1. INTRODUCTION
Formation flight is expected to bring out new possibility
of space missions. One important issue of formation
flying satellites is the amount of propellants, when conventional
propulsion system is applied to keep the formation.
It often limits the mission lifetime. Electromagnetic
formation flight (EMFF) technique is proposed to
keep the formation without any propellants, and overcome
this problem (Ninomiya et al. 2001; Miller et al.
2003.2). This technique uses electromagnetic force generated
by magnetic dipole on each satellite. Usually, huge
amount of magnetic dipole is required to keep the formation
against Kepler motion, and it requires superconducting
coil to be equipped.
To apply such electromagnetic formation flight technique
for low earth orbit missions, interference between huge
magnetic dipole and earth magnetism causes problems.
It generates huge torque on the satellite, and the angular
momentum rapidly excess momentum wheel capability.
To suppress this interference, polarity of magnetic dipole
should changes in short period, compared to the orbital
period. The authors also proposed to use inductancecapacitance
resonant circuit to change magnetic dipole
polarity (Hashimoto et al. 2002). Desired electromagnetic
force can be generated with proper phase difference
between exciting current, and this phase difference can
be controlled with impulse voltage input. The advantage
of this proposed method is its small energy consumption.
This paper describes the details of this proposed method.
Experimental was also curried out to control the current
phase of superconducting coil, and it reveals the effectiveness
of our method. It is also demonstrated with hardware
in the loop simulation, which combines satellite dynamics
model and actual superconducting coil circuit.
2. FORMATION CONTROL USING MAGNETIC
FORCE IN LEO
2.1. Mission Example and Satellite Configuration
This paper discusses on formation flight missions in
LEO. It is known that farther orbit, such as Halo orbit
around the second libration point of the Sun-Earth system
(L2), is also attractive from the view point of perturbations,
thermal environment and so on. However,
lower orbit has another advantagesuch as lower launch
cost, higher data rate of communication link, etc. In addition,
X-ray or Gamma-ray observation hate radiation
belts and prefer LEO.
To discuss the control system design in the concrete, here
some example LEO mission is assumed. The example
mission in this paper is some X-ray or Gamma-ray observation.
It means that the mission consists of two satellites,
such as mirror and detector. These two satellites are
Target
Chaser
one coil
along z-axis
3 magnets along x, y z axis
N
S
3 coils along x, y z axis
one magnet
along z-axis
Figure 1. Formation flight with super-conducting magnets
called here gTargeth and gChaserh (Fig. 1). The chaser
satellite controls the relative position to maintain the formation,
in contrast to the target one which has no ability
of active position control. To function as a telescope, the
relative position must be maintained in inertial coordinate,
to point some target. It is assumed that the focal
length or satellite distance should be maintained to be
10[m], with accuracy of 2 [mm]. In this example mission,
both satellites weigh 500 [kg] and are injected into
LEO of about 600[km] altitude.
2.2. Required Force and Magnetic Moment
The required force to maintain the relative position in
LEO can be calculated,
σ2
k ? a ? σ2
k1 + 3cos2 , (1)
where a and k are the magnitude of control
acceleration and orbital angular velocity, respectively
(Hashimoto et al. 2002). is the inclining angle
of the relative position vector against the orbital plain.
Equation (1) describes the minimum and maximum required
force during orbital period. Formation with =
90[deg] means the gorbit normalh formation case, depicted
in Fig. 2, and the required force is independent
from the satellite position in orbit (eq. 1). On the contrary,
= 0[deg] gin-orbith separation (Fig 2) requires
force varying between σk and 2σk. Obviously, the latter
case is more challenging case from the view point of
control, thus gin-orbith formation ( = 0[deg]) is discussed
in this paper.
K
I
Keplerian Orbit
Formation Flying Orbit
Initial Displacement
J
I
Initial Displacement
Formation Flying Orbit
Keplerian Orbit
Figure 2. gOrbit normalh(left) and gIn-orbith(right) formations.
Hashimoto et al. (2002) calculates required force in orbital
coordinate system, and it can be transformed into
inertial coordinate. For gin-orbith formation case, it is
F = mσ2
k
2 ?3 sin2kt
0
?1 ? 3 cos 2kt. (2)
m denotes reduced mass of satellite 1,
t = mCmT
mC + mT
, (3)
1Note that action-reaction force is discussed here.
where mT , mC are the mass of target and chaser satellites,
respectively. This force is disturbance force to the
position control system, thus it is called gorbital disturbanceh
or gtidal disturbanceh in this paper. The frequency
of this disturbance force is 2 k, as shown in eq. (2).
When MT and MC denote the magnetic dipole moments
on target and chaser satellites respectively, magnetic
force acting on the chaser target can be described as
follows 2,
F = (MC E BC) , (4)
where BC is the magnetic flux density, which can be formulated
withMT ,
BC = 0
4 ?
MT
3 +
3(MT E )
3 + BEC. (5)
where 0 is the permeability of free space, BEC is the
magnetic flux density caused by the Earth magnetic field,
and is the relative position vector between the satellites.
For example, if two magnetic moments of same magnetic
momentM align with distance , magnetic force Fmag is
Fmag =
30M2
2r4 . (6)
Equations (6) and (1) suggest the amount of magnetic
moments. Kaneda et al. (2004) plots this relations versus
relative distance. The example mission in this paper assumes
the distance of 10 [m] and orbit altitude 600 [km],
which means k = 0.0011[rad/sec], and eq.(1) estimates
the magnitude of orbital disturbance force to be 6.1 [mN].
Magnetic moments of 30,000 [Am2] generates 54 [mN]
force with eq. (6), and can overcome the tidal disturbance
force, even if the efficiency is down with sinusoidal driving
described in the following sections.
2.3. Necessity of Alternating Magnetic Moment
Then the effect of earth magnetic field should be considered.
Magnetic force is proportional to the spatial gradient
of magnetic field, as eq. (4) shows, thus the force on
the magnetic moment caused by earth magnetic filed is
negligible. However, the magnetic torque is proportional
to the magnitude of magnetic field,
T =M ~ B. (7)
Roughly speaking, the magnetic moment of 30,000
[Am2] generates about 0.9 [Nm] DC torque, which is not
able to be accumulated in practical momentum wheels.
For this problem, the authors proposed to use alternating
magnetic moment (Hashimoto et al. 2002). If sinusoidal
magnetic moment such as M = M0 sin(ct) is applied,
and if the angular frequency c is much higher than the
frequency of magnetic field or orbital angular frequency
k, then this accumulation of angular momentum comes
to be small enough.
2Note that EB formulation is used here, not EH formulation, thus
unit of magnetic moment is [Am2], not [Wbm]
To control the magnetic force with such sinusoidal
moments, the authors proposed to use the phase difference
between the target and chaser magnetic moment
(Kaneda et al. 2004). If magnetic moment on chaser
satellite has phase difference compared to the target
magnetic moments, simplified example eq.(6) turns into
Fmag =
30M2
0
4r4 (cos(2ct + ) ? cos ) , (8)
and the average of Fmag during a period is
Fmag = ?
30M2
4r4 cos . (9)
Equation (9) indicates that DC components of magnetic
force can be changed with the phase difference , thus it
can be used as a control input if the feedback controller
bandwidth is much lower than c. In other words, the
first term of eq.(8) behaves as disturbance force around
this DC components, with frequency of 2 c. This disturbance
is called gcoil 2 c disturbanceh in the following
parts. Note that this frequency is always higher than
the control bandwidth, thus it can not be suppressed by
control. From the view points of controller bandwidth or
disturbance frequency, coil driving frequency c should
be high enough. However, there is some trade-off on frequency
choice, since higher frequency results high coil
voltage. Relationship between the frequency and disturbance
force gives some suggestions about the goptimalh
frequency in this trade-off. To evaluate the relative position
error caused by 2 c components of magnetic force,
transfer function from the disturbance to position error
should be considered. Since the frequency c is out of
the control bandwidth as mentioned above, it can be calculated
only with satellite dynamics of translational motion,
P(s) =
1
s2 , (10)
where s denotes Laplace operator. With this dynamics
and AC components of eq.(8), relative position error can
be expressed
c =
30M2
44
1
42
c
. (11)
As mentioned in 2.1, assumed accuracy requirement is 2
[mm]. Then c is chosen here to be 0.08 [Hz], which
causes 0.11[mm] 2c position error as eq.(11) shows.
2.4. Understanding about the Gravity Gradient
Torque on the System
Torque on the magnetic moment caused by earth magnetic
field is briefly mentioned in the previous subsection.
Here we discuss on magnetic torque which appears
in the target-chaser system. Substituting the first term of
eq.(5) into eq.(7) and simplified using same assumption
as eq.(6), magnetic torque on chaser caused by targetfs
magnetic field, TTC, is
TTC = 0M2
0
43 (cos(2ct + ) ? cos ) . (12)
In this equation, the average of the first term is equal to
zero, however, the second term depends on the phase different
, or the magnetic force to control the formation.
This relationship indicates the important aspect of EMFF.
When two satellites are gconnectedh with magnetic force,
then it can be considered as a long rod. Such a long
rod in LEO is, of course, affected by gravity gradient
torque. Cross product of eq.(2) and [0, 0, r]t gives this
torque Tgg,
Tgg = 0,
3
2m22
k sin 2kt, 0. (13)
Time integration of this torque results the angular momentum,
Lgg,
Lgg = 0, ?
3
4m2k cos 2kt, 0, (14)
which can be calculated to be 20.2 [Nms], using m =
250[kg], k=0.0011 [rad/sec] and =10[m]. Since EMFF
maintain the formation with magnetic force, or internal
force, this angular momentum of eq.(14) must be accumulated
in the system. Therefore, to maintain the formation
in inertial frame, two satellites must accumulate this
angular momentum, and to maintain the satellite attitude,
the remaining possibility is the momentum wheels on the
satellites. In another words, magnetic moment to generate
control magnetic force also generates torque in the
magnetic field of the other satellite, as shown in eq.(12),
and to cancel this magnetic torque, angular momentum
should be finally accumulated in the momentum wheels.
The authors point out here that this is important understanding
about EMFF mechanism.
2.5. Sizing of Actuators
At the end of this section, the size of actuators are estimated
reflecting above discussions. Magnetic moment
of 30, 000[Am2] requires super-conductive magnet, and
based on some discussions with super-conductive coil
manufacturer, magnetic coil described in table 1 is practical
enough and meets the requirements. The wire material
is high-temperature superconducting one, thus the
maximum temperature is 77 [K]. A cooling machine
weight required to cool three coils is estimated to be 100
[kg].
Another component which should be discussed here is
momentum wheels. As discussed, maximum disturbance
torque caused by magnetic moment in earth magnetic
field, will be 0.9 [Nm], although accumulation as angular
momentum is negligible. Torque in the magnetic field
of the other satellite is small, however, it generates angular
momentum such as 20 [Nms]. Momentum wheel of
10-15[kg] will have such capability of torque and angular
momentum.
Table 1. Example spec. of required superconductive magnet.
Radius Length Wire Turns Current Weight
0.9 m 0.5 m 2381 T 15 A 40 kg
3. RELATIVE POSITION CONTROL SYSTEM
3.1. Feedback Controller Design
Feedback controller design is briefly introduced in this
subsection. The requirement for the controller is suppress
the tidal disturbance force to achieve relative position
accuracy of 2 [mm]. The constraint is that the
control bandwidth must be lower enough than c, since
gaverageh magnetic force is used as the control input as
expressed in eq.(8). To meet these requirements and the
constraint, PID controller is designed using Coefficient
Diagram Methods (CDM) (Manabe 1998.8), with following
parameters,
KI =
12.5m
3 ,KP =
12.5m
3 ,KD =
5m
, (15)
where is so-called equivalent time constant and chosen
to be 80[sec]. Figure 3 shows the designed feedback
controller performance with transfer function from disturbance
to relative position. The frequency of two main
disturbances, tidal disturbance and coil 2c disturbance,
is also plotted.
10-3 10-2 10-1 100
10-3 10-2 10-1 100
-50
-40
-30
-20
-10
0
10
Gain [dB]
-180
-135
-90
-45
0
45
90
Frequency [rad/s]
Phase [deg]
-9.0 dB (5.8 mN)
Orbital (tidal) disturbance
-48.0 dB (27.0 mN)
Coil disturbance
Figure 3. Transfer function from disturbance to relative
position.
3.2. Magnetic Force Regulator using Phase Difference
between exciting currents
Basic idea to control the magnitude of magnetic force
has already introduced in previous section, using eq.(8)
and eq.(9). In this paper this concept is called gmagnetic
force regulatorh, and this section discusses the extension
of eq.(9) to three dimensional equation.
Equation (4) can be also expressed as
F = DBC, (16)
where D is 3 ~ 3 symmetric matrix,
D =
????????
Bx
x
By
x
Bz
x
Bx
y
By
y
Bz
y
Bx
z
By
z
Bz
z
????????
. (17)
The configuration of magnetic moment is depicted in
Fig. 1, thus MT = [0, 0,MTz]. Using this MT , each
element of this matrix can be developed,
D11 = Dmag 2MTxx + (MT E r) ?
5 (MT E r) x2
2
= Dmag MTzz ?
5MTzz
2 x2 (18)
D12 = Dmag MTyx +MTxy ?
5 (MT E r) yx
2
= Dmag ?
5MTzz
2 xy (19)
D13 = Dmag MTzx +MTxz ?
5 (MT E r) zx
2
= Dmag ?
5MTzz
2 zx (20)
E E E
D33 = Dmag 2MTxz + (MT E r) ?
5 (MT E r) z2
2
= Dmag 3MTzz ?
5MTzz
2 z2, (21)
where
Dmag =
30
45 . (22)
To simplify eq.(21), approximation around operational
point [x, y, z]t = [x,y, z]t is applied, as
D11 = DmagMTzz 1 ? 5x2
z2
D12 = DmagMTzz ?5yx
z2
D13 = DmagMTzz ?5x
z
E E E
D33 = ?2DmagMTzz
(23)
and if assume x/z 1 and y/z 1, the D comes
to be diagonal matrix, with
D11 = DmagMTzz, (24)
D22 = DmagMTzz, (25)
D33 = ?2DmagMTzz. (26)
Therefore, each component of magnetic force,
FCx, FCy and FCz can be independently controlled
with MCx,MCy and MCz, respectively. These three
components can be described easily with almost same
equation, such as eq.(8) or (9). Finally, phase difference
which generates required force can be found to solve
inversion problem of eq.(9), using arc cosine or its
linearly approximation (Kaneda et al. 2004).
4. IMPLEMENTATION AND EXPERIMENTS OF
PHASE DIFFERENCE CONTROL
4.1. Proposed Circuit for Phase Difference and Amplitude
Controller
This section discusses how to generate sinusoidal magnetic
moment and how to control its phase. If current
control technique is applied using power electronics devices,
any required waveform of current can be generated,
however, such approach is energy consuming. Therefore,
it is proposed to use resonant circuit using superconductive
coil and large capacitor, such as electric double layer
capacitor. Then, how the phase should be controlled for
such LC resonant circuit? The authors proposed to apply
impulsive voltage input to change the phase of excitation
current. Figure 4 shows the concept of the proposed
method. As this figure shows, this method also has the
capability to control the amplitude of the current. It is
desirable capability, since there remains some small resistance
in the whole circuit, even if superconductive coil
is used.
The dynamics of the circuit depicted in Fig.5 can be analyzed
as follows. With a state variable x = [q ir]T ,
?x
= ???
Aoff x . . . S:OFF
Aon x + BonVE . . . S:ON
(27)
Aoff = ???
0 ?1
1
LC ?
RC
L
???
, ( R = RE + RC)
Aon = ????
?
1
RC ?
RE
R
RE
RLC ?
RERC
RL
????
, Bon = ????
1
R
RC
RL
????
.
where L,RE, C, VE are the value of inductance, resistance,
capacitor and voltage source, respectively. q, ir
denotes the amount of capacitor charge and resonance
current, respectively.
Using eq.(27) and some approximations, the amount of
phase shift and capacitor voltage change Vc can be
calculated when switch S is ON for t [sec] as follows,
vc0 =
1
2REC {2VE cos ?vc0 (1+ cos 2)} t,
= ?
1
2q0RE
(2VE sin ?vc0 sin 2) t, (28)
where q0, vc0 is the amplitude of capacitor charge and
voltage. is the capacitor phase when switch S turns
ON, and = 0 means the capacitor voltage is equal to
zero. Equations ( 28) indicate that both phase and amplitude
can be controlled independently at = 2n and
= /2 + 2n, respectively, where n = 0, 1, 2 . . . .
Capacitor voltage
Phase shift
Input of impulse voltage
Amplitude
increase
Before applied
After applied
Capacitor voltage
Input of impulse voltage
Amplitude
increase
Before applied
After applied
Figure 4. The idea to shift the phase (left) and to change
the amplitude (right) of the resonance current.
VE , -VE L
RE RC S
iE
ir
Resonance Circuit
C
q
+ + + + +
PSC
vC
HTS
Figure 5. Circuit structure to achieve phase-shifting and
amplitude-changing of the resonant circuit.
-10
-5
0
5
10
0
Phase Change [rad(deg)]
-/6
(-30)
/6
(30)
Amp. Change??vc0 [V]
Impusive Voltage Input Timing : Phase of Capacitor Voltage [deg]
0 /4 /2 3/4 5/4 3/2 7/4 2
0 /4 /2 3/4 5/4 3/2 7/4 2
0 V
10 V
21 V
42 V
63 V
84 V
VE
Figure 6. Phase and amplitude change is plotted vs. voltage
input timing , for various VE.
4.2. Experimental Results of Phase Difference and
amplitude Controll
Experiments using superconductive coil were carried out,
to evaluate the proposed methods, to control the phase
and amplitude of resonance current with impulsive voltage
input. Fig. 7 is a photo of the experimental setup and
Table 2 shows the specification of superconductive coil
in this experimental setup. In this setup, a current sensor
measures the resonance current ir, and it is transferred to
the computer. The computer calculate the amount of t
and waits the proper timing, the output a signal to turn on
the switch S, which is implemented with FET device.
Figure 8 shows one example of experimental results. In
this experiment, amplitude control was applied to sustain
the resonance current against the resistance decay. Another
experimental result is shown in Fig. 9, when dynamics
phase control was applied. In this experiment,
step reference of phase was input, and actual phase follows
this reference with some time delay. Figure 10 plots
the amount of phase shift and amplitude change, using
both results of the actual experiments and the calculation
of eq.(28). These results indicate the effectiveness
of proposed method for phase and amplitude control of
coil exciting current.
Superconductive Magnet
Normal Coil
Figure 7. Photo of experimental setup.
0 5 10 15 20 25 -15
-10
-5
0
5
10
15
Time [sec]
Voltage [V]
Current [A]
Capacitor Voltage Coil Current Input Current
-15
-10
-5
0
5
10
15
Figure 8. Experimental result of amplitude control.
0 100 200 300 400 500 600 700 800 900 1000
Phase Difference
Time [sec]
0
-/2
/2
3/2
Reference
Actual
Figure 9. Experimental result of phase difference control.
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
-0.2
0
0.2
0.4
0.6
0.8
0
0.5
1
Impulsive Pulse Width t [ms]
Phase Change [rad] Amp. Change vc 0 [V]
Simplified Linear Model
Nonlinear Simulations
Experimental Results
Simplified Linear Model
Nonlinear Simulations
Experimental Results
Figure 10. Comparison of numerical model and experimental
results for phase shift and amplitude change.
Coil Radius/Tickness/Length 3.7 / 3.9 / 9.5 [cm]
Coil Inductance 0.47 [H]
Wire Material Bi2223
Table 2. Specification of superconductive coil for the experiments.
5. EVALUATION WITH HARDWARE-IN-THELOOP
SIMULATIONS
Finally, this section describes the demonstration of the
proposed EMFF method using sinusoidal magnetic moment.
As commonly known, the dynamics of spacecraft
can be simulated with practical accuracy, and on the contrary,
proposed phase control method should be evaluated
more deliberately. From this perspective, hardware-inthe-
loop simulations (HILS) were carried out. The setup
for this HILS included actual hardware of superconductive
magnet and drive circuit with proposed phase controller.
Computer software measures the coil current by
current sensors, then calculates the magnetic force and
the satellites dynamics. The proposed relative position
controller is also implemented in the same software, and
output the reference of current phase difference. The
hardware system described in the previous section controls
the phase and amplitude of the actual resonance current,
to follow this reference. Of course, the size of superconductive
coil is smaller than the ones required for the
satellites, thus the current value is multiplied by constant.
Moreover, the resonance frequency is also different, 0.08
[Hz] and 0.7 [Hz] for actual satellite and HILS, respectively,
thus the calculation in the HILS is for accelerated
simulation. Figure 11 depicts the system configuration
for this HILS. Pure computer simulations, which simulate
also the coil current or phase controller, were also
carried out for comparisons.
The control results of relative position is plotted in Fig. 12
for both HILS and pure computer simulation, and Fig. 13
is the enlarged view of the same results. In the initial condition,
target satellite position is displaced from the reference
position, by 0.2 [m] in y? and z? axis direction.
This initial offset converged within 2000-3000[sec], and
then the relative position error caused by tidal disturbance
appears, e.g., on x?axis of Fig. 13. This residual error is
about 1.0-2.0[mm], in consistency with estimation at the
controller design. It indicates that the proposed system
works properly. On the contrary, the z-axis response in
HILS has position error of about 5.0 [mm]. The reason
of this slightly large error is assumed to be the time delay
of current phase control system, which was slightly
worse than expectation.
Figure 14 is the time response of magnetic force on the
chaser satellite. The results of HILS and numerical simulations
almost meet with each other, indicating the validity
of model or analysis about the phase control circuit.
Data
Signal
+ + + + + L RC
ir
C
,q vC
RL
VE , -VE
RE
S
ie vC
ir
ie
Figure 11. HILS system using acutal superconductive
coil and drive circuit.
0 1000 2000 3000 4000 5000 6000 -2
-1
0
1
2
0 1000 2000 3000 4000 5000 6000 -0.1
0
0.1
0.2
0.3
0 1000 2000 3000 4000 5000 6000 -10.2
-10
-9.8
-9.6
x-axis y-axis z-axis
Time [sec]
Relative Position [m]
Numerical Simulation HILS
Figure 12. Results of HILS (red) and numerical simulation
(blue) : relative position.
0 1000 2000 3000 4000 5000 6000 -10.01
-10.005
-10
-9.995
-9.99
x-axis y-axis z-axis
Relative Position [m]
Time [sec]
0 1000 2000 3000 4000 5000 6000 -2
-1
0
1
2
0 1000 2000 3000 4000 5000 6000 -2
-1
0
1
2
10-3
10-3
Numerical Simulation HILS
Figure 13. Results of HILS (red) and numerical simulation
(blue) : relative position, closeup.
6. CONCLUSION
The electromagnetic formation flight (EMFF) using superconducting
magnets was discussed, and it revealed
that magnetic torque caused by earth magnetic field is
serious problem to apply EMFF for LEO missions. Sinusoidal
driving of magnetic moment and magnetic force
control method using phase difference was proposed in
this paper. Novel method to shift and control the resonance
current using impulsive voltage input was also
proposed, and it was evaluated with experimental results
using actual superconducting coil. Then hardware in the
loop simulation (HILS) was carried out, to demonstrate
whole proposed method for relative position control. In
this HILS, hardware of superconducting coed and phase
control driving circuit was lined to the software to calculate
the satellitesf dynamics. The results indicate the
effectiveness of proposed methods for EMFF in LEO.
0 1000 2000 3000 4000 5000 6000
0 1000 2000 3000 4000 5000 6000
0 1000 2000 3000 4000 5000 6000
0
10-3
10-3
10-3
-10.0
-5.0
0
5.0
10.0
-10.0
-5.0
0
5.0
10.0
-10.0
-5.0
5.0
10.0
-4.3
0.0
5.8
-2.9
4.3
x-axis y-axis z-axis
Time [sec]
Magnetic Force [N]
Magnitude of Tidal Force Disturbance
Force Reference Magnetic Force (Mean)
0 1000 2000 3000 4000 5000 6000
0 1000 2000 3000 4000 5000 6000
0 1000 2000 3000 4000 5000 6000
0
10-3
10-3
10-3
-10.0
-5.0
0
5.0
10.0
-10.0
-5.0
0
5.0
10.0
-10.0
-5.0
5.0
10.0
4.3
-4.3
0.0
5.8
-2.9
x-axis y-axis z-axis
Time [sec]
Magnetic Force [N]
Magnitude of Tidal Force Disturbance
Force Reference Magnetic Force (Mean)
Figure 14. Results of HILS (upper) and numerical simulation
(lower) : magnetic force.
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Saitoh, T. 2002, in International Symposium Fomation
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Kaneda, R., Yazaki, F., Shin-ichiro Sakai, Hashimoto, T.,
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on Formation Flying Missions & Technologies, Washington
D.C, U.S.,, CD?ROM No.79
Manabe, S. 1998.8, in 14th IFAC Symposium on Automatic
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Breckenridge, Colorado
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