Dynamic Simulator for HTV Capture
with Space Station Remote Manipulator System
Ryo YOSHIMITSU*, Yudai YUGUCHI*, Akinori KOBAYASHI*, Riku TAKANO*, Kenji
NAGAOKA*, Kazuya YOSHIDA*, Satoko ABIKO*, Hiroki NAKANISHI†, Mitsushige ODA†,
and Hiroshi UENO§*Tohoku University, 6-6-01, Aramaki Aoba, Aoba-ku, Sendai, Miyagi 980-8579, Japane-mail: { yoshimitsu, yuguchi, a-kobayashi, takano, nagaoka, yoshida} @astro.mech.tohoku.ac.jp
abiko@space.mech.tohoku.ac.jp†Tokyo Institute of Technology, 2-11-1, Ookayama, Meguro-ku, Tokyo 152-8550, Japane-mail: nakanishi.hiroki@mes.titech.ac.jp
oda.m.ab@m.titech.ac.jp§Japan Aerospace Exploration Agency, 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa
252-5210, Japane-mail: ueno.hiroshi@jaxa.jp

Abstract
This paper presents a dynamic simulator with a contact model for capture operations using a large space manipulator. Capture operations in orbit have commonlyused enclosed wires. The contact dynamics between thewires and the target generate complicated motion that isdiﬃcult to predict. Additionally, the joint flexibility of themanipulator makes capture operations more diﬃcult. For
these reasons, there is a potential risk, and such missions,which require a high degree of safety, may be endangered.
In this study, we developed a simulator for capturing a target in orbit with joint flexibility and contact dynamics. An
empirical equation for the contact dynamics with a wire
was derived, and the performance of the simulator was
evaluated by parameter matching with a flight data. Finally, a case study was conducted, and an example of therisk was developed.

1 Introduction
On-orbit transportation is necessary technology for
activity on the International Space Station (ISS). The HII Transfer Vehicle (HTV), which was developed by theJapan Aerospace Exploration Agency (JAXA), is currently responsible for one of the transportation means(Figure 1). HTV-4 was launched on August 4, 2013, andtransported essential materials to the ISS. The retirementof NASA’s space shuttles has accelerated demand for the
HTV. The HTV is docked with the ISS using the Space
Station Remote Manipulator System (SSRMS). The SSRMS, which is a large flexible space manipulator withc
Figure 1. HTV captured by SSRMS ⃝NASA
seven degrees of freedom, can capture and guide the HTV.
In addition, the SSRMS can be used to build large spacestructures, such as the ISS, and assist astronauts during
extra-vehicular activities. Thus, capture operations by the
SSRMS play important roles in on-orbit service. When
carrying out these space activities, the SSRMS needs tocapture a target.
To capture the HTV, the SSRMS is equipped with adedicated holding mechanism called the Latching End Effector (LEE). The LEE has three snare wires that form acurvilinear triangle in the cylinder of the end eﬀector. The
HTV is equipped with a Grapple Fixture (GF) that vertically extends from the HTV and can be captured by the
LEE. Figure 2 shows an overview of the LEE and the GF.
In the capture sequence shown in Figure 3, (a) the operator first guides and inserts the SSRMS to cage the tip of
the GF in the curvilinear wire triangle of the LEE. Subse-

cFigure 2. LEE and GF ⃝NASA
Target Rod

Camera

GF Shaft
Wire

HTV

LEE
Wire

GF Shaftxz

Initial angle

z

y

(a)

We have therefore developed a dynamic simulator thatbe used to evaluate and analyze the capture operations
quantitatively. The simulator is intended for use in determining the potential risks described above and in the
training of the operator. Roman Tutor [1], a simulator thatis related to the SSRMS simulator, is also used in training astronauts to operate the SSRMS. However, in Roman
Tutor, the contact dynamics are not modeled. Despite theexistence of Roman Tutor, there has not been much examination of the contact between a wire and the GF. Therefore, we have studied these contact dynamics in [2], [3].
However, these studies did not confirm consistency withthe on-orbit dynamics.
In this study, we developed a dynamic simulator for
use in simulating capture of the HTV by the SSRMS. An
overview of the simulator is presented in section 2. The
joint flexibility model of the SSRMS, which is needed tofinely simulate on-orbit dynamic behavior, is presented in
section 3. The contact dynamics are described in section
4. Section 5 describes how reasonable values were determined for simulation parameters to match behavior in thesimulator with the flight data. Finally, an example of therisk is presented through a case study in section 6.

(b)

2

(c)

Figure 3. HTV capture sequence by LEE
quently, (b) the GF is latched by narrowing the triangle of
the wires. Note that the operator sees a target rod on the
GF through a camera of the LEE but cannot observe thesize of the narrowing curvilinear triangle and the contact
point between the wires and the GF. Finally, (c) the LEE
and the GF are constrained geometrically owing to thewires fully tightening and are docked by the wires drawing
the GF into the cylinder of the LEE. This capture method
using the LEE and the GF has been commonly used in orbit, however, its secure operation depends greatly on theskill of the operator. In general, the capture operation involves diﬃcult operational techniques and a high level oftraining because the operator cannot observe the contact
point and because the SSRMS cannot completely stop before holding the GF, owing to the joint flexibility of the
SSRMS. Furthermore, in a microgravity environment, thecontact phenomenon is quite complicated, and it can be
subject to high risk even with a weak contact force. The
potential risks need to be known to avoid a deadly accident. Therefore, the contact phenomenon must be examined.

HTV Capture Simulator

Figure 4 shows the LEE and the GF in the simulator.
The LEE and the GF are modeled based on their actual
size, and the wire curve in the LEE is described by using
an elliptic function. Figures 5 and 6 show an overview of
the HTV capture simulator and its GUI display, respectively. The LEE and the GF, as well as the dynamic modelof the HTV, use actual values. The dynamic model of the
SSRMS is presented in the following section. In practice,an astronaut operates two joysticks and watches the monitor. Therefore, this simulator reproduces the interface actually used. In addition, the display is designed to makeconducting the contact analysis and the case study easy.
The partitions in the display represent the following:i. The relative position and velocity between the LEE
and the GF and the joint angle and velocity
ii. The values for determining the contact position between the wire and the GF to conduct the case studyiii. Buttons for changing the camera position
iv. Buttons for changing the control mode of the SSRMS
v. Buttons for initializing, starting, and stopping thesimulation
vi. A monitor for the viewing the simulation graphics(The view angle can be changed by the camera position button)vii. A simulation time display
viii. A power gauge for the joystick inputs

link frame 6

GF

LEE

SSRMS

Wire

z

y
link frame 7xzylink frame 5

x
y

z

y

link frame 3

2000
Joint Torque τ [Nm]Rotational Joystick

ϸ

Ϲ
Ϻ
ϻ

0

䢯∆

τ∆
-τ ∆

∆

-1000
-2000
-2

Ͽ

-1

0
1
Twist angle δm [rad]

2
x 10

-3

Figure 8. Joint characteristic of SSRMS

ϼ
Figure 6. Simulator display

1000

g

Figure 5. Overview of HTV capture simulatorϾzFigure 7. Joint connectivity of SSRMS

GUI

Ͻ

y

link frame 2xz ylink frame 1x

External camera viewzlink frame 4xz yFigure 4. Illustration of LEE and GF in simulator

Translational Joystickxx

Target Rod

where Kg = 1.33 × 106 [Nm/rad], ∆ = 9.17 × 10−4 [rad],τ∆ = 434.5 [Nm], and the twist angle δm is defined as the
motor angle minus the link angle. All joints have the samecharacteristics, illustrated in Figure 8.

3 Dynamics of SSRMS
3.1 Nonlinear characteristic of joints
In depicting the motion of the SSRMS, the simulator
considers the geometric connection relations of the joints
and the nonlinear stiﬀness of the joint. The geometric connection relations are constructed based on Figure 7 andTable 1 [4]. Each link of the SSRMS is represented byframe, as shown Figure 7. In Table 1, mi represents themass of link i; ci and Ii represent the mass center location
vector in each link frame and the inertia moment matrixof the mass center, respectively; and pi,i+1 represents the
position vector that expresses the i+1 joint location in link
frame i.
Each joint of the SSRMS has nonlinear flexibility owing to low stiﬀness. As described in [4], based on groundtests and on-orbit data, and neglecting hysteresis, the joint
characteristics can be represented by the following nonlinear function g(δm ):3.2

τg = sign(δm )g(δm ) τ∆|δm | ≤ ∆
 2 δ2m
g(δm ) = ∆ Kg (|δm | − ∆) + τ∆ otherwise

where

(1)
(2)

Modeling of flexible manipulator

We modeled the joint flexibility of the space manipulator using a 2-inertia system [5]. The 2-inertia systemgives a virtual joint in which each joint has two masses
with a rigid link and a rotary motor. These are connectedby a linear torsional spring that generates elasticity by the
coupling eﬀect. In this case, because a gear reducer behaves like a spring element, we used a model that could
describe the inertia of a link and an actuator. Therefore,
the motion of the SSRMS can be represented by solving
the following two simultaneous equations of motion forthe manipulator and the motor:
Ma (qa ) q̈a + C(qa , q̇a ) − τg (δm ) = J eT Fe
Mm q̈m + D q̇m + τg (δm ) = τcqa ∈ R7×1 : the angle of the actual joint axis
qm ∈ R7×1 : the angle of the motor axis

(3)
(4)

Table 1. Inertial properties of SSRMS [4]3456
105.98314.88279.2
105.98
0
3.55
3.55
0
-0.2316-0.08
0-0.33700
00i
mi [kg]ci [m]

1
246 .66
0.669
0
0

2
105.98000.2983Ii [kgm2 ]I xx = 9.336
Iyy = 44.413

I xx = 12.19
Iyy = 12.13

I xx = 8.088
Iyy = 3.061

I xx = 15.41
Iyy = 2094.71

I xx = 9.522
Iyy = 1966.28

Izz = 44.413
I xy = 0

Izz = 3.061
I xy = 0

Izz = 8.446
I xy = 0

Izz = 2103.19
I xy = 49.52

Iyz = 0Izx = 0Iyz = 0Izx = 0Iyz = 0Izx = 01.358900000.70260-0.5692
0pi,i+1 [m]7105.9800-0.4048
243.660.669
00I xx = 8.305
Iyy = 3.061

I xx = 12.13
Iyy = 12.13

I xx = 9.336
Iyy = 44.41

Izz = 1966.28
I xy = −39.95

Izz = 8.386
I xy = 0

Izz = 3.061
I xy = 0

Izz = 44.41
I xy = 0

Iyz = 0Izx = 0Iyz = 0Izx = 0Iyz = 0Izx = 0Iyz = 0Izx = 0Iyz = 0Izx = 07.11
-0.475
0

7.11
0
0

0
-0.5692000-0.7026

1.358900Ma ∈ R7×7 : the inertia matrix of the SSRMS
Mm ∈ R: the inertia matrix of the motorC∈R: the nonlinear velocity-dependent term of the
SSRMS

7×7

7×1

D ∈ R7×1 : the viscous damping coeﬃcient of the motorTFe ∈ R6×1 : the force and moment exerted on theend-eﬀector
J e ∈ R6×7 : the Jacobian matrix with respect to theend-eﬀectorτc ∈ R7×1 : the torque vector on the jointsδm ∈ R7×1 : the twist angle vector between the motor andthe linkτg ∈ R7×1 : the gearbox torque vector with respect to thetwist angle vector
The inertia matrix of the motor is represented as follows
in [4]:
 Izz η2 0Mm =  .
 ..
00Izz η2
..
.
0

···
···
..
.
···


0 

0 .. 
. 
Izz η2letting J c (qa ) be a Jacobian matrix for the camera coordinate system, the desired joint angular velocity vector q̇da isderived as shown:
[ d ]
ve
(6)
q̇da = J c (qa )+
ωde

(5)

where Izz = 2.67×10−4 [kgm2 ] denotes the inertia momentand η = 1845 denotes the gear reduction ratio. The valueof the viscous damping coeﬃcient of the motor was determined by means of parameter matching with the flightdata.

3.3 Control method
While operating the SSRMS, the operator observes a
relative position with respect to the GF only through thecamera on the LEE. Therefore, the SSRMS in the simulator should be operated using the camera coordinate systemrather than the inertial coordinate system. For this reason,T

where [vde ωde ]T denotes the desired velocity of the endeﬀector for the camera coordinate system because the operator determines the desired value from joysticks, (·)+ operator denotes the pseudo inverse of a matrix. The desired
joint angle vector qda is derived as the integral of q̇da , andthe joint torque τc is given by the following PD controller:τc = k p (qda − qa ) + kd ( q̇da − q̇a )(7)where k p and kd represent the proportional and derivative
gain matrices, respectively, and which are determined byparameter matching.

4

Contact dynamics between wire and GF

This section describes the contact dynamics between
a wire and the GF. Because the shape of a wire-applied
force changes with time, as shown Figure 9, contact dynamics between a wire and the GF are complicated, in
contrast to rigid body contact. Therefore, the simulator
must finely duplicate dynamic behavior attributed a contact reaction force. In general, a contact force can be divided into a normal force Fn and a frictional force F f . The
normal force Fn is defined as the linear sum of kinetic andstatic elements, i.e., Fn = Fk (δ̇) + F s (δ). Let k be thestiﬀness and c be the viscous damping. The normal force
Fn can be expressed as a function of the displacement ofpenetration δ [6]:Fn = cδ p δ̇q + kδn(8)where p, q, and n are constant values. When p = 0 andq = n = 1, this model represents the following spring-Table 2. Wire configuration in the experiments
Length l
180 mmDiameter
2 mm
Horizontal displacement w
0, 5, 10 mm
Contact position a
70, 80, 90, 100,110 mm (from the left end)

Fn
Wire
Ff
δ

GF

Ff
z
x

y

Figure 9. Contact model between wire and GF

Force/torquesensorPA10

dashpot model:
Fn = cδ̇ + kδ

(9)We have focused on the contact dynamics between awire and the GF to capture the HTV safely. Eq. (9) was
selected as the contact dynamics model in [2], assumingthat a wire is modeled as the superposition of a beam anda string and that its stiﬀness k can be defined by the ratio of their stiﬀnesses. The static force model used in [2]is, however, insuﬃcient to express the contact kinematics
between a wire and the GF. A wire would not become aperfectly rigid body during penetration because it is deformed geometrically by contact with the GF. In addition,
tension was assumed to be applied to the straight shapeof the wire. However, a wire has no tension initially, andin practice, the displacement of the GF is started from abowed state. In [3], these assumptions were improved
based on the results of ground experiments. The results
showed that the force observed was greater than that predicted by the simple spring-dashpot model and that it canbe approximated by a quadratic function of the following
form: Fn (δ) = Aδ2 + Bδ + C.
For further study, other factors need to be considered
as well. In the previous experiments mentioned, the load
was applied in the direction perpendicular to the groundplane, and the reaction force was distributed laterally. In
addition, given the limited amount of experimental dataobtained less, an approximate equation was obtained bybased only on the discrete response. To derive a more
realistic and precise static force equation, we carried out
further experiments.

4.1 Experimental conditions
In our experiment, a device that fixes both ends of awire was set in a rigid frame. The wire used in the experiment is thinner and more flexible than the actual wire on
the LEE. An overview and a schematic view of the experimental devices are shown in Figures 10 (a) and (b), respectively. Both of the end points of the wire are rotation
points fixed by idlers. This device is equipped with a slide
mechanism for setting the horizontal displacement of theend point of the wire. To measure the force, the end point
is equipped with a force/torque sensor produced by Nitta
Corporation (IFS-90M31A 50-I 50). To apply the load toa wire, we used a PA10 industrial robotic arm producedby Mitsubishi Heavy Industry. The tip of the PA10 is also

Bowed wire
Force/torquesensorGrapple Fixture(a) Overview

l
Fs

w

a
(b) Schematic view

Figure 10. Experimental setup for analysisof the contact dynamics
equipped with a force/torque sensor (IFS-90M31A 50-I50) and a rod that represents the GF. In the experiments,
we measured the reaction force of the wire with respect
to the bending displacement during static loading applied
to the bowed wire by the PA10. There was no frictional
force because the force was applied to the bowed wire vertically. An OptiTrack FLEX:V100R2 motion capture system produced by NaturalPoint was used to measure thedisplacement δ. The experimental conditions for the wire
are presented in Table 2. Note that of the contact positions
between the wire and the rod listed in Table 2, the 90 mm
position is at the center of the wire.

4.2

Experimental results

The graphs shown in Figure 11 illustrate the relationship between the displacement δ and the static reaction
force F s for each condition. These graphs show that thestiﬀness of the static reaction force F s increases because
a dominant factor changes with the displacement δ. In thecases of the 5 mm and 10 mm horizontal displacements inparticular, the stiﬀness change was remarkable. The stiﬀness then started to change linearly as the wire extended
to a certain extent and reached a stable value. Moreover,the stiﬀness did not change when the horizontal displace-䢢

Experiment
Approximation

12

Force Fs[N]

10

8
6
4
2

8
6
4
2

0
0

0
0

䢢

2
4
6
Displacement δ [m] x 10-3(a) w = 0 [mm], a = 90 [mm]
14

䢢

䢢

Force Fs [N]10Force Fs [N]

10

6
4
2
0
0
䢢

Experiment
Approximation
2
4
6
Displacement δ [m] x 10-3(c) w = 5 [mm], a = 90 [mm]14䢢Experiment
Approximation

12

4

0
0
䢢

2
4
6
Displacement δ [m] x 10-3(e) w = 10[mm], a = 90[mm]

-0.02
-0.01
0
Horizontal displacement y [m]

0.01

z

6
4

0
0
䢢

Experiment
Approximation
2
4
6
Displacement δ [m] x 10-3

4.8 s
2.9 s

(d) w = 5 [mm], a = 70 [mm]
14

y

䢢

Experiment
Approximation

Wire

0.0 s

GF

8
6
4
2

2

0.0 s
0

8

2

Force Fs [N]

6

0.01

(a) Trajectory from telemetry data on y-z plane

10

8

2.9 s
0.02

-0.01
-0.03

䢢

12

10

4.8 s
0.03

(b) w = 0 [mm], a = 70 [mm]
12

8

2
4
6
Displacement δ [m] x 10-3

14

12Force Fs [N]

0.04

䢢

Experiment
Approximation

12

10

Force Fs [N]14

Vertical displacement z [m]14(b) Estimated relative trajectory between wires and GF

0
0
䢢

2
4
6
Displacement δ [m] x 10-3

Figure 12. Trajectory of telemetry and estimation(f) w = 10[mm], a = 70[mm]Figure 11. Experimental measurements of wire stiﬀness
ment exceeded over 5 mm. Therefore, we conclude thatthe static reaction force can be regarded as a superpositionof two functions.
Based on these results, we selected the following anempirical equation:
F s (δ) = α(eβδ − 1) + γδ(10)where α, β, and γ represent arbitrary constant parameters.
The graphs made using Eq. (10) are shown together inFigure 11 and show that Eq. (10) represents the stiﬀness
change of the wire well.
Considering the characteristic of Eq. (10), constantvalues for the kinetic element of the normal force Fk (δ̇) in
the simulator were set as p = 2 and q = 1, and the frictional force F f applied was represented by the Coulomb
friction model, as shown below:
Fk = cδ2 δ̇
F f = µFn
where µ denotes the coeﬃcient of kinetic friction.

(11)
(12)

5 Parameter matching of simulator
This section presents the matching of the undetermined parameters to precisely incorporate the SSRMS
motion and the contact dynamics in the simulator. In thematching process, we utilized the flight data used in [7],which was estimated from the practical telemetry data of
the sensor output of the HTV and the camera images on
the LEE and the ISS.

5.1

Relative trajectory between wires and GF

In determining the values of the parameters of interest, it is important to estimate where the GF contacts thewire in the LEE, because the contact point is not filmedby the camera. Hence, we first analyzed how far the GF
was moving with respect to the wires, using both the flightdata and the captured movie. Figure 12 (a) represents theresults plotted as a trajectory on the y-z plane from 0 s to
20 s in the flight data. As Figure 12 (a) shows, the GF
started moving from the lower right to the upper left ofthe curvilinear triangle at 0 s and made contact at 2.9 s and4.8 s, respectively. In addition, the GF being fixed by thewires can be represented by drawing a circular trajectory
inside a curvilinear triangle. Because the GF follows such

Table 4. Simulation parameter values obtained by matching with flight dataαβγc [kgs/m2 ]µ70.0043 2162.2 648.6 0.83 × 10
0.08
k p,i [Nm/rad] kd,i [Nms/rad] Dii [Nms/rad]
120
240
18000

a trajectory, we estimated that the GF moved as shown in
Figure 12 (b).

5.2 Result of parameter matching
When matching the behavior in the simulator with theflight data, the contact force between the wire and the GF
was based on the empirical equation though the materialof the wire used in the experiment diﬀers. In addition, theinitial states of the SSRMS were set to be the same as in
the flight data. The tightening time, which is the moving
rate of the end point of the wire from the initial angle to thefinal angle, also uses the same values. These conditions
are summarized in Table 3. The values of the parameters
for the wire reaction force α, β, γ, c, µ, the control gain of
the SSRMS k p , kd and viscous damping coeﬃcient of the
motor D were determined by parameter matching.
The result of the parameter matching is shown in Figures 13 and 14. Figure 13 shows the time response of thesimulator behavior and the flight data. Figure 14 shows
successive pictures of the simulator. The simulation parameter values obtained by matching with the flight data
presented in Table 4. Figures 13 and 14 illustrate thetrends of the estimation shown in Figure 12, however thesimulator behavior has higher amplitude than the flight

Relative
position y [m]Relative
position z [m]Table 3. Initial states of SSRMS and tightening values of wire −31.87  42.73  −66.72 
◦
Initial joint angle [ ]  105.1 
SSRMS(based on Figure 7 ) −178.6  −174.6 
 −131.5  −0.4760 
Initial relative position  0.013 

vector [m] −0.003 
 0.030 
Initial relative velocity  −0.012 
vector [m/s] 0.008 
 0.0108 
Initial relative attitude 0.763 vector [◦ ]
0.110
wire
initial angle [◦ ]130
final angle [◦ ]200
tightening time [s]
5

0.02
0
-0.02
-0.04
-0.06
0

䢢

Telemetry data
Matching data

䢢

5

0.06
0.04
0.02
0
-0.02
0

10
15
Time [s]2025䢢Telemetry data
Matching data

䢢

5

10
15
20
Time [s]Figure 13. Time response of relative position between LEE and GF

25

z
y

0.0 s

2.5 s

5.2 s

6.4 s

7.0 s

8.4 s

Figure 14. Successive pictures of capture sequence
data. We considered that higher amplitude could be tolerated as the wide margin because the purpose developing
the simulator analyzes the safeness of capture operations.
Notice that the values in Table 4 do not ensure uniqueness of the combination of parameters because the number of parameters is large and uncertainly factor may be
included. However, in terms of matching the flight data,
the numerical model simulates the relative motion of capture operation.

6 Case Study
This section describes a case study conducted examine the safeness of capturing the HTV. When an astronaut
operates a large space manipulator and captures a target
using the LEE, the criteria for the capture possibility aredefined to be whether the mission can be safely accomplished. If this criteria are not satisfied, a capture sequencemust be stopped immediately. The relative position andangle in the approaching phase before the contact are defined as part of the assessment that the criteria can be met,
but the relative translational and rotational velocity are notdefined explicitly. Therefore, the margin of safety of thecapture velocity with respect to the SSRMS operation velocity needs to be examined.

z

x

y

0.05

䢢

Acknowledgment

0
-0.05
0

Relative
position z [m]Relative
position y [m]Figure 15. Initial state of case study

oped to analyze safe capture operations and is therefore
focused on joint flexibility and the contact dynamics between a wire and the GF. An empirical equation that represents the contact dynamics was introduced based on the
results of ground experiments and was integrated into thesimulator to match its behavior with available flight data.
The simulator can contribute to the analysis of the safetyof capture conditions, as demonstrated by the case study
presented in this paper. The potential risks inherent in thecapture operation will be gradually clarified by conducting additional case studies.

䢢

0.31 m/s
20.32 m/s
0.33 m/s
46Time [s]0.31 m/s

0.32 m/s

0.3

8

10
䢢

0.2
0.1

We would like to express thanks to the JAXA HTV
project team that provided us with the telemetry dataneeded to carry out this research.

0.33 m/s

References

0
-0.1
0
䢢

2

4

6

8

10

Time [s]Figure 16. Results of case study

6.1 Case study results and discussion
We conducted a case study under the following conditions.
• The matching parameters listed in Table 4 were used.
• The case study was started from the state at which
the GF was inserted into the enclosed region of the
LEE.
• In the worst case, the GF was located in a corner ofthe enclosed region, as shown Figure 15.
• The curvilinear triangle began narrowing at 0 s.
In addition to the above conditions, the LEE was suppliedwith an initial velocity in the z-axis direction. We thendetermined the limiting initial velocity at which the GF
and the LEE could be constrained.
The results are shown in Figure 16. When the initial
velocity was less than 0.32 m/s, the LEE captured the GF
because the relative velocity between the two was 0 m/s.
However, when the initial velocity was greater than 0.33
m/s, the LEE failed to capture the GF. Therefore, for thiscase study, the limiting initial velocity was found to be
0.32 m/s. This velocity is much greater than the typicaloperating velocity of the SSRMS, which is 0.03 m/s.

7 Conclusions
This paper describes a dynamic simulator for the
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