1. Introduction
A spacecraft capture task using a space robotic manipulator in orbit is a key technology for ISS or JEM
operation/construction, and furthermore, for a future mission, for example, Space Solar Power System (SSPS)
construction or assembly other huge space structure. Therefore, we consider it is significant that a dynamics simulation
of both behavior of a manipulator and a captured target during/after capturing operation, applying contact dynamics
model. The present, a EE applied tree-wired mechanism shown in Fig.1 is practically adapted, which grapples a
specified interface, that is, the pin of GF (illustrated in Fig.2) by snaring and rigidizing using three wires mechanism.
Thus, it is probable that a contact characteristic of contact point is very complicated.
The behavior of the target vehicle after making contact during the capturing process is very difficult to predict, since
the contact dynamics are influenced by a complicated condition as above. In these capturing cases, contact will occur
due to residual relative motion between the EE and the GF pin on the target spacecraft. Relative motion of these two
vehicles after an uncontrolled contact may ultimately cause a serious collision. Therefore, we need to conduct a various
cases simulation to predict behavior of the manipulator and the target spacecraft with high precision. However, that
requires much time and computing power. Thus, we have been researching an effective modelling method that
describes the dynamics simply and precisely is required. Research on the dynamics of space manipulators [2-4] and
theoretical research aimed at describing contact phenomena [5] have been widely conducted, and practical models
integrating these approaches have been prepared.
In addition, we set up a 1/2 scale mockup of EE mechanism model so that we can make a simulation model more
accurate by measuring contact and constraint conditions between snare-wire and GF pin in ground experiments.
Fig.1 Three-Wired EE Fig.2 GF Pin
cNASA
cNASA
2. Numerical Simulation
We focus the case that a capturing operation of a heavy spacecraft which has a similar weight to HTV by a large
manipulator, such as SSRMS as shown in Fig.3.
Fig.3 Spacecraft Capturing Case
2.1 Simulation Model
We set up a large RMS simulation model using a general-purpose mechanical analyze tool. The RMS model has
similar physical specification[1] to the SSRMS(Fig.4(a)), and the RMS model is attached to ISS model that has similar
feature of weight and inertia parameter to ISS as shown in Fig.4(b).
Contact Point
RMS Model
(a) RMS Simulation Model (b) ISS Simulation Model
Fig.4 RMS Simulation Model
Fig.5 indicates a target spacecraft, which has approximately 1.3ton and similar inertia parameters to HTV. The GF
model is attached the target spacecraft, which is defined as a contact point to EE during being captured.
Grapple Fixture Model
Spacecraft Model
Fig.5 Target Spacecraft Model
2.2 Joint of RMS Model
The RMS simulation model has 7-DOF as same as SSMRS. We apply stiffness and friction model to those joint and
the stiffness contain backlash model as illustrated in Fig.6.
Joint Stiffness Torque
Joint Rotatinon Angle
Backlash
Æ
B Æ 2Æ B
Parabolic curve
Joint Friction Torque
Joint Rate
Backdrive Torque
Æ&
Stiffness
iBacklashj
Friction
Link i iBackdrivej
Link i+1
Joint i
Fig.6 Joint Model
cJAXA
2.3 EE Model
The EE model we applied to the simulation is indicated in Fig.7. A mass property is adopted from the publication as
same as the other models, such as RMS and ISS.
We consider that a constraint condition of EE, which is composed with a three-weird mechanism, the EE housing,
and a GP pin, can be regarded as the combined model of a ball joint connected to the housing by springs and springdumper
model attached to a motion constraint virtual parts respectively. Fig.8 shows the EE model we applied. The EE
model allows rigidizing operation by pulling a virtual part coupled a spring-ball join model.
Ball Joint Model
Moving Constant Velosity
Spring Model
GF Model
Pin
Fig.7 EE Model Fig.8 Constraint Model of EE
2.4 Contact Model
We apply simply gspring ? dashpot modelh as the contact model (Eq.(1))
Fn = DcÂ& + KcÂ (1)
Here,
Fn : normal force,
Kc : stiffness parameter,
Dc : constant damping parameter,
Â : penetration displacement
Conventional friction parameters of surface-lubrication materials, which are based on ground and on-orbit
measurements, are used initially. A number of simulations are conducted by widely varying the parameters to predict
the worst case analysis as a lower boundary for the problem[8].
3. Simulation Results
First, we verified an effect of contact condition, that is, stiffness and damping parameters. Table 1 shows examples of
contact parameter. We verified a various combination of contact parameters and initial condition of RMS posture,
relative position and velocity of the RMS tip to the GF. Fig.10 and Fig.11 show the comparison of simulation results in
respective contact conditions Table 1. Figures indicate simulation results of position and angular rate profiles after
contact of the EE of RMS and the GF of Spacecraft without rigidizing operation, which applying an initial condition
indicated in Table 2. The initial conditions are relative motion of the EE to the GF represented in EE coordinate system.
We adopt a condition #02 as contact parameter between the EE and the GF pin based on the simulation results.
Table 1 Contact Condition of Simulation Table 2 Initial condition of Relative Motion
X 0.0028
Y -0.009
Z -0.025
Yaw 0
Pitch 0
Roll 0.025
Initial Velocity
[m/s]
Initial Rate
[deg/s]
KC
DC
Â
Fig.9 Contact Model
Fig.10 Velocity of Spacecraft Fig.11 Angular Rate of Spacecraft
Then, we conduct dynamics simulation of rigidizing operation. The initial condition of the case is listed in Table 3.
The simulation sequence is as follows.
1)Assume that the GF pin of target spacecraft is completely snared by three-wires of the EE, and it is constrained as a
ball joint that has rotation stiffness and dumping.
2)The target Spacecraft has residual velocity and miss alignment to the EE.
3)The EE pulls the GF pin in 2 seconds at 5s from a simulation start, then the GF is regidized while GF contacts to a
surface of EE housing.
4)After rigidizing GF, the spacecraft motion is restrained by joints stiffness and friction of the RMS.
Fig.12 shows an example of simulation result. In this case, the spacecraft collides with the EE inner surface during
regidizing about 7 seconds from the start. We can find that the collision causes an over load of rigidizing force from the
result of the simulation case.
We will improve the simulation model applying data of experimental results mentioned in section 4, and practically
use for capturing analysis of spacecraft /space structure, or safety analysis, for example, collision of ISS and THV, over
load of EE/joint, and so on.
Table 3 Initial Condition of Rigidizing Simulation
X -0.12
Y 0
Z 0
Yaw 0
Pitch -7
Row 0
Initial Miss-Alignment
(RMS Cordinates System)
[m] , [deg]
X 0.024
Y 0.024
Z 0.024
Yaw -0.08
Pitch 0
Roll 0
Initial Velocity
[m/s]
Initial Rate
[deg/s]
0 10 20 30 40
-0.4
-0.2
0
0.2
0.4
Time , [sec]
Position , [m]
0 10 20 30 40
-0.04
-0.02
0
0.02
0.04
Time , [sec]
Velocity , [m/s]
0 10 -1 20 30 40
0
1
Time , [sec]
Angular Rate , [deg/s]
0 10 20 30 40
Time , [sec]
Pull Force
Velocity of Spacecraft Rate of Spacecraft
Position of Spacecraft Rigidize Force of EE
Fig.12 Simulation Result of Rigidizing Operation
Condition 01
Condition 02
Condition 03
Condition 04
Condition 01
Condition 02
Condition 03
Condition 04
4. Ground Experiments
In this section, we introduce experimental system and results conducted for detecting a constraint condition and
contact parameters of EE.
4.1 Experimental Setup
We setup a capturing operation dynamics simulator composed of a large RMS mockup and a spacecraft dynamics
simulator using an industrial 6-DOF manipulator and a force/torque sensor. The RMS mockup has 1-DOF and allows
observation of passive dynamics of a large RMS. The three-wired EE mockup is attached to a tip of RMS as shown in
Fig.13.
The spacecraft dynamics simulator can realize a virtual 3-dimensional motion feeding-back values of 6-axis
force/torque (FT) sensor and solving an equation of motion of assumed spacecraft inertia properties.
4.2 Three-wired EE Mechanism Mockup
We developed a three-wired EE mechanism model that is approximately 1/2 scale of Latching End-Effector (LEE) of
SSRMS. Fig.14 shows overview of EE mechanism model and GF pin model that is also 1/2 scale. The mechanism can
be driven manually using worm-gear, as shown in Fig.15, and can snares a GF pin, although it does not have rigidize
function.
Spacecraft Simulator
iusing 6DOF Manipulatorj
RMS Mockup
X
Y Z
Fig.13 Ground Experimental SystemFig. 14 Three-Wired EE Mechanism Model
Fig.15 Snaring Function
4.3 Experimental Results
The experiment of constraint condition measuring is conducted so that we can apply the results to simulation model of
the EE and the GF pin. It is assume that the GF pin is snared at the center of EE, then, we measure a constrain force and
torque by moving the GF pin model, that is integrated on the FT sensor, +-3mm to x,y-direction, +-10mm to z-direction
respectively. Fig.16 to 18 show experimental results of the constraint condition measuring experiment.
10 20 30
-30
-20
-10
0
10
20
30
Time , [sec]
X Force , [N]
10 20 30
-4
-2
0
2
4
Time , [sec]
X Position , [mm] 5
10 15 20
-10
0
10
Time , [sec]
Y Force , [N]
5 10 15 20
-4
-2
0
2
4
Y Position , [mm]
Time , [sec]
Fig.16 X-direction Translation Experiment Result Fig.17 Y-direction Translation Experiment Result
10 20 30
-4
-2
0
2
4
Time , [sec]
Z Force , [N]
0 10 20 30
-10
0
10
Time , [sec]
Z Position , [mm]
Fig.18 Z-direction Translation Experiment Result
It can be regarded that stiffness of x-direction and y-direction is liner to deflection. The results of Deflection-Force
curve of each axis is shown in Fig.19. Although a slight hysteresis is observed, a relationship of deflection and stiffness
force is liner as above. On the other side, the deflection-force curve of z-direction is not liner, which indicates constant
friction and a hysteresis is not negligible because the z direction is outer-plane direction of the plane formed by three
wired. We can verify the characteristics of stiffness in those experiments.
-4 -2 0 2 4
-20
-10
0
10
20
X Deflection , [mm]
Force , [N]
-4 -2 0 2 4
-10
0
10
Y Deflection , [mm]
Force , [N]
-10 0 10
-10
0
10
Z Deflection , [mm]
Force , [N]
Fig.19 Results of Deflection-Force Curve
5. Conclusion Remarks
We setup the contact dynamics simulation tool and the ground experimental system of a spacecraft capturing by a
space robotic manipulator with a specific end-effector. The simulation tool is an efficient one applying a spiting-dumper
contact model to interfaces of contact point. In addition, we improved the simulation model, which can realize snaring
and rigidizing operation applying spring-constrained ball joint and pulling virtual parts connected to the ball joint with
certain spring stiffness. We conducted contact dynamics analysis of the spacecraft capturing by the end-effector of
space robotic manipulator on various initial conditions, and we make it clear that the dynamics of target spacecraft
during capturing, rigidizing, and after rigidized completely, which applying joints elastic and friction of the manipulator.
We verify the overload of pulling force of EE mechanism occurs in some cases of initial conditions.
However, the result of simulation is much predominated by initial conditions and contact conditions. Therefore, we
need more detail data of contact characteristics of contact interface, especially three-wired mechanism and GF pin.
Thus, we develop three-wired mechanism model for ground experiment, that is 1/2 scale of that of SSRMSf LEE, and
conduct a constraint condition and contact characteristics measuring experiments. It is made clear that the
characteristics of deflection-force of GF pin load in the condition that the pin is restricted in position by three snared
wires. The experimental data is analyzed, and we will apply them to the simulation model so that we can improve the
model and conduct more precision analysis.
6. Reference
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Astronautics vol. 161, Teleoperation and Robotics in Space, AIAA, pp. 353-410.
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Floating Links with Extended Generalized Inertia Tensor,h Proc. 1992 IEEE Int. Conf. on Robotics and Automation,
pp.899? 904, 1992.
[3] Yoshida, K., Nakanishi, H., Ueno, H., Inaba, N., Nishimaki, T., and Oda, M.,hDynamics, Control, and Impedance
Matching for Robotic Capture of a Non-cooperative Satellite,h Advanced Robotics Vol. 18, pp. 175-198, 2004.
[4] Asada, H. and Ogawa, K., gDynamic Analysis of Robotic Arms Using Inverse Inertia Matrices and Its Application
to Task Planning and End-Effector Designh Proc. The Society of Instrument and Control Engineers, Vol. 23, No. 9,
pp.961? 968, 1987.
[5] Gilardi, G. and Sharf, I., gLiterature survey of contact dynamics modeling,h Mechanism and Machine Theory 37 pp.
1213-1239, 2002.
[6] Ma, O., Yang, G., and Diao, X.,h Experimental Validation of CDT-Based Satellite Docking Simulations Using
SOSS Testbed,h Proc. The 8th International Symposium on Artificial Intelligence, Robotics and Automation in Space,
CD-ROM, 2005.
[7] Kawasaki, O., Yamanaka, K., Imada, T. and Tanaka, T., gThe On-orbit Demonstration and Operations Plan of the
H-II Transfer Vehicle (HTV), gIAF-00-T.2.08, 2000.
[8]Inaba, K., Sawada, H., Funaki, Y., Ueda, S., gAn Effective Modeling Method of Contact Dynamics for Satellite
Captureh, 25th International Symposium on Space Technology and Science, Jun, 2006, Kanazwa, Japan.