy Vz i measurements i=..4 for 9 unknowns j foreground bodies 4 from N foreground bodies icubesat 26, Oxford, #8 / 27

9 Earth-to-Mars E2M : initial results... If +m/s is applied on Y-axis at jettisoning wrt Reference Trajectory T do we correctly reconstruct the expected shift wrt T? Monte-Carlo series to estimate the mean reconstructed value <X>=f(σin) accuracy measurement σin << arcsec icubesat 26, Oxford, #9 / 27

10 Earth-to-Mars E2M : and limits If +m/s is applied on Y-axis at jettisoning wrt Reference Trajectory T do we correctly reconstruct the expected shift wrt T? Monte-Carlo series to estimate the mean reconstructed value <X>=f(σin) accuracy measurement σin = arcsec icubesat 26, Oxford, # / 27

11 Earth-to-Mars E2M : and limits If +m/s is applied on Y-axis at jettisoning wrt Reference Trajectory T do we correctly reconstruct the expected shift wrt T? Monte-Carlo series to estimate the mean reconstructed value <X>=f(σin) accuracy measurement σin = 5 arcsec icubesat 26, Oxford, # / 27

12 Elementary dynamic model Y+kY Y+kY actual trajectory reference trajectory km 3 /s 3 t3 ta a S be dies u o C of nd B y r u cto egro e j r a r tr al fo a e n tilin fictio c Re h 4 wit k s m/ alo 3 ng AU 2 2 AU 4 km. AU AU AU Z Y X icubesat 26, Oxford, #2 / 27

13 Elementary dynamic model Y+kY Rectilinear trajectory of CubeSat at 3km/s along 3 AU with 4 fictional foreground Bodies 3 actual trajectory reference trajectory km 3 /s 2 2 AU 4 km. AU AU AU Z Y X icubesat 26, Oxford, #3 / 27

14 Y+kY dispersions even at small σin The actual shift is small and constant (km) => assumption of small shift is not involved (Taylor dev.at st order) Numeric degeneracy is likely involved, due to small angular variations with large distances (begin & end). σin = (!) Y X icubesat 26, Oxford, #4 / 27

15 Y+kY dispersions even at small σin σin = -5 arcsec (!) Y X σout on dy *and* dvy, dvx! σout larger at large distances, on dv as well icubesat 26, Oxford, #5 / 27

16 Y+kY dispersions even at small σin σin = -3 arcsec (!) Y X σout on dy *and* dvy, dvx! σout larger at large distances, on dv as well icubesat 26, Oxford, #6 / 27

17 Y+kY dispersions even at small σin σin =. arcsec Y X σout on dy and dvy, dvx! σout larger at large distances, on dv as well icubesat 26, Oxford, #7 / 27

18 Realistic model E2M with small σin E2M σin =. arcsec and σin = arcsec Ea rth M to ar n2 i s 8 om t f r ns a T es atio t b r u g gw f C ropa n o i n p e on dies uis tory s i r t o t C c T e) traje ry at je nd B v r o t u is c ou k c listi rajec Y-ax regr c a a (bl 2 re ef.t s on r fo a R m/ an + copl on n 4 icubesat 26, Oxford, #8 / 27

19 E2M dispersions at small σin +m/s on Y: the actual shift wrt T is larger over time => assumption of small shift not valid in late σin =. arcsec => Mean value ~km accurate (wrt a few s km expected) in transverse or longitudinal directions σin =. arcsec icubesat 26, Oxford, #9 / 27

20 E2M dispersions at small σin +m/s on Y: the actual shift wrt T is larger over time => assumption of small shift not valid in late σin = arcsec => Mean value ~km accurate (wrt a few s km expected) in transverse or longitudinal directions σin = arcsec icubesat 26, Oxford, #2 / 27

21 E2M : <δx,δy,δz> at small σin σin =. arcsec => σout ~3 m (X,Z).. 5 m (Y) better results in the middle of the cruise? icubesat 26, Oxford, #2 / 27

22 E2M : <δx,δy,δz> at small σin σin = arcsec => σout > 2km (Y).. 4km (X,Z)!!! Mean value could be acceptable but it cannot be trusted due to σout icubesat 26, Oxford, #22 / 27

23 E2M : <δr>foreground bodies at small σin σin =. arcsec => σout ~5 m distance shifts are moderate, then increase σout few s of km icubesat 26, Oxford, #23 / 27

24 E2M : <δr>foreground bodies at small σin σin = arcsec => σout ~5 m distance shifts are moderate, then increase σout ~25 km (3 km / 2nd body) icubesat 26, Oxford, #24 / 27

25 E2M : <δvx,δvy> at small σin Velocities vary during On-board OD: at least in direction and +/-. m/s in intensities σin =. arcsec => σout > m/s σin = arcsec => σout > m/s (!!) icubesat 26, Oxford, #25 / 27

26 Temporary assessments Lessons from Y+kY fictional model Some dispersion with σin Numeric degeneracy (INV function) σout vs. σin is very sensitive, optical accuracy is the st driver close foreground bodies is the 2nd driver for the overall accuracy Shifts 2..3km vs km/s dimensionless approach Lessons from E2M realistic model The sensitivity seems to be well explained through Y+kY 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) icubesat 26, Oxford, #26 / 27

27 Conclusion: We've got a roadmap! Study about On-board Orbit Determination is still in progress : need to improve by 2-3 orders of magnitude on-board Steepest descent algorithm non-uniform velocity, N=5 measurements needed select the N best observables The required accuracy depends on the TCM potential BIRDY Technology is also a student project: More than 54 students have participated from 24 in France and in Taiwan Involved Institutions:.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, 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,.Centre d'etudiant pour la Recherche et l Exploration Spatiale,.Research University Paris Sciences Lettres, 2.Pierre and Marie Curie University, 3.Universite Lille Sciences et Technologies, 4.Institut Polytechnique des Sciences Avancees, 5.Ecole d'ingenierie des Sciences Aerospatiales, 6.Consortium Liquid Micro Pulsed Plasma Thruster, 7.KopooS Consulting Ind., 8.Ecole Centrale Lille, 9.Joint Institute for VLBI in Europe, 2.Ecole Centrale-Supelec Involved actors (chronological order, number in brackets = institution) A software-bench is functional to quantify the error propagation Need to adapt and assess in the asteroid context Anticipate an Extended Kalman Filter: Ⱶ Ⱶ The right physical model? (sampled, analytical,...) Students to date (5/26) : J.Vannitsen(8), A.Ansart(5,8), Q.Tahan(5,8), M.Agnan(,8), J.Velardo(,3), A.Deligny(,3), G.Quinsac(,,3), A.Porquet(,3,7), A.Lassissi(,3), N.Gerbal(5), O.Sleimi(4,8), S.Durand(,3,4), R.Klajzyngier(8), J.Diby(8,,3), T.Mallet(8,8), J.Foissaud(8), L.Orsatto(8), E.Colin(8), N.Heim(8), J.Lin(8,,3), A.Tsai(8), A.Chen(8), J.Tsai(8), T.Chang(8), D.Boisseau(5,8), A.Sibué(), J.Evens(), A.Schnitzer(,3), S.Thibault(,3), H.Poincelin(.3), S.Delaire(2), I.Berber(2), T.Charoy(2), A.Nirello(2), A.Sabir(2), M.Bougadouha(2), F.Le-coz(2), M.Gonzalez(2), M.Romero-Lopez(2), D.Gonzalez(2), I.Ouattara(8), K.Chun(8), F.Rizzitelli(8), E.Fournier-Bidoz(2), S.Wohlgemuth(2), F.Orstadius(2), C.Shen(8), J.Franel(8), T.Guidez(8), S.Sueur(8), A.v.Wesemael(8), B.Kalidas(8), R.Sabrekov(8), N.Traore(,3,4). Supervisors, experts and sponsors : B.Segret (4,9,3,), B.Mosser (4,,), K.Wang (8), J.C.Juang (8), J.J.Miau (8), C.Koppel (6,7), J.Daniel (), Y.Desplanques (8), D.LePicart (8), P.Boutin (2), F.Deleflie (7,3,6,2,3), M.Cabane (5,2), M.Dudeck (2), K.L.Klein (4), N.Vilmer (4), R.Heidmann (), P.Brisson (,2), D.Coscia (5), G.Cimo (9). Set-up of the noise co-variance matrices? (process noise, measurement noise) icubesat 26, Oxford, #27 / 27