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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
Small Satellite Conference, Logan, Utah, August 3-16, 2012 2
1. INTRODUCTION
2. 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
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
Small Satellite Conference, Logan, Utah, August 3-16, 2012 3
• 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
Small Satellite Conference, Logan, Utah, August 3-16, 2012 4
• 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
Small Satellite Conference, Logan, Utah, August 3-16, 2012 5
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
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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
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Utah, August 3-16, 2012 7
Experiment animation (real data)
Reconstructed model
animation
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 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
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3.2. Radial and cross-track displacement
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The satellites were aligned with predefined target locations on the Earth,
such as Cape Town, Piran
Animation
(real data)
Next day: Punta Arenas
Small Satellite Conference, Logan,
Utah, August 3-16, 2012 11
Small Satellite Conference, Logan, Utah, August 3-16, 2012 12
Piran May 9,2012
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• 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
REMOTE SENSING EXPERIMENT
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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
Small Satellite Conference, Logan, Utah, August 3-16, 2012 15
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:
Small Satellite Conference, Logan, Utah, August 3-16, 2012 16
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
Linear model - method of perturbation
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
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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
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]
y
[m
]
HCW
Nonlin,Lin-Pert, STK EMP
STK J2,HPOP, HPOPa
Hill-Clohessy-Wiltshire
Linear model - method of perturbation
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
Small Satellite Conference, Logan,
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.