Validation of Astrodynamic Formation Flying Models Against ... · Validation of Astrodynamic Formation Flying Models Against SPACE-SI ... (AGI - STK) was used to ... STK EMP STK J2,HPOP,

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 12, 1000 Ljubljana, Slovenia

Robin Larsson, Eric Clacey, Christian Svärd, Thomas Karlsson

OHB Sweden AB

Small Satellite Conference, Logan, Utah, August 3-16, 2012 1


1. INTRODUCTION

2. OBSERVATION OF NON-CO-OPERATIVE

OBJECTS EXPERIMENT

3. SIMULATED DISTRIBUTED INSTRUMENT

REMOTE SENSING EXPERIMENT

4. SIMULATED RADAR INTERFEROMETRY


5. FORMATION FLYING MODELS

6. VALIDATION OF THE MODELS AGAINST

THE PRISMA EXPERIMENT

7. CONCLUSION

OUTLINE

1. INTRODUCTION

• To investigate newly emerging technologies

SPACE-SI and OHB Sweden performed a

set of formation flying experiments in

September 2011 with Prisma satellites.

• Mango and Tango were launched into a sun synchronous orbit with 725 km altitude and

06.00h ascending node in June 2010.

• 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


• 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 space-crafts, 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:

2. OBSERVATION OF NON-CO-OPERATIVE

OBJECTS EXPERIMENT

Orbit identification

Close observation


• 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 25 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.

2.1 Orbit identification


Fig. 4: Real camera shot 2011 09 20, 09:26:50.254,. 09:26:53.254 and 09:26:56.254

Animation

STK simulation (upper) and VBS camera shots of:

Geosat (ID 15595) – right 3 pictures and

SL-14 R/B (ID 22237) – left 4 pictures

Timeframe: 2011 09 20, 09:25:57 - 09:26:56


SpaceDebris.wmv

Debris_kratek.wmv

2.2. 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 2012

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 20 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

Small Satellite Conference, Logan,

Utah, August 3-16, 2012 7

Experiment animation (real data)

Reconstructed model

animation

Kuw_Dji_in_obkrozanje_fullHD.wmv

Tango_3D_DVS.wmv

3. SIMULATED DISTRIBUTED INSTRUMENT


• 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 high-

resolution 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 3-16, 2012 8

3.1. 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 2012


3.2. Radial and cross-track displacement


The satellites were aligned with predefined target locations on the Earth,

such as Cape Town, Piran

Animation

(real data)

Pir_Cap_Pir_kratek.wmv

Next day: Punta Arenas


Utah, August 3-16, 2012 11


Piran May 9,2012


• 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 200 m for three consecutive

orbits.

• The results were presentet at the 4S Symposium Portorož, June 2012

4. SIMULATED RADAR INTERFEROMETRY



5. FORMATION FLYING MODELS

Slika z oznakami

Leader follower

2

2RR R

R

2R

R

R

R

Follower dynamics in the Leader RIC co-ordinate system.

Leader orbit:

μ - Earth gravitational constant

φR - True anomaly

a - Accelerations

32

2

2 2 22

(( ) )y

yy x x y a

R x y z

322 2 2(( ) )

z

zz a

R x y z

32

2

22 2 2

( )2

(( ) )x

R xx y y x a

RR x y z


R a R

n

1

1

R R

2

1

2

1 1

2 3

1

2 11 12 1 3

2 ...2 2R

R an n Ra

R nana

R

11 2 2 31 1 1

21

2 2(... . .

2.)

R RR n n

a aa

R

Application of the Method of perturbations to leader‘s orbit equations:

1 1

2nR

a

2

1 1 12 3R an n R

HCW

HCW = Hill-Clohessy-Wiltshire

Linear model - method of perturbation

Higher order terms

Linear model –

method of

perturbation

Animation

1

1

1

(0)

(0) 0

(0) 2

R a

R

n

3n

a

= mean motion

n R a

Expanding Leader orbit eq. into Taylor series

and collecting terms with respect to ε yields:

film21_fullHD.wmv


1

1

1

( ) ( )

( ) ( )

( ) ( )

x t x t

y t y t

z t z t

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

p c

p c

p c

x t x t x t

y t y t y t

z t z t z t

2 2 2

1 1 1

2

2 3

2 3

1

2

22

( 4 cos 2 2 sin 4 cos )

(2 6 cos )

(...) (...)

(...) (...

...

.2 ) ..

2 c c c

c

c c c

c x

x ny nt ny n y nt n x n x nt

n x n x n

x ny n x

n x at

2 2 2

1 1 1

2

2 3

2 3

2

2 2

1

( 4 cos 2 2 (...) (...)

(...) (..

sin 4 cos )

( 3 c .

...

.s ) .o ) .

2c c c

c

c c

c y

cy nx nt nx n x nt n y n y nt

n y n

y nx n y

n y y n at

2 2 32

1

2

1( 3 cos ) ..(...) (...) .c c zn z n z ntz z n z a

Application of the Method of perturbations to the Follower‘s dynamics equations

Hill-Clohessy-Wiltshire


Higher order terms

Expanding Follower dynamics eq. into Taylor series

and collecting terms with respect to ε yields:

17

Small Satellite Conference, Logan, Utah, August 3-16, 2012

HCW Linear model –

method of

perturbation

Animation

2 2 2

1 1 12 3 (10 4 )cos 2 sinc c cx ny n x n x ny nt n y nt

2 2

1 1 3 cos .cz n z n z nt

22 3

2

2

c c c x

c c

c c z

ya

x ny n x a

y nx

z n z a

1 1 1 0

1 0 1 1

(0) (0) 0; (0)

(0) ; (0) (0) 0

x z y y

x ny y z

2 2

1 12 ( 4 )cos 2 sinc c cy nx n y nx nt n y nt

film43_fullHD.wmv


6. VALIDATION OF THE MODELS AGAINST

THE PRISMA EXPERIMENT

195 196 197 198 199 200 201 202 203 204-1.5

-1

-0.5

0

0.5

1

1.5

y [m]

x [

m]

measured

HCW

Nonlin,Lin-Pert, STK EMP

STK J2,HPOP, HPOPa

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

t [s]

x

[m

]

HCW


STK J2,HPOP, HPOPa

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

t [s]

y

[m

]

HCW


STK J2,HPOP, HPOPa

Hill-Clohessy-Wiltshire


STK J2 & HPOP

2 2 2

0

1 Nm m m

i i i i i i

i

D x x y y z zN

Optimization cost function:

5. CONCLUSION


Utah, August 3-16, 2012 19

• A set of experiments performed by SPACE-SI and OHB Sweden in

September 2011 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.

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Validation of Astrodynamic Formation Flying Models Against ... · Validation of Astrodynamic Formation Flying Models Against SPACE-SI ... (AGI - STK) was used to ... STK EMP STK J2,HPOP,