Validation of Astrodynamic Formation Flying Models Against SPACE-SI Experiments with Prisma Satellites

Transcription

1 Validation of Astrodynamic Formation Flying Models Against SPACE-SI Experiments with Prisma Satellites Drago Matko, Tomaž Rodič, Sašo Blažič, Aleš Marsetič, Krištof Oštir, Gašper Mušič, Luka Teslić, Gregor Klančar, Marko Peljhan, David Zobavnik Space-SI, Aškerčeva cesta, 000 Ljubljana, Slovenia Robin Larsson, Eric Clacey, Christian Svärd, Thomas Karlsson OHB Sweden AB Small Satellite Conference, Logan, Utah, August 3-6, 0

2 OUTLINE. INTRODUCTION. OBSERVATION OF NON-CO-OPERATIVE OBJECTS EXPERIMENT 3. SIMULATED DISTRIBUTED INSTRUMENT REMOTE SENSING EXPERIMENT 4. SIMULATED RADAR INTERFEROMETRY REMOTE SENSING EXPERIMENT 5. FORMATION FLYING MODELS 6. VALIDATION OF THE MODELS AGAINST THE PRISMA EXPERIMENT 7. CONCLUSION Small Satellite Conference, Logan, Utah, August 3-6, 0

3 . INTRODUCTION To investigate newly emerging technologies SPACE-SI and OHB Sweden performed a set of formation flying experiments in September 0 with Prisma satellites. Mango and Tango were launched into a sun synchronous orbit with 75 km altitude and 06.00h ascending node in June 00. In the SPACE-SI formation flying experiments the critical maneuvers for three types of missions were investigated with respect to in-orbit performances: Observation of non-co-operative objects - space debris In-flight simulated distributed instrument In-flight simulated radar interferometry Small Satellite Conference, Logan, Utah, August 3-6, 0 3

4 . OBSERVATION OF NON-CO-OPERATIVE OBJECTS EXPERIMENT It is expected that non-co-operative objects such as space debris will become a serious problem in the near future. The orbits of debris often overlap with trajectories of operational spacecrafts, and represent a potential collision risk. In order to remove the debris, it must be identified. Two experiments were performed to simulate the required procedures: Orbit identification Close observation Small Satellite Conference, Logan, Utah, August 3-6, 0 4

5 . Orbit identification On the basis of the space debris Two Line Elements (TLE) the Mango s VBS camera was directed in the direction of the point of the closest approach and several images were taken in a sequence. The Simulation toolkit (AGI - STK) was used to simulate the trajectories of the Mango and debris. The newest TLE database was used to identify the satellites or debris flying closer to Mango than 5 km as well as the corresponding time frame. The criteria for choosing the objet to be observed with Mango vision based camera (VBS), was the distance and the vicinity period. Also additional constraints were considered: the camera should not be pointing neither towards the Sun nor towards the Earth. Small Satellite Conference, Logan, Utah, August 3-6, 0 5

6 STK simulation (upper) and VBS camera shots of: Geosat (ID 5595) right 3 pictures and SL-4 R/B (ID 37) left 4 pictures Timeframe: , 09:5:57-09:6:56 Animation Small Satellite Conference, Logan, Utah, August 3-6, 0 6

7 .. Close observation Several pictures of Tango (which simulated the debris) were taken in order to make a 3D model of the observed object. Mango was pointing with its Digital Video System (DVS) camera towards Tango, A. The satellites were flown in the (in-track) distance of 5 m,tango was rotating around (with a bit of wobbling) its cross-track axis, pointing all times with its solar panels toward the sun. Reconstruction was presentet at 4S Symposium Portorož, June 0 B. A circumvolution of Tango by Mango and an encircling of Tango by Mango in a relative 60 degrees inclined orbit on a circle with radius 0 m was performed. The timing of imaging (during encircling) was adjusted to have some areas of interest on the Earth (Kuwait, Djibouti and Crete) in the background Experiment animation (real data) Small Satellite Conference, Logan, Utah, August 3-6, 0 Reconstructed model animation 7

8 3. SIMULATED DISTRIBUTED INSTRUMENT REMOTE SENSING EXPERIMENT A satellite camera is formed by two satellites. One of the satellites holds the optical system with lenses and/or mirrors and the other one the detectors (sensors). In this case the idea is to form a telescope that can acquire highresolution multispectral images of the Earth s surface with the use of two small satellites instead of one big and more expensive satellite. In this experiment the Tango was simulating the holder of the optical system with lenses and/or mirrors while Mango, simulating the holder of detectors (sensors), was driven to an appropriate position. This experiment was performed in two different versions: In-track displacement (satellites flying one after the other) Radial and cross-track displacement (satellites flying one above the other) Small Satellite Conference, Logan, Utah, August 3-6, 0 8

9 3.. In-track displacement To obtain a high multispectral resolution and to keep the combined instrument as small as possible both satellites should be placed close to each other, in the range of less than 5 m. One of the satellites must carry a mirror at an angle of approximately 45 that reflects the beam to the detectors on the other satellite. This formation is preferable as the consumption of propellant is very small. The results were presentet at the 4S Symposium Portorož, June 0 Small Satellite Conference, Logan, Utah, August 3-6, 0 9

10 3.. Radial and cross-track displacement The satellites were aligned with predefined target locations on the Earth, such as Cape Town, Piran Animation (real data) Small Satellite Conference, Logan, Utah, August 3-6, 0 0

11 Next day: Punta Arenas Small Satellite Conference, Logan, Utah, August 3-6, 0

12 Piran May 9,0 Small Satellite Conference, Logan, Utah, August 3-6, 0

13 4. SIMULATED RADAR INTERFEROMETRY REMOTE SENSING EXPERIMENT The along-track synthetic aperture radar interferometry uses two separate radar antennas arranged longitudinally along the direction of flight; one of the satellites acts as the SAR transmitter and receiver, while the other is a receiver only Mango and Tango were flown one behind the other (along-track) separated by a distance of approximately 00 m for three consecutive orbits. The results were presentet at the 4S Symposium Portorož, June 0 Small Satellite Conference, Logan, Utah, August 3-6, 0 3

14 5. FORMATION FLYING MODELS Follower dynamics in the Leader RIC co-ordinate system. ( R x) x y y x a x (( R x) y z ) y y x x y a y (( R x) y z ) 3 3 R z z (( R x) y z ) Leader orbit: R R R R R R R R 3 a z Slika z oznakami Leader follower μ - Earth gravitational constant φr - True anomaly a - Accelerations Small Satellite Conference, Logan, Utah, August 3-6, 0 4

15 R (0) a R (0) 0 (0) n Application of the Method of perturbations to leader s orbit equations: R a R n R R Expanding Leader orbit eq. into Taylor series and collecting terms with respect to ε yields: R an n R R a a 3 an Rn 3 R... Rn RR n R 3 (...)... a a a R an 3n R n R a HCW R a n n 3 a = mean motion HCW = Hill-Clohessy-Wiltshire Linear model - method of perturbation Higher order terms Small Satellite Conference, Logan, Utah, August 3-6, 0 Linear model method of perturbation Animation 5

16 Application of the Method of perturbations to the Follower s dynamics equations x ( t) x ( t) x( t) p c y ( t) y ( t) y( t) p c z ( t) z ( t) z( t) p c x( t) x ( t) y( t) y ( t) z( t) z ( t) Hill-Clohessy-Wiltshire Linear model - method of perturbation Higher order terms Expanding Follower dynamics eq. into Taylor series and collecting terms with respect to ε yields: x ny n x 3 c c c ( x 4nyc cos nt ny n yc sin nt n x 4n xc cos nt) (...) (...)... 3 n xc (n x 6n xc cos nt) (...) (...)... y nx n y c c c a 3 ( y 4nxc cos nt nx n xcsin nt n y 4n yccos nt) (...) (...) 3 c ( n y 3n c c t (...) (... x... ny y o s n ) )... a y z z n z ( n z 3n z cos nt) (...) (...)... a 3 c c z Small Satellite Conference, Logan, Utah, August 3-6, 0 6

17 HCW x ny 3nx a y nx c c c x c c a y z nz a c c z Linear model method of perturbation x (0) z (0) 0; y (0) y 0 x (0) ny ; y (0) z (0) 0 0 Animation x ny 3 n x (0n x 4 ny ) cos nt n y sin nt c c c y nx n y nx nt n y nt ( c 4 c) cos c sin z n z n z nt 3 c cos. Small Satellite Conference, Logan, Utah, August 3-6, 0

18 x [m] x [m] y [m] 6. VALIDATION OF THE MODELS AGAINST THE PRISMA EXPERIMENT Optimization cost function: N m m m i i i i i i N i 0 D x x y y z z Hill-Clohessy-Wiltshire Linear model - method of perturbation STK J & HPOP HCW Nonlin,Lin-Pert, STK EMP STK J,HPOP, HPOPa measured HCW Nonlin,Lin-Pert, STK EMP STK J,HPOP, HPOPa y [m] HCW Nonlin,Lin-Pert, STK EMP STK J,HPOP, HPOPa t [s] t [s] Small Satellite Conference, Logan, Utah, August 3-6,

19 5. CONCLUSION A set of experiments performed by SPACE-SI and OHB Sweden in September 0 with Prisma satellites was reviewed. The observation of non-co-operative objects - space debris experiment has demonstrated that space debris, can be identified on the basis of the TLE data and optically tracked by a narrow angle camera. The simulated distributed instrument experiment, where one of the satellites holds the optical system with lenses and/or mirrors and the other one the detectors (sensors), provided attractive pictures by the positioning of the satellites in order to align with predefined targets (Piran, Cape Town, Punta Arenas). The simulated radar interferometry remote sensing experiment data were used to validate different formation flying models, among them the newly proposed linear model for small eccentricities, developed by the method of perturbations. Small Satellite Conference, Logan, Utah, August 3-6, 0 9