16th IEEE International Conference on Robot & Human Interactive Communication

WC1-5

August 26 ~ 29, 2007 / Jeju, Korea

An Avoidance Method of Singular Configurations in a Master-Slave
System Using Intervening Impedance
Kouichi WATANABE1 , Kiyohiro SOGEN1 , Naoki KAWAKAMI2 , and Susumu TACHI2
Graduate School of Information Science and Technology, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 Japan1e-mail :{ Kouichi_Watanabe ,Kiyohiro_Sogen } @ipc.i.u-tokyo.ac.jp
2e-mail :{ kawakami, tachi } @star.t.u-tokyo.ac.jp
Abstract— It is necessary to naturally avoid singular configurations of each slave robot in order to achieve an ideal
telexistence master-slave system. We propose a method for the
avoidance of singular configurations by using intervening
impedance. In this method, the parameters of the intervening
impedance are adjusted by the manipulability ellipsoid. Thismethod is applied to a master-slave robot. As a result, singularconfigurations are avoided by the proposed method.

I. INTRODUCTION
Telexistence [1] is a technology by which we can experience advanced realistic sensations of a remote environment by remote operation and remote communication.
We have been researching this technology. In telexistence,
there is a master-slave relationship between an operator anda remote robot. Information transmitted from the operator to
the remote robot and information about a remote environment is transmitted back to the operator from the robot.
Our primary goal for the telexistence master-slave system is to operate at will various types of slave robots byusing a single universal master system. Recently, various
types of robot systems have been studied and developed;
however, a universal master system has hardly been studied.
There are some problems in developing a universal mastersystem. A universal master system should be designed universally so as to cover the motion space of all slave robots.
However, a slave robot has a state that degenerates the degrees of freedom of the robot, i.e., singular configuration. If
a universal master system is designed, the singular configurations of a slave robot will be included in the motion
space. Therefore, a method that avoids singular configurations in a master system is required.
The issue of avoiding singular configurations commonlyoccurs not only in a remote robot system but also in all robots. Self-contained robots and industrial robots also havesingular configurations. There are some methods for the
avoidance of singular configurations. For example, there aremethods that can be used to control or stop motion in thevicinity of a singular configuration and to limit motion to anarrow range to prohibit a robot from attaining a singularconfiguration. These methods can be effectively used evenwhen the target robot operates itself automatically or when
there is only one target slave robot in a master-slave system.
However, in our ideal master-slave system, it is necessary to achieve an avoidance of the singular configuration inslave robots with different configurations. If singular configurations, which are calculated in each slave, are trans-

978-1-4244-1635-6/07/$25.00

2007 IEEE.

mitted to the master side and this information is displayed tothe operator, the operator will be able to avoid singularconfigurations. However, by adopting a new control method,
the cost might increase and the manipulability of the operator might be impaired. The process that creates and displays this information must be executed as efficiently as
possible.
We consider using inherent information in master-slave
systems. In a master-slave system, bilateral control isneeded for exchanging information between a master and aslave. In bilateral control, an apparent impedance arises inthe environment interface between the master and the slave.
We focus on this impedance called “intervening impedance” [2].
The operator will experience operating a slave robot
through the intervening impedance. In our ideal master-slave system, this intervening impedance should become
zero as much as possible because the operator should be
able to operate slave robots as if it is own. Tachi and Sakaki
have proposed an impedance-controlled bilateral control
system [3, 4]. This control method is able to control theintervening impedance by means of control parameters.
Therefore, a master-slave system can be realized without the
influence of intervening impedance. On the other hand, we
try to increase the influence of this impedance. By increasing this influence, the robot manipulability of the operator will be degraded and operation will be limited.
Therefore, by increasing the intervening impedance in thevicinity of singular configurations, the operator can naturally avoid the singular configuration of slave robots.
In this paper, we propose a system that can avoid thesingular configuration of slave robots by changing the intervening impedance on the basis of the manipulability ellipsoid. We show that the operator can naturally avoid thesingular configuration. In addition, we consider the applicability of this method to universal master-slave systems.
II. AN AVOIDANCE OF SINGULAR CONFIGURATIONS USINGINTERVENING IMPEDANCE

A. INTERVENING IMPEDANCE IN
IMPEDANCE-CONTROLLED BILATERAL CONTROLIn the literatures [3, 4], the intervening impedance in an
impedance-controlled bilateral control system is expressedby the following equation:1102

Fs − Fm = mˆ X&& ms + bˆX& ms + kˆX ms
2 M (1 − k )2 B (1 − k )dm , bˆ =
d
b
1+ k
1+ k
f
f
X +X
2 K (1 − k )
d
k ,X
s
kˆ =
= m
ms
1+ k
2
f

(1)

mˆ =

where Xm and Xs denote the end position and posture of themaster and slave, respectively; Fm and Fs, the received
forces of the operator and slave robot, respectively; Md, Bd,
and Kd, the setup local impedance parameters; kf, km, kb, andkk, the force gain, acceleration gain, velocity gain, and displacement gain, respectively.
Md, Bd, and Kd in equation (1) are free to change, as are kf,
km, kb, and kk. Therefore, it is possible to operate the intervening impedance by changing these parameters, althoughstability must be maintained.
B. MANIPULABILITY ELLIPSOID
The manipulability ellipsoid [5] is one of characteristics
used to obtain the condition of robots.
We consider the set of all end point velocities that can berealized by joint velocities. The set of these velocities iscalled the manipulability ellipsoid. A long axis along themain axis of this ellipsoid implies that the end point of thearm can achieve a large velocity along the direction of thatparticular axis. On one hand, a short axis implies that it canachieve only a small velocity along the direction of thatparticular axis. These axes indicate the extent to which theend point of the arm can freely move, that is, the manipulability of the end point of arm. Fig 1 shows the concept ofthe manipulability ellipsoid for an elbow joint.
The manipulability ellipsoid is represented by the equation given below:(2)
X& T ( J + )T J + X& ≤ 1+
where J is the pseudo-inverse Jacobian of the robot,
and it is a function of the joint angle. The manipulability
ellipsoid is decided by a certain joint angle.
Further, the volume of the manipulability ellipsoid is
proportional to the manipulability, which is decided by thefollowing equation:w = det( JJ T )where det() is the determinant of the matrix.

(3)

Manipulability
Ellipsoid
Singluar
Configuration

Side View of Robot
Fig.1: Manipulability ellipsoid at elbow joint

This manipulability factor becomes zero because therank of the Jacobian degenerates when the robot is in thecondition of singular configuration. In the vicinity of asingular configuration, the ellipsoid that has a short major
axis is calculated; for a location that is distant from thesingular configuration, the ellipsoid that has a long major
axis is calculated. Therefore, it is considered that the lengthof the main axis of the ellipsoid indicates the distance fromthe singular configuration.
C. SELECTION OF IMPEDANCE PARAMETERS
USING MANIPULABILITY ELLIPSOID
It is possible to increase the intervening impedance by
the method described in other studies [3, 4]. Because agreater force is needed as the intervening impedance increases, it becomes difficult for the operator to operate theslave robot. Although in general, the existence of intervening impedance becomes a difficult problem, the intervening impedance can solve the problem of avoidance of
singular configurations if utilized.
Using the information of the length and direction of themain axis of this ellipsoid, we try to adjust the intervening
impedance by using the impedance-controlled bilateralcontrol method. That is, when the calculated main axis islong, local impedance parameters should be provided since
the intervening impedance is as close to zero as possible. As
the length of the main axis is gradually reduced, its control-like parameters are gradually increased. These operations are executed against each direction of the main axis of
the ellipsoid. The operator has to exert more force while
operating the robot because of an increase in the intervening
impedance parameters; hence, it becomes very difficult for
the robot to attain a singular configuration. As a result, theavoidance of singular configuration is realized naturally.
When the intervening impedance parameters are updated, they cannot simply be changed according to the direction along which the intervening impedance increases byusing the manipulability ellipsoid. The robot and the operator will not be able to move from there because the intervening impedance parameters continue to maintain verylarge values, i.e., to maintain a very “firm” state in the
singular configuration.
Therefore, we consider a method to change the intervening impedance parameters in compliance with the direction of force. Now, it is assumed that the end of the armof the robot is to be fluctuated along a certain direction.
Then, the fluctuation in each joint angle is given by thefollowing equation:(4)∆Θ = J + ∆X
where delta X is the fluctuation along the positive or
negative axes in the Cartesian coordinate system. The details of the coordinate system are described in Section III.
The Jacobian J (Θ + ∆Θ ) is re-calculated by using thisangle variation, and the main axis of the manipulability ellipsoid is also calculated. The intervening impedance parameters are updated by using the component of variation
along the direction of the main axis obtained upon process.
As a result, it becomes possible to setup the impedance
parameters along the direction of variation of force. When1103

the arm moves away from the vicinity of a singular configuration, it can move toward any point other than the
singular configuration because the length of the main axis of
the ellipsoid that is calculated increases along the direction
away from the ellipsoid.
In this study, we use local impedance parameters tochange the intervening impedance parameters. The local
impedance parameters are setup parameters Md, Bd, and Kd
in equation (1) and the common value in the master-slave
system. Fig. 2 shows the control diagram of impedance-controlled bilateral control. For changing the local
impedance parameters for the main axis of the manipulability ellipsoid, we use the following weighting function:a(5)
impedance weight = exp( 2 )xwhere a is a constant and x is the input value.
The length of the axis is provided as input to equation(5) and the returned value is multiplied by the base local
impedance parameters. For a location that is distant from thesingular configuration, equation (5) returns a value of nearly
1.0. Then, the operator can manipulate the system using theinitial parameters in the normal operation. The initial parameters should be set such that the intervening impedanceis decreased as much as possible. Therefore, at a locationthat is distant from the singular configuration, the operator
can operate the system while maintaining a low value ofintervening impedance. In the vicinity of a singular configuration, the input to the function becomes nearly 0.0 andthe returned value increases at a faster rate. As a result, theintervening impedance parameters increase and the operator
can avoid the singular configurations.
Among the intervening impedance parameters in equation (1), stiffness kˆ should become zero at a location that is
distant from a singular configuration. If kˆ is not equal tozero, the operator always experiences a reactive force while
operating the system.
Therefore, the parameters should be set such that kˆ
becomes zero. As shown in equation (1), k̂ is controlled bythree parameters—Kd, kf, and kk. Either Kd = 0 or kk = 1 mustbe satisfied to achieve kˆ = 0. Kd = 0 is undesirable from theviewpoint of control stability. Hence, we set kk to 1.0.
Master arm local impedance

Kd

Intervening impedance

^
m

Md

Slave arm local impedance

Md

Kd

k^
Bd

Bd

Master arm local control
force

^
b

Slave arm local control

Intervening
impedance

F = M d X&& + Bd X& + K d X

Impedance control
F = M d X&& + Bd X& + K d X
reference position posture

Motor control
position posture

torqueManipulator

Impedance control

F = mˆ X&& + bˆX& + kˆXmˆ = f ( M , k , k )d m fbˆ = f ( B , k , k )d b fkˆ = f ( K , k , k )
d k f

force

reference position posture

Motor control
torqueposition posture

Manipulator

Fig.2: Control diagram of impedance-controlled bilateral control

However, if kˆ = 0, the operator does not experience areactive force even if the arm is in the vicinity of a singularconfiguration. If the velocity and acceleration of the end
point were to become zero at the vicinity of a singular configuration, the arm would move toward a singular point. To
describe briefly, there is a risk that the arm may attain asingular configuration. To avoid this situation, we adjust thegain kk by using the following equation:
gain weight = 1.0 − exp( −b ⋅ x )(6)
where b is a constant and x is the input value.
As mentioned above, kk should be 1.0 so that kˆ becomeszero at the vicinity of a singular configuration. kk should beapproximately 1.0 to set the constant value b properly. In thevicinity of a singular configuration, kk becomes less than1.0; consequently, k̂ becomes greater than zero. Because Kd
also simultaneously increases by equation (5), considerable
stiffness appears in the vicinity of a singular configuration.
As a result, the arm is thrust back along a direction thatdeparts from a singular configuration, and the risk of thearm attaining a singular configuration is eliminated.
III. IMPLEMENTATION AND EVALUATIONIn this section, we evaluate the proposed method of
singular configuration avoidance by simulation and application to an actual robot. In particular, the avoidance ofelbow singular configuration is described.
The system configuration image is shown in Fig. 3. The
system comprises a master robot, a slave robot, and a network; the master and slave robots exchange reciprocal information. The information transmitted not only includes
position, posture, and force but also the main axis of themanipulability ellipsoid.
We employed the master-slave system “TELESAR II”[6], which was developed in our laboratory, for the implementation. The TELESAR II system comprises a masterside and a slave side. The master robot has a pair of exoskeleton arms with 6° of freedom. The slave robot has a pairof humanoid arms with 7° of freedom. Each joint has a
motor with an encoder and a potentiometer. The end pointof each arm has a 6-axis force/torque sensor (BL Autotech,Inc.). The master side and the slave side are controlled byseparate PCs. Each PC (Pentium 4, 2.4 GB processor) isconnected by MEMLINK (1 MB/s). The lengths of the arms
are shown in Table1.
The axes of coordinate systems for the master and slave
side are directed as shown in Fig 4. We define the X coordinate along the front direction and the Z coordinate along
the vertical upward direction. The base coordinate system
origins are attached to the point of intersection of shoulder
pitch and roll joints. To evaluate the avoidance singularconfiguration of the elbow joint, the master arm is moved
only along the X direction. Using simulations, we estimate
the operational force required to move the arm at a constantvelocity along the direction to the right of the X-axis. From
this evaluation result, we can determine the effect of theintervening impedance parameter bˆ in the vicinity of asingular configuration. In this evaluation, the manipulating
velocity is set to 0.01 m/s. We evaluate not only the force1104

that approaches a singular configuration but also the force
that recedes from a singular configuration because we want
to determine the effect of the direction of the intervening
impedance parameters. Further, we estimate the operational
force that is required to remain stationary at an arbitrary
point on the X-axis (velocity and acceleration is zero). From
this evaluation result, we can determine the effect of theintervening impedance parameter kˆ in the vicinity of asingular configuration. In the implementation, we estimate
the operational force along with the simulation. The experimental setup and the global coordinates are shown in
Fig. 4.
The initial impedance control parameter settings areshown in Table 2. Parameter a of weighting function (5) is
set to 1/64, and the parameter b of weighting function (6) is
set to 64.

Control PC

Control PC

Network

Impedance
Control

Impedance
Control

Send Information
Manipulability
EllipsoidSingular
Configuration

Jacobian

Manipulability
Ellipsoid
JacobianForce
SensorMotor
Encoder
Force
SensorMotor
EncoderFig.3: System configuration

IV. RESULT AND DISCUSSION
Fig. 5 and Fig. 6 show the local impedance parameters b̂
and kˆ , respectively, in the vicinity of a singular configuration when the master arm is moved at a constant velocity.
Further, Fig. 7 shows the operational force of the operator
when the arm is moved at a constant velocity. Fig. 8 shows
the operational force of the operator when the arm remains
stationary at a point on the X-axis. In each figure, the horizontal axis represents the X-axis position of the end point,
and the vertical axis represents the intervening impedance(Fig. 5 and Fig. 6) and operational force (Fig. 7 and Fig. 8).
The simulation result and the implementation result are
shown in a single figure. We define the force that approaches a singular point as “forward” and the force thatmoves away from a singular point as “backward” in eachfigure.
As observed from Fig. 5 and Fig. 6, the intervening
impedance parameters increase drastically when the end
point position approaches the vicinity of a singular configuration.
Table 1: The length of arm

MasterSlave

Upper arm

0.45[m]0.32[m]Lower arm

0.35[m]0.25[m]Table 2: Initial local impedance parameters and control gain

Impedance parameters

Control gain

Md

1.0 [kg]k m ,k b ,k f

0.5

Bd

21.2 [N/(m/s)]

kk

1.0

Kd

50.0 [N/m]Fig.4: Experimental setup

Consequently, as observed in Fig. 7, the operational
force of the operator increases so that it can approach thesingular configuration. From the simulation result, at 0.45 m,
a control force of approximately 0 N is needed, while at
0.545 m, a control force of approximately 15.0 N is needed.
A similar trend is observed in the implementation result; at
0.45 m, a control force of approximately 1.0 N is needed,while at 0.535 m, a control force of approximately 20.0 N isneeded. Based on the values shown in Table 2, the end point
position is found to be approximately 0.57 m. Apparently, it
becomes difficult for the arm to attain a singular configuration. The operational force which human able to exert as
300 N high as [7]. By contrast, our system can produce thereactive force larger than human’s force through the powerful motor application if the output from motor is sufficient.
Therefore, it is impossible for user to reach the singularconfiguration.
In simulation, the forward force increases in the vicinityof a singular configuration, but the backward force is relatively less. Thus, the direction of the intervening impedance
parameter proposed in chapter 2 is reflected in the system.
However, the proposed method not only employs the direction of the intervening impedance parameters but also themethod that utilizes the stiffness only in the vicinity of
singular configurations. Hence, the thrust-back force works
in the vicinity of singular configurations, as shown in Fig. 8.
From Fig. 8, it is observed that in the vicinity of a singularconfiguration, if the arm remains stationary, the operational
force increases because the intervening impedance pa-

1105

Intervening impedance b [Ns/m]

600

simulation forward
simulation backward
implementation forward
implementation backward

500

simulation
implementation

Operation force [N]15105Singular point

0
0.45

0.47

0.49

-5

0.51

0.53

0.06

0.04
0.03
0.02

Singular point

0.47

0.49

0.51

0.53

200

Fig. 9: Manipulability

100

0.55

0.57

0.59

Table 3: Cycle time and overhead in control loop
Singular point

50

0.47

0.49

0.51
0.53
X-axis position [m]

0.55

0.57

0.59

40
35
30
25
20
15
10
5

Singular point

0
0.45

0.47

0.49

0.51
0.53
X-axis position [m]

0.55

0.57

0.59

Fig.6: Intervening impedance parameter kˆsimulation forward
simulation backward
implementation forward
implementation backward

105
Singular point

0.47

0.49

0.51

0.53

-5
X-axis position [m]0.55

cycle timeoverheadsimulation forward
simulation backward
implementation forward
implementation backward

45

0
0.45

0.59

simulation
implementation

0.05

X-axis position [m]

15

0.57

Fig. 8: Operation force of the operator (remain stationary)

300

20

0.55

X-axis position [m]00.45

Fig.5: Intervening impedance parameter bˆ

Intervening impedance k [N/m]

20

0.01

400

0
0.45

Operation force [N]Fig. 7: Control force of the operator

Manipulability

rameter k̂ increases there (Fig 6). The backward force of
implementation in Fig. 7 changes, maintaining the positive
direction due to the effect of this thrust-back force. As aresult, the backward intervening impedance parameters of
the implementation in Fig. 5 and Fig. 6 are approximately
equal to the forward intervening impedance parameters.
Fig. 9 shows the manipulability of the simulation andimplementation. The horizontal axis represents the X-axis
position of the end point; the vertical axis, the manipulability. The manipulability, which is given by equation (3), also
decreases in the vicinity of a singular configuration
Although the implementation result of the operational
force shows a similar trend to the simulation result, the implementation result does not entirely correspond to thesimulation result. At a location that is distant from a singularconfiguration, a constant operational force is required of theoperator. Moreover, in the vicinity of a singular configuration, the measured operational force is smaller than that ofsimulation result.

0.57

0.59

without the
proposed method
1.16 [ms]with theproposed method
1.25 [ms]7.74 [%]

These results can be attributed to selected motor control,
control parameters, and environment setup. In this evaluation, the end position of the operator’s arm does not correspond to that of the slave arm because we have selected PD
control. In addition, the adjustment of the control parameters is unclear. If the motor control method and the control
gain were properly selected, the operational force would
approach that in the simulation result. However, it is difficult to select the method and parameters because the stability of control and fluctuation in the sensor values must be
considered. We plan to solve this issue along with the optimization of other control parameters in a future study.
Even if the system was ideal and the conditions were
optimum, the proposed weighting function gives a verysmall output value at locations that are distant from singularconfigurations. Hence, it is difficult to make the operational
force equal to zero by using the proposed method. By setting the threshold to apply the weighting function, the operational force becomes zero. We will evaluate this method
in a future study.
This method cannot distinguish the force caused by thevicinity of singular configurations from the interaction force.
In the near future, we will evaluate in detail whether this
distinction is needed.

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Table 3 shows the overhead of the cycle time that arises
by using this method. The values in Table 3 are the averagesof 10000 repetitions of cycle time in the control loop. As
observed in Table 3, the loop time is 1.25 ms when thismethod is applied, and 1.16 ms when not applied. Therefore,
the increase in the processed time is approximately 7.74%;
thus, the overhead of this method is less. In the near future,even if a loop time of 1 ms is required in a master-slave
system, this method can be applied. Hereafter, a further
evaluation, including application, will be needed for providing a quantitative proof.
V. RELATED WORKS
Many researches have been conducted on the avoidanceof singular configurations [8-11]. In these researches, themain aim was the characteristic clarification of the singularconfiguration and formulation. Nakai et al. attempted to
avoid singular configurations by using properly selectedkinematics in [12]. Further, Hwang et al. kinematicallyanalyzed and evaluated the singular configuration existingin a single-master-multi-slave system [13]. However, there
are few examples of the implementation of a humanoid
robot with 7° of freedom. A virtual fixture was also proposed [14]. It is relevant to our research with respect to thelimitation of motion space. It has been implemented in thearm with 1° of freedom. The intervening impedance wasformulated [5]. However, there are few researches on its
applications to information displays.
We focused on the avoidance of singular configuration
in a humanoid robot with multiple degrees of freedom andon the intervening impedance in a bilateral control system.
We propose a system that can avoid the singular configuration of a slave robot by changing the intervening impedance on the basis of the manipulability ellipsoid. In thisregard, our study is unique.
VI. CONCLUSION
We proposed a method that utilizes the intervening
impedance existing in bilateral control systems to avoid thesingular configuration of robots. In our proposed method,
by applying the impedance-controlled bilateral control
method to the manipulability ellipsoid, it is possible to limit
the motion that causes singular configurations.
We implemented our proposed method using a telexistence master-slave system. As a result, the intervening impedance parameters were increased in the vicinity of asingular configuration and the operator could avoid singularconfiguration. In this evaluation, in the vicinity of a singularconfiguration, an operational force greater than 20.0 N was
needed. Moreover, the overhead of control time by applying
this method was 7.74%. Therefore, the overhead of the
proposed method was less.
In future, we will evaluate this method quantitatively bycomparing it with other methods. In addition, to verify its
advantage in universal master systems, we will estimate its
influence on the switching of different slave robots. Further,
we will consider a better displaying method for a singularconfiguration in order to realize intuitive sensation.
VII. REFERENCES[1]

S Tachi, K Tanie, K Komoriya and M Kaneko, "Tele-existence(1):Design and Evaluation of a Visual Display with Sensation of Presence", in Proceedings of the 5th International Symposium on Theory
and Practice of Robots and Manipulators (CISM-IFToMM RoManSy'84), June 26-29, 1984, pp. 245-254[2] Yasuyoshi Yokokohji and Tsuneo Yoshikawa, "Bilateral Control of
Master-Slave Manipulators for Ideal Kinesthetic Coupling-Formulation and Experiment", IEEE Transaction on Robotics
and Automation, Vol.10, No.5, 1994, pp.605-620[3] Susumu Tachi and Taisuke Sakaki, "Impedance Controlled Master-slave Manipulation System. Part I. Basic Concept and Application
to the System with a Time Delay", Advanced Robotics, Vol.6, No.4,
1992, pp.483-503[4] Taisuke Sakaki and Susumu Tachi, “Impedance Controlled Master-slave Manipulation System: Part II. Modification of Force Sensation and Extension of Operation Capability”, Advanced Robotics,
Vol.7, No.1, 1993, pp.3-24[5] Tsuneo Yoshikawa, "Dynamic Manipulability of Robotic Mechanism", Journal of Robotic Systems, Vol.12, No.1, 1985, pp.113-124[6] Riichiro Tadakuma, Kiyohiro Sogen, Hiroyuki Kajimoto, Naoki
Kawakami, and Susumu Tachi, "Development of Multi-D.O.F. Master-Slave Arm with Bilateral Impedance Control for Telexistence",
14th International Symposium on Measurement and Control in Robotics (ISMCR 2004), September 16-18, 2004, pp. D21-Page
1-D21-Page 5[7] Warick, D. , G. Novak, A. Schultz and M. Berkson, "Maximum voluntary strengths of male adults in some lifting, pushing, and pulling
activities ", Ergonomics, 23(1), 1980, 49-54,[8] Nazareth S. Bedrossian, "Classification Of Singular Configurations
For Redundant Manipulators", In Proceedings of the IEEE International Conference on Robotics and Automation, May 13-18, 1990, pp.
818-823[9] J. Seng, Kevin A, O'Neil, Y.C.Chen, "Escapability of Singular Configuration for Redundant Manipulators via Self-Motion", In Proceedings of the IEEE/RSJ International Conference on Intelligent
Robots and Systems 95. 'Human Robot Interaction and Cooperative
Robots', August 5-9, 1995, pp. 78-83[10] Li-Ping Cheng and Kazem Kazerounian, "Study and Enumeration ofSingular Configurations for the Kinematic Model of Human Arm", In
Proceedings of the IEEE Bioengineering Conference, April 8-9, 2000,
pp. 3-4[11] Katsuya Kanaoka and Tsuneo Yoshikawa, "Dynamic Singular Configuration of Flexible Manipulators", In Proceedings of the IEEE/RSJ
International Conference on Intelligent Robots and Systems, October
31-November 5, 2000, pp. 46-51[12] Kentaro Nakai, Kazuhiro Kosuge and Yasuhisa Hirata, "Control of
Robot in Singular Configurations for Human-Robot Coordination",
In Proceedings of the IEEE International Workshop on Robot andHuman Interactive Communication, September 25-27, 2002, pp.
356-361[13] Gilgueng Hwang, Noriaki Ando, Peter Szemes, Hideki Hashimoto,"Development of Single-Master Multi-Slave Tele-micromanipulation
System", In Proceedings of the 2004 IEEE International Congerenceon Industrial Electronics, Control and Instrumentation (IECON'04),
November 2-6, 2004, pp. 690-695[14] Jake J. Abbott and Allison M. Okamura, "Virtual Fixture Architectures for Telemanipulation", In Proceedings of the IEEE International Conference on Robotics and Automation, September 14-19,
2003, pp. 2798-2805

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