情報処理学会 インタラクション 2014
IPSJ Interaction 2014

B0-4
2014/2/28

力覚共有マウスを実現するためのマルチラテラル遠隔制御に関する設計法と国際間ゲームへの適用
森田 陽介†1,a)

小川 裕也†1

今村 孝†2

Kawaguchi Akira†3

三好 孝典†1

寺嶋 一彦†1

概要：本研究では，力位置帰還型マルチラテラル遠隔制御システムを使用しインターネットを介して複数の人が力覚を共有できるシステムを開発することを目的とする．本研究では，スキャッタリングマトリッ
クスの新たな知見よりマルチラテラル遠隔制御システムを安定させるためにスキャッタリングマトリック
スと位相制御フィルタを適用する．さらに，力覚共有マウスシステムに対する設計法を導出する．我々のシステムにおいて，トポロジーはネットワークで通常使用されるスター型のサーバ・クライアントシステ
ムの形態を取り，クライアントとサーバ間の接続の成否にシステム全体が影響を受けない構成となっている．我々は，システムの有用性を確認するためにハプティックデバイスを使用しソウル -フロリダ-豊橋間で実験を実施し，位置がハプティックデバイスに印加された力によって制御された．実験より我々は，3つのクライアント間の力覚共有が通信遅延を含むマルチラテラルシステムで実現できることを確認した．

Design Method for Multilateral Tele-Control to Realize Shared Haptic
Mouse and Its Application to Intercontinental Game
Yosuke Morita†1,a) Yuya Ogawa†1 Takashi Imamura†2 Akira Kawaguchi†3
Takanori Miyoshi†1 Kazuhiko Terashima†1

Abstract: In this study, we aim to develop the system that many people can share a sense of force throughthe Internet, using a force-position multilateral tele-control system. We apply scattering matrix and phase
control ﬁlter in order to stabilize the multilateral tele-control system with a new knowledge of scattering matrix. Additionally, we derive a design method for system shared haptic mouse . The unique characteristicof our design method is that stabilization is achieved by focusing on phase. In our system, topology takes
the form of a commonly used star-shaped client/server system network topology and is conﬁgured such thatthe success or failure of speciﬁc connections between the client and server do not aﬀect the entire system.
We have conducted experiments between Stuttgart, New York, and Toyohashi using three haptic devices
to verify the usefulness of this system, and successfully position was controlled by the force applied to thehaptic device. Through experimentation, we verify that the shared haptic sensing between three clients is
conﬁrmed to have been realized in a multilateral system that included a communication delay.

1. Introduction
The challenge faced by tele-control on a network is ﬁnding a way to overcome the instability arising from the
†1
†2
†3
a)

communication delays that arise between the master andslave, and while numerous solutions have been proposedby researchers to date.

But the following three basic

problems remain unsolved: 1) how to stabilize the master/slave connections in a non-passive system, 2) how to

現在，豊橋技術科学大学
Presently with Toyohashi Uniersity of Technology
現在，新潟大学
Presently with Niigata Uniersity
現在，ニューヨーク市立大学
Presently with City College of New Yorky morita.@syscon.me.tut.ac.jp© 2014 Information Processing Society of Japanstabilize multilateral control in a system conﬁgured withn : m connections, and 3) how to stabilize multilateral
tele-control in an Internet environment, despite the indeterminate number of connections resulting from users

346

Gnet(s)Master

um

+

fm

+

Gm(s)
xm

+
+

Gmm(s)

T1

u's

Ws(s)

M1

S1

M2

S2

vm

W m (s )

v'm

Slave

us +

T2

vs

Network Side

fs

−

Gs(s)
−
+
Gss(s)

xs

Terminal Side

Fig. 2 Block diagram of bilateral tele-operation system using
Scattering matrix
Fig. 1 Image of the shared haptic mouse which enables people
in the world to share the force each otherbeing able to connect and disconnect their systems freely.
The ﬁnal image of this study is shown in Fig. 1. The
mouse is moved by strings or wires stretched in four di-

2. Characteristics of the Scattering Matrix

rections. This shared haptic mice used worldwide employ

In order to clarify the characteristics of the scattering

force sensors to measure the operating force applied bymatrix, we consider force and position feedback-type bi-

the operators, and the mice move in response to it’s force.

lateral control that includes a time delay. In Fig. 2,

For example, if Operator A in the United States attempts

Gm (s) is the master, Gs (s) is the slave, fm (t) is the force

to move the mouse to the right but Operator B in Japanapplied by the operator, fs (t) is the force received by the

and Operator C in Korea resist that movement, the mouseslave, xs (t) is the device location computed by the slave,will not move. The mouse location is the same regardlessand xm (t) is the location received by the master. The scat-

where it is viewed around the world.

tering matrix is the cross-coupled portion of the drawing.

This paper presents new insights for scattering matri-

Herein, the inner side is of the scanning matrix is referredces, and upon solving the aforementioned problems for ato as the network side and the outer side is referred to as

certain class of models, derives a design method for a sys-

the terminal side.

temshared haptic mouse . Typically, control design isSpong et al. were the ﬁrst researchers to incorporate aoften stabilized in terms of the norm or gain. However,scattering matrix into tele-control[1]. They demonstrated

the unique characteristic of our design method is that sta-that a scattering matrix is passive regardless of the time-bilization is achieved by focusing on phase. In the case ofinvariant delay T and that if the non-linear systems ofan Internet-based multilateral tele-control system with aGm (s) and Gs (s) have passivity, the system will be sta-large unspeciﬁed number of connections, it is diﬃcult toble. This conﬁguration is commonly known as the Cayley

design a gain-dependent control system, because the op-transform, but the achievement of Spong et al. can also be

erating force response from a teleoperate site can range

considered to be the introduction of the concept of timefrom 1 [N] for a single person to a response on the orderdelay.

6of 10 [N] from several tens of thousands of people.

However, it is unlikely that real-world stability prob-

The design class targeted by this paper is a model inlems can be solved with passivity alone. In digital control,

which a one-input one-output linear passive system is con-for example, due to S/H, the phase delay will reach -180

nected in series to each of the output terminals of an n-[deg] at the Nyquist frequency, and even the motion of a

input n-output linear passive system, as will be describedspring-mass-damper system or a point mass, which is thelater, and the entire system is non-passive. Although it ismost basic system in mechanics, will result in a second-

limited as perceived, this model is useful for the purpose

order delay system and therefore be non-passive. To solveof this paper, which is to realize a shared haptic mouse.

this problem, Miyoshi et al. have previously proposed aThis paper is organized as follows. Section 2 presentsbilateral control system stabilization method for the non-new insights into scattering matrices, which are used inpassive linear Gs (s) and Gm (s) systems[2]. In the present

Section 3 to demonstrate the stability of the shared hap-study, a norm compensator that suppresses norms of 1 ortic sensation mouse. Section 4 shows the experimental

greater that have been generated due to non-passivity inresults, which are summarized in the Conclusion.

the communication circuit is used to ensure stability.

© 2014 Information Processing Society of Japan

347

us +

50

Gnet(s)

0

fs
−

0
-2
Re[Gs(s)] -1

0

1

2

-4

vs

Im[

-100

4

s)]

-50

+

xs

(a)Physical Matrix(a) |Gss(s)| according to Re[Gs(s)] and Im[Gs(s)] (3D View)

f 's

us
Gnet(s)−Gs(|Gss(s)| [dB]

100

-1

fs

parcialscatteringmatrixxsvs(b)Partial Matrix

Fig. 4 Phase of scattering matrix according to Re[Gnet (s)] andIm[Gs(s)]Im[Gnet (s)] on complex plane420

as seen from the terminal side, is expressed by the follow-

Re[Gs(s)]P-2ing equation which is similar to Eq. (1).

θ
Gnet (s) − 1
Fs (s)=Xs (s)
Gnet (s) + 1-4
1
3-3 -2 -1 0
2(b) |Gss(s)| according to Re[Gs(s)] and Im[Gs(s)] (Density Plot)

Fig. 3 Magnitude of Gss (s) according to Re[Gs (s)] and(2)

At this time, we obtain the follow Proposition.

Im[Gs (s)] on complex plane

Proposition2
When r(ω) = |Gnet (jω)| (r(ω) ≤ 1), lower bound 6 ∆(ω)

2.1 Characteristics of Gain in Network-Side

F 0 (jω)

input to the scattering matrix is us and the output fromFs (jω)of phase of Xss (jω) = − X
in scattering matrix is givens (jω)2r(ω)
as 6 ∆(ω) = − arctan. Moreover, upper bound1 − r(ω)2
6 ∆(ω) is given as

the scattering matrix is vs , is expressed by the following
6

In Fig. 2, the system is disconnected at us and vs on theslave side, when the transfer function Gss (s), where theWhere the phase of the sign-inverted fs0 is shown virtu-

equation using Gs (s).
Gss (s) =Vs (s)Gs (s) − 1=
Us (s)Gs (s) + 1

2r(ω)∆(ω) = arctan 1−r(ω)
2.

ally in Fig. 4 (b). Assuming that a portion of the scat(1)It is apparent that the magnitude of the gain, whentering matrix has been extracted, the portion from xs to
fs0 is hereinafter referred to as apartial scattering ma-

represented on an Gs (s) = a(ω) + b(ω)i complex plane, istrix (PSM). The reason for considering the negative sign

represented by Fig. 3 and Proposion 1, and in terms of

is indicated in paragraph 2.3 and 3.3.

the relationship with passivity.
Proposition1
When θ(ω) = 6 Gs (jω), in −π ≤ θ < −π/2，π/2 < θ ≤ π,
upper bound√|Gss |(ω) of |Gss (jω)| is given as

In the scattering matrix, if the H∞ norm is less thanor equal to 1, it is known that the output thereof will
be passive, which is consistent with the results of theabovementioned Proposition. In other words, if r ≤ 1,

1 − cos θ(ω). Moreover, |Gss |(ω) = 1,in
1 + cos θ(ω)−π/2 ≤ θ ≤ π/2.

the phase is within the range of −π/2 to π/2, and the

Proposition 1 means that the upper bound of the gainof the scattering matrix, as seen from the network side,of change of a(ω) = Re[Gnet (s)], and b(ω) = Im[Gnet (s)].
√As r = a2 + b2 expands outward centered about the ori-

can be uniquely determined by the phase of the terminal

gin, it can be conﬁrmed that the range of possible phasesside. In other words, the scattering matrix is a component

expands. The angle also changes according to the phasethat can control the network-side gain with the phase onof Gnet (s) itself, but does not fall below the lower bound.

|Gss |(ω) =the terminal side.

passivity in a linear system is shown. Fig. 5 shows athree-dimensional (3D) graph of the 6

Fs0 (jω)Xs (jω) at the time

Proposition 2 means that the lower limit of the phase of
the scattering matrix, as seen from the terminal side, can

2.2 Characteristics of Phase in Terminal-Sidebe adjusted by modifying the gain on the network side.

Consider Fig. 4 (a), which is an extracted right portion

In other words, the scattering matrix is a component thatof Fig. 2. If the transfer function Gnet (s) is connected to

can use the network-side gain to control the phase of thevs and us , the transfer function of the scattering matrix,

terminal side.

© 2014 Information Processing Society of Japan

348

1

fm
G

0.5

m (s

0.
1.57
0.
angle[rad]
-1.57
-1

-1
-0.5

0.

1

f 's

fs

us

Gs(s)

Gnet(s) p.s.m.

xsvsGain control space

TuvsPhase control space(a) stability analysis

et (s)

1

u'

Td

s

Ws(s

1

)

vs

0.5

-1

fs
G90(s)xs

Gs1(s)

passive

) +
−
−

fs1

+ x
s1
Gmm2(s)
u's
fs2
+
+
fm2
Ws(s)
Tu2
−
+
Gm(s)
Motion server
−
++
xm2
Td2
vs + xs2
Client 2
f sn.........

Gnet(s)p.s.m.

+++1 (sIm[Gnet (s)] on complex plane-1

1

Client 1 G

Fig. 5 Phase of scattering matrix according to Re[Gnet (s)] and

f 's

Gn

mm

a(ω)

us

+

)

xm

b(ω)

-0.5

1

m
Gm

Client npassive(b) combination of two passive system

s)
n(

+

phase control domain with scattering matrix

T un

+

f mn s )(Gm
x mn

Fig. 6 Stability condition between gain control domain ands)
u' s Ws(

++

+

−
−

+

x sn

vs
T dn

Fig. 7 Block diagram of shared haptic mouse with multilateral

2.3 Stability Condition of Closed Loop Including

control system

Scattering Matrix
Consider the stability in Fig. 6 (a). Here, the square islateral system having the topology of Fig. 7. That is,a PSM, Gnet (s) has a certain gain r(ω) (at any arbitrary

n shared haptic mice (hereinafter referred to as clients)

phase), and Gs (s) has a phase of θ(ω) (at any arbitrary

existing worldwide are coupled via a network and scatter-gain). In this situation, the follow Lemma can be derived.

ing matrix to a motion server, and each exerts mechanicalLemma1 When Gnet (s) has an arbitrary phase andinterference on the others. Because of the complex in-

Gs (s) has an arbitrary gain and prescribed phase θ(ω) =tertwining of non-passive systems with diﬀerent commu-

Gs (jω) (−π ≤ θ(ω) ≤ −π/2), stability
condition of the√nication delays Tui ,Tdi (i = 1, 2, . . . , n) existing for each6closed loop system is |Gnet (jω)| ≤1+cos θ(ω)
1−cos θ(ω) . Moreover,when Gs (s) consists of Gs1 (s)×G90√(s), the stability condi-

network, stabilization is not easy to realize.
To date, as methods used to stabilize multilateral sys-

1+sin θ(ω)
1−sin θ(ω) , and closed

tems, Katsura et al.[3], have proposed a relaying topol-

loop is fed back with two passive components. Whereogy to implement the haptic sensing. However, with thisphase lag of G90 (s) exceeds -90 [deg] and θ(ω) = 6

topology, all haptic sensing will be interrupted if the net-tion of Fig. 6 (b) is |Gnet (jω)| ≤Gs1 (jω)(− π2 ≤ θ(ω) ≤ 0).

work is cut even at just one location. Therefore, in prac-

This Lemma holds special signiﬁcance for tele-control

tice, shared haptic sensing via the Internet would notstabilization because, in an environment where the net-

possible. In contrast, because the topology proposed inwork side phase has indeterminacy due to an indeﬁnite

this study takes the form of a commonly used star-shaped

communication delay, and in an environment where theclient/server system network topology and is conﬁgured

terminal-side gain also has indeterminacy due to an in-such that the success or failure of speciﬁc connections be-deﬁnite number of accesses and parameter ﬂuctuations,

tween the client and server do not aﬀect the entire sys-stability can be improved in both directions by manipu-

tem, the number of connections can be increased verylating |Gnet (jω)|.

easily.

3. Stabilization Method in Multilateral
Systems
3.1 Server Model
This paragraph describes the stabilization of a multi-© 2014 Information Processing Society of Japan

Behzad et al.[4] have proposed dual-user tele-

operation systems, and allowed interaction between bothusers. However, this system can be applied only two operators. Duc et al.[5] have proposed a control methodthat is besed on bilateral tele-operation system, and conducted the experiment using one master robot and two349

∑
ms2 + cs + ki
1Tξi 2 Fsi (s) +Tξi Tξj Fsj (s)ki s(ms + c)s(ms + c)
n

f s2
k2

c
f s1

k1

m

j=1(j6=i)

x s2

xξ

kn

ξ

x s1

f sn
x sn
Fig. 8 Physical model of multilateral tele-control system=

1
Fsi (s) +
ki

n
∑
j=1

1
Tξi Tξj Fsj (s)s(ms + c)(4)(i = 1, 2, . . . , n)

The second term represents the value of xξ determinedby fsj , and the ﬁrst term represents the relative positionof xsj from there. This function is not positive deﬁnite,slave robots. However, this system applied by one mas-and is therefore non-passive.

ter and many slave, that is, operator is only one person.

This is converted to the block form of Fig. 10.

Kanno et al.[6] have proposed multilateral tele-operation

Xs (s) =based on wave-variables. With this system, small position

1
GsO (s)Fs (s)ms + c(5)

tracking errors occur due to wave variables and local PD
control , whereas, our method does not have any error insteady state because it does not use any feedback signal
for stabilization. Ohnishi et al.[7] have proposed centralized controller for multilateral control system. However,this system has the constrain in which each operator’s position has to be consistent with each other. On the otherGsO (s) =
m
c

Tξ1 2
Tξ1 Tξ2
k1 s+ k1 + s
s

Tξ2 2
Tξ2 Tξ1mc
sk2 s+ k2 + s





..
.

..
.

Tξn Tξ1sTξn Tξ2
s

···
···
..
.



Tξ1 Tξns
Tξ2 Tξn
s







..
.

· · · kmn s+ kcn +

Tξn 2
s

hand, our proposed system does not have any constraint

Where, Xs (s) = [xs1 (s), xs2 (s), ..., xxn (s)]T ,for each client.

1, andFs (s) = [fs1 (s), fs2 (s), ..., fsn (s)]T , Gsi (s) = ms+c

The physical model of the motion server is shown in
Fig. 8. An operating force fsi [N] is provided as an input
via a spring ki [N/m] to a mass point having a mass m

GsO (s) is positive real and passive system as follows.
{}
GsO (jω) + GsO T (−jω)
c cc= diag, ,···,
≥0
2
k1 k2
kn

[kg]. With the spring end position xsi [m] at this time as
the output, fsi and xsi belong to a local coordinate system

3.2 Client-Side Model

Xi that forms an angle from the global coordinate system

In contrast, the master model Gm (s) is an admittanceξ to Tξi = cos φi . Here, Tξi indicates the direction of force

control system that is assumed to consist of a force sensor

added by the i-th client, and is assigned arbitrarily. For

capable of detecting the operating force and is attachedexample, if Tξ1 = 1 and Tξ2 = −1, they will be placed

to a linear slider capable of positioning a servo motor, as

opposite each other. For the purpose of simpliﬁcation,

shown in Fig. 9 (a). The operator transmits the oper-

the mass point SO is assumed to move only in the direc-

ating force fm via the sensor, and the server transmits

tion of the xξ [m] coordinate system, and in proportion to

the position reference xm to the linear slider. Here, if

the speed in the ξ direction, during which the mass point

Gservo (s) is the transfer function for positioning the linear

encounters the resistance of the coeﬃcient of viscosity cmotor, the Gm (s) transfer function is as given by Fig. 9[N/(m/s)]. xsi is determined under the inﬂuence of all(b) and Eq. (6). Additionally, Kh [N/m] is the spring

inputs fs1 , fs2 , . . . , fsn .

constant of the reaction force generated according to the

At this time, the model is expressed by Eq. (3).
Tξ1 fs1 + Tξ2 fs2 + ... + Tξn fsn = mẍξ + cẋξ
 ks1 (xs1 − Tξ1 xξ ) = fs1
(3)
..


.



 k (x − T x ) = f
sn sn
ξn ξ
sn
We will get input-output relation by applying laplacetransformation method to above equation.

rigidity of the operator’s hand when the slider is moved,and Dh [N/(m/s)] is damper coeﬃcient between the slider
and the operator’s hand. These quantities are determinedby the mechanical properties of the operator’s arm [2].
Although the sign of the scattering matrix in Fig. 7 ispositive, this is not intended to indicate positive feedback.
When the slider is moved in the positive direction, the resistive force generated by the operator’s hand is in thenegative direction.

Xsi (s) =© 2014 Information Processing Society of Japan

350

fm

Additionally, in Fig. 2, assuming that that the H∞ norm
0of the transfer function from vm
to um is less than or equal

fh+

Dhs+KhForce sensor

to 1 and is stable, the gain does not change with the time-

−
Gm(s)

m

From the above, it is shown that the entire system can be

Gservo(s)Linear motorxm(b) transfer function(a) Photographm (s)invariant delay T1 and T2 , and therefore || U
V 0 (s) ||∞ ≤ 1.

Fig. 9 Photograph and block diagram of client systemstabilized by introducing a ﬁlter Ws (s) conﬁgured as√√
m2 ω 2 + c2 − mω
0 ≤ |Ws (jω)| ≤ √(7)
m2 ω 2 + c2 + mωWs (s) is a ﬁlter that functions to control the phase delay of the scattering matrix, generate the phase margin on
the terminal side, and to stabilize the system. Therefore,-1

Gnet(s)it is referred to as a phase control ﬁlter (PCF) below.

p.s.m.

Actually, although the multilateral system is MIMO

Gs1(s)

system, the stability condition will remain intact. Whenxyj
the j-th fsj
becomes passive by using PCF written in Eq.

Gso(s)-1(7), whole the left part of Fig. 10 also becomes passive

Gnet(s) p.s.m.

because passive diagonal matrix is constructed.
Thus, although the number of clients n, the delay timeGsn(s)

Tui and Tdi , the operator rigidity Kh and Dh , and most

passive system

passive systemother parameters are indeterminate, the server-side sys-

Fig. 10 Block diagram of multilateral tele-control system

tem reduces to the combination of two passive system inwhich one is GsO (s) and the other one consists of Ws (s),Fm (s) = (Dh s + Kh )Gservo (s)Xm (s)(6)

scattering matrix, and Gsi (s).

' (Dh s + Kh )Xm (s)3.4 Client-Side Stability
In Eq. (6), Gm (s) is passive regardless of the values of
3.3 Server-Side Stability
Fig. 7 can be rewritten in Fig. 10 from Eq. 5. Herein,
1
GsO (S) and Gsi (s) = ms+c
correspond to G90 (s) andGs (s) in Fig. 6 (b) respectively, and Gnet (S) is the transfer function of network side in Fig. 7
In Eq. (5), in a case where ki is large and m and c aresmall, the 1/s term becomes dominant, and at 0 [rad/s],GsO (s) may become approximately -90 [deg]. In otherwords, if estimated on the phase-delayed side, a phasedelay of approximately -90 [deg] can be estimated overthe entire frequency band. On the other hand, because
Gsi (s) is a ﬁrst-order delay system, the phase becomes−mc ω and approximately 0 [deg] at low frequencies. Accordingly, from Lemma 1, Gnet (s) that realizes stability
for whole system, must exist and have suﬃcient conditions
for stabilization.
√

1 + sin(arctan(− mc ω))
1 − sin(arctan(− mc ω))√√m2 ω 2 + c2 − mω√=m2 ω 2 + c2 + mω|Gnet (jω)|=© 2014 Information Processing Society of JapanKh and Dh , and therefore Proposition 1 prescribes that
|Gmm (jω)| ≤ 1. Gm (s) is also stable because the loop
in the scattering matrix physically has negative feedback.
Accordingly, by setting the PCF Wm (s) = 1, the assumption provided in the previous paragraph is satisﬁed.
3.5 Boundary Condition for PSF Ws (s)When considering a stable steady state in this conﬁguration, as shown in Fig. 2, the cross-coupled signals at
points S1 and M1 are positive and negative signals thatcancel. Furthermore, the signals at points S2 and M2 also
cancel. Accordingly, when Ws (0) = 1 and Wm (0) = 1, it
is ensured that fm = fs and xs = xm , and the force andposition on the master and slave are in agreement.

4. Experimental Results of the Multilateral System
Some experiments were conducted by connecting a totalof three one-degree-of-freedom haptic devices to a server
as clients. Fig. 11 shows the experimental landscapes
between Toyohashi, Newyork, and Stuttgart. In this ap-

351

New York

0.4
RTT [sec]

Aplication Window

0.2

0
0

10

20

30
Time [sec]

40

50

60

(a) Between Toyohashi and New York

Stuttgart

Toyohashi

Fig. 11 Photograph of experimental landscapes using 3 clients

RTT [sec]

1

0.5

0
0

10

20

30
Time [sec]

40

50

60

plication window, vertical bar means player, left player(b) Between Toyohashi and Stuttgart

is Stuttgart operator, center player is Toyohashi opera-

Fig. 12 Experimental results of round trip timetor, and right player is New York operator. Additionally,each client was considered to reside on the same axis andthe operating force fsi is applied as an input to a spring
mass damper system at the server. In this experiment,
the force applied to each haptic device by an operator

Table 1 Typical parameters of experiments
unit value
unit
value
Tu1 + Td1

[ms]

190.8

Tξ

-

1

Tu2 + Td2

[ms]

323.0

ki

[N/m]

200

Tu3 + Td3

[ms]

0

m

[kg]

0.775

is transmitted as the respective client force fmi through

Pl1

[% ]

0.03

c

[N/(m/s)]

1.58

a communication delay Tui to the server. The resultant

Pl2

[% ]

0.00

force of this client is computed by the server to derive a

Pl3

[% ]

0

position xsi . The position xsi computed by the server istransmitted through a communication delay Tdi to each

operated. Fig. 13 (a) shows the resultant force of eachclient, and the position of each haptic device is controlled.

client and the position output from the server, and Fig. 13

In the case of resistance by another operator, the position(b) shows the force of each operator. After approximately

does not change as intended even when force is applied,

30 seconds, the operators of New York and Stuttgart be-

and the operator is able to tactually perceive the operat-

gan jostling so that the positions of their haptic devices

ing force of the other operators.

did not change. At about 45 seconds, the operator ofRound trip time (RTT) during Toyohashi and New

Toyohashi applied a force in the positive direction, andYork, and Toyohashi and Stuttgart is shown Fig. 12. As

then at about 63 seconds, applied a force in the negativefor Fig. 12, variation of RTT was almost constant. For

direction.

this result, we veriﬁed good network condition.

From Fig. 13, it can be seen that during the interval

Table 1 shows the main experimental conditions. Ad-

from the beginning of operation at the time of 30 sec-

ditionally, even though the PCF value has been adjusted

onds until the start of the Toyohashi operation, the force

and a compensator has been added to increase the phaseapplied by New York operator and the force applied bymargin on the terminal side, remarks related to this is-

Stuttgart operator were balanced, and thus there was al-

sue are omitted here. Where Pli is establishment of themost no position change. Additionally, because the forces

packet loss [%] mesured by experiment. Note that theof New York operator and Stuttgart operator were bal-client numbers and the haptic device numbers correspond

anced, during the time intervals from 45 to 51 seconds

to each other. In this experiment, client number 1 is New

and from 63 to 73 seconds, it was conﬁrmed that the force

York, number 2 is Stuttgart, and number 3 is Toyohashi.

applied by Toyohashi and the resultant force Σfmi change

Experimental results of the client force fmi (= force ap-

in the same direction, and that the each position and theplied to a haptic device) and the position xsi output fromresultant force Σfmi also change in the same direction.

a server (= position of each client) are shown in Fig. 13

Furthermore, during the time intervals from 76 to 85 sec-

for the case of operating all haptic devices.

onds, each position ﬂuctuates slightly, but the balanced

In the experiment of Fig. 13, three haptic devices were

© 2014 Information Processing Society of Japan

force relationship keeps its position stable.

352

15

1

10

[3]

0

Position [m]Force [N]

0.5
5
0

5

NewYork
Toyohashi
Stuttgart

10
15
30

0.5

Σ fmi
40

[4]

50

60
Time [sec]

70

80

90

1

[5]

(a) Relationship between force and position calculated byserver15[6]Force [N]

10
5

[7]

0
5
NewYork
Toyohashi
Stuttgart
15
30
40
10

50

60
Time [sec]7080

passive Operating System”，IEEE International Conference on Applications，4-6，2006.
Takumi Ishii，Seiichiro Katsura “Articuled Multilateral
Control for Haptic Broadcasting System”，IEEE Industrial Electronics on Society，7-10，2010.
Behzad Khademian, and Keyvan Hashtrudi-Zaad “A
Four-Channel Multilateral Shared Control Architecture
for Dual-User Teleoperation Systems“，IEEE Intelligent
Robots and Systems，pp.2660-2666，2007.
Nam Duc Do, and Toru Namerikawa, “Cooperative Control Based on Force-Reﬂection with Four-channel Teleoperation System“，IEEE Conference on Decision and Control and European Control Conference，pp.4879-4884，
2011.
Kanno Takahiro, and Yasuyoshi Yokokohji，“Multilateral
Teleoperation Control over Time-Delayed Computer Networks using Wave Variables“，IEEE Haptics Symposium，pp.125-131，2012.
Daisuke Yashiro, Dapeng Tian, and Kouhei Ohnishi，“Centralized Controller based Multilateral Control with
Communication Delay“，IEEE International Conference
on Mechatronics，pp.991-996，2011.

90(b) Applied force of 3 position
Fig. 13 Experimental results of haptic games

From the above, the shared haptic sensing between multiple clients is conﬁrmed to have been realized in a multilateral system that included a communication delay.

5. Conclusion
In this paper, we have presented new insights concerning scattering matrices and, using the characteristics
thereof, have demonstrated the stability of a client/server
multilateral system that has a communication delay. Additionally, through experimentation, we have demonstrated the eﬀectiveness of our proposed system, which
has the advantage of maintaining stability over the entire
system and the shared haptic sensing between multiple
clients is conﬁrmed to have been realized in a multilateralsystem, when there are three clients connected between
Stuttgart, New York, and Toyohashi.

6. Acknowledgments
This work was supported by the Martin Buss in Technische University Munich and JSPS KAKENHI Grant Number 24360090.
参考文献
[1]

[2]

R.Anderson，M.Spong，“Bilateral Control of Teleoperators with Time Delay”，IEEE Transactionson AutomaticControl，Vol.34，No.5，pp.494-501，1989.
Takanori Miyoshi，Kazuhiro Terasima and Martin Buss，“A Design Method of Wave Filter for Stabilizing Non-

© 2014 Information Processing Society of Japan353