2011 IEEE/RSJ International Conference onIntelligent Robots and Systems
September 25-30, 2011. San Francisco, CA, USA

Robust Manipulation for Temporary Lack of Sensory Information
by a Multi-Fingered Hand-Arm System
Akihiro Kawamura, Kenji Tahara, Ryo Kurazume and Tsutomu Hasegawa
Abstract— This paper proposes a novel vision-based grasping
and manipulation scheme of a multi-fingered hand-arm systemrobust for a temporary lack of sensory information. Visual
information is one of the fundamental components for reliablegrasping and manipulation by a multi-fingered hand-arm system. However, in case that visual information such as position
and attitude of an object comes to be unavailable due to the
occlusion or if the object goes out-of-sight temporarily, unstableand unfavorable behavior is often induced. The proposed
method, which utilizes the stable grasping control and theconcept of virtual frame, enables to grasp and manipulate an
object stably even if the visual information becomes suddenly
and temporarily unavailable during manipulation. Firstly, adynamical model of object grasping using a multi-fingered
hand-arm system is formulated. Next, a new control scheme
for robust object grasping and manipulation using the virtualframe is proposed. Finally, numerical simulations are performed to verify the usefulness of the proposed method.

I. I NTRODUCTION
Visual information is one of the fundamental components
for reliable grasping and manipulation by a multi-fingered
hand-arm system [1]. However, in some cases, the visual
information such as object’s position and attitude becomessuddenly and temporarily unavailable due to the occlusion orif the object goes out-of-sight. This causes serious unstablebehavior in grasping and manipulation tasks.
To overcome these problems and make the visual servo
control more stable against the temporary lack of object
information, several methods have been proposed so far.
These methods can be classified into two groups.
The method in former group is based on the accurate
estimation of the position and attitude of a grasped object
in order to compensate the lack of information [2], [3].
Hasegawa et al. proposed a manipulation method which isrobust against various error of a stereo vision by using atactile sensor [2]. The position and attitude of a grasped
object is estimated by solving a minimization problem toensure the consistency between vision and tactile information. Yokokohji et al. also proposed a control method which
is similar to the Hasegawa’s method. In addition to that,
this method compensated quantization errors related to theThis work was partially supported by ”Kyushu University Research
Superstar Program (SSP)”, based on the budget of Kyushu University
allocated under President’s initiative and Grant-in-Aid for JSPS Fellows.
A. Kawamura is with Graduate School of Information Science andElectrical Engineering, Kyushu University, Fukuoka, 819-0395, JAPAN

kawamura@irvs.is.kyushu-u.ac.jp
K. Tahara is with Faculty of Engineering, Kyushu University, Fukuoka,
819-0395, JAPAN tahara@ieee.org
R. Kurazume and T. Hasegawa are with Faculty of Information Scienceand Electrical Engineering, Kyushu University, Fukuoka, 819-0395, JAPAN{kurazume, hasegawa}@ait.kyushu-u.ac.jp
978-1-61284-455-8/11/$26.00 ©2011 IEEE

sampling period to make a servo loop more stable [3].
However, these methods are valid only for a small and shortlack of visual information such as self-occlusion, and not
sufficient for the case in which a large amount of information
is missed. Additionally, the accurate geometric informationof the grasped object such as the size must be provided inadvance.
In the method in later group, the robust control input for
stable object grasping and manipulation is designed even
if the visual information becomes unavailable or unreliable
temporarily [4], [5]. Ozawa et al. [4] and Cheah et al. [5]proposed robust control methods to regulate the position ofan end-effector even if visual information obtained by vision sensors contains geometric uncertainty. However, thesemethods considered some specific tasks such as reaching
to the object by an end-effector, and object grasping andmanipulation tasks are not considered. Since object grasping
and manipulation tasks require not only kinematic information of the robot itself, but also geometrical information of
the grasped object, it is difficult to apply the above method
directly to the grasping and manipulation tasks.
Meanwhile, Tahara et al. have proposed a grasping andmanipulation method without external sensing [6]. Thismethod employs the concept of “virtual frame” which isdefined by the position of each fingertip instead of an actual
object frame. This method is, however, limited to grasp an
object which consists of two flat and parallel surfaces.
For arbitrary shaped objects, we have proposed a stableobject grasping method and a attitude control method foran arbitrary polyhedral shaped object using a multi-fingered
hand-arm system with soft hemispherical fingertips [7], [8].
This method enables stable grasping and attitude control ofa grasped object by a sensory feedback control under thecondition that the object attitude information is available inreal-time. No other information, e.g. the shape of the object
and the contact points between fingertips and object surfaces,
is required.
In this paper, a novel grasping and manipulation method
which is robust for the temporary lack of sensory information
is proposed. This method is based on our previous works[7], [8] but the robustness is enhanced by introducing theconcept of “virtual frame” [6], [9]. Thanks to this concept,
the proposed method enables to regulate position and attitudeof a grasped object stably even if the sensory informationof the object becomes suddenly and temporarily unavailable
during manipulation.
Both the position and the attitude of the virtual frame
proposed by Tahara et al. and Wimböck et al. are defined4201

Center ofcontact area

qa5

qa3

q32

Center of
finger tip

Object

qa4
q31
q12

y

q34

CiX

q13

q22

x0i

ω

q11 q21

rY

CiY

q14

x03

qa2

x

O
z
Fig. 1.

xi

ri

rX

q23

q15

x

q24

x01

Δri

CiZ

q33

rZ

Finger tip

x02

qa1

Center of theobject mass

Multi-fingered hand-arm system

Fig. 2.

based on the center position of each fingertip. Therefore,
the attitude control input may interfere with other control
inputs which are also based on the center position of eachfingertip. For example, the attitude control input and theposition control input are interfered each other. To avoid theinterference, this paper proposes a new concept of the virtualframe in which the attitude of the virtual frame is defined
based on the attitude of each fingertip.
The virtual frame is calculated from joint angles obtainedby internal sensors in multi-fingered robotic hand-arm system. By switching the real frame and the virtual frame
according to the availability of the sensory information, theproposed method enables to control the object position andattitude even if the sensory information is lacked temporarily.
This paper is organized as follows: Firstly a dynamical
model of object grasping using a multi-fingered hand-arm
system is formulated in Section II. A new control scheme forrobust object grasping and manipulation using new virtualframe is proposed in Section III and IV. In Section V,
numerical simulations are performed to verify the usefulnessof proposed method.
II. A M ULTI F INGERED H AND A RM S YSTEM
In this section, we model a hand-arm system composedof an arm and a multi-fingered hand. In our proposed
grasping method, we assume that a robotic hand-arm system
has enough number of fingers and each finger also hasenough number of DOFs, in order to accomplish stable object
grasping and attitude control of a grasped object. Namely,
there is no limitation of the system configuration, as long as
the assumption is satisfied. An example of a multi-fingered
hand-arm system treated here is illustrated in Fig. 1. Assume
that all fingertips maintain rolling contact with the object
surfaces, and do not slip and detach from the surfaces during
manipulation. Also assume that fingertips roll within theranges of its hemispheric surfaces, and they do not deviate
from each contact surface. Note that the gravity effect isignored in this paper for the sake of modeling easily at thisstage. As shown in Fig. 1, the symbol O denotes the origin

Contact area

Contact model at the center of the contact areaof Cartesian coordinates, and x0i ∈ R3 is a position of thecenter of each fingertip. Hereafter, the subscript of i refers to
the ith finger in all equations. The number of DOFs of the armand the ith finger are represented as Na and Ni , respectively.
A joint angle vector of the arm is expressed by q a ∈ RNa .
Similarly, A joint angle vector of the ith finger is expressedTby q 0i ∈ RNi . Also, q = (q a , q 01 , q 02 , ..., q 0N ) denotes a
joint angle vector of the arm and all the fingers, where N
is the number of the fingers. As shown in Fig. 2, xi ∈ R3
is a position of the center of each contact area. The positionof the center of the object mass in Cartesian coordinatesT
is expressed as x = (x, y, z) ∈ R3 . An instantaneousrotational axis of the object at x in Cartesian coordinatesT
is expressed by ω = (ωx , ωy , ωz ) ∈ R3 . An attitude of theobject in Cartesian coordinates is expressed by the rotational
matrix R = (r x , r y , r z ) ∈ SO (3), where r x , r y , r z ∈ R3
are mutually orthonormal vectors on the object frame. In addition, we define contact frames at the center of each contact
area by each rotational matrix RRCi = (C iX , C iY , C iZ ),and the y-axis of them C iY is taken as normal to the contact
surface. For each hemispheric fingertip, ri is the radius ofeach fingertip, and Δri is the distance between the centerof the fingertips and the contact surfaces. Namely, ri − Δrisignifies each fingertip’s deformation displacement towardnormal to the surface induced by the softness.
A. Constraints
A 3-dimentional rolling constraint with area contact [7]can be expressed as a Pfaffian constraint as






X ix
X iω
X iq
q̇ +
ẋ +
ω = 0,
(1)
Z iq
Z ix
Z iω
where
⎡

4202

T
X iq = Δri C T
iZ J Ωi − C iX J 0i
⎢ X = CT
ix
⎢
iX
⎢
T
⎢ X iω = {C iX × (x − x0i )} − Δri C T
iZ⎢TT⎢ Z iq = −Δri C iX J Ωi − C iZ J 0i⎢
⎣ Z ix = C TiZT
Z iω = {C iZ × (x − x0i )} + Δri C T
iX ,

(2)

rz vir

x01

_

xC

x03

rx vir_ry vir_Fig. 3.

x02

Virtual frame

N

and J Ωi ∈ R3×(Na + i=1 Ni ) is the Jacobian matrix for theattitude angular velocity of each fingertip
with respect to the
Na + Ni=1 Ni . Moreover, J
joint angularvelocity
q̇
∈
R
0i ∈
N
R3×(Na + i=1 Ni ) is the Jacobian matrix for the center of
each fingertip x0i with respect to the joint angular velocityq̇.

frame, and if a real object frame becomes unavailable, avirtual frame instead of the real object frame is utilized tomanipulate the grasped object. The concept of the virtualframe has been reported by Wimböck et al. [9] and Tahara
et al. [6]. In their methods, the virtual frame is defined by arelative position vector between each fingertip, and a control
input to regulate the attitude of the object is designed togenerate a task-space artificial potential energy according to adesired attitude. However, the attitude of their virtual frame isdefined based on the center position of each fingertip similar
to the definition of the virtual object position, and thereby
the object attitude control input might cause an interferencewith other control inputs, such as the stable object grasping
control input, or the object position control input which arealso based on the center position of each fingertip. In thissection, a new virtual frame which is defined based on theattitude of each fingertip is proposed. In this formulation
based on the attitude of each fingertip, there is no interferenceof the attitude control input with other control inputs. Firstly,
the position of the virtual frame xc is designed as

B. Overall Dynamics

N

Given the constraints shown by (1), Lagrange’s equationsof motion of the overall system are given by applying thevariational principle as follows:
For the multi-fingered hand-arm system:


N
1
∂Ti T
H (q) q̈ +Ḣ (q) + S (q, q̇) q̇ +
2
∂ q̇
i=1
T
T
JT
0i C iY fi + X iq λiX + Z iq λiZ = u,

Rvir

(3)
r xvir

For the object:N

M ẍ +

r yvir= 0 (4)i=1

r zvirNI ω̇

+

ω × Iω −
N

+

∂Ti
∂ω
i=1

T

{C iY × (x − x0i )}fi
i=1
N
T
XT
iω λiX + Z iω λiZ = 0,(5)

+
i=1


(6)

Next, we define the virtual frame at xc by a rotational matrix
Rvir as shown in Fig. 3. It is given as

i=1

T−fi C iY + X T
ix λiX + Z ix λiZ

1
x0i .
N i=1

=

(r xvir , r yvir , r zvir ) ,

(7)

where

N

+

xc =

=
=

r̃ xvir,r̃ xvir Nr̃ xvir =r̃ xvir × r̃ yvir,
r̃ xvir × r̃ yvir 

r xfi

(8)

i=1
N

r̃ yvir =r xvir × r yvir .

r yfi

(9)

i=1

(10)

In (8) and (9), r xfi and r yfi in the rotational matrix Rfi
are mutually orthonormal vectors, and this rotational matrix
expresses the attitude of each fingertip.

NN
where in (3), H ∈ R(Na + i=1 Ni )×(Na + i=1 Ni ) is aninertia matrix for the arm and each
finger, S (q, q̇) is a skewN
symmetric matrix, and u ∈ RNa + i=1 Ni is a vector of the
input torque. In (5), M = diag (m, m, m) is a mass of theobject, I = RĪRT , and Ī ∈ R3×3 is an inertia tensor forthe object represented by the principal axes of inertia. In
addition, fi is a reproducing force in the normal direction
to the object surface at the center of each contact area, Ti
is an energy dissipation function which acts as a viscosity
between fingertips and object surfaces in twist direction. AlsoλiX and λiZ denote Lagrange’s multipliers.

=

IV. C ONTROL S CHEME
Let us design a switching control scheme which depends
on whether the geometrical information of the grasped object
is available or not. Assume that the accurate position andattitude of the object is available in an initial state. The
procedural steps are shown as follows:

III. C ONSTRUCTION OF THE V IRTUAL F RAME

1) The object is manipulated using a real object frame.
2) The real object frame is NOT available.
3) The controlled target (the real object frame) is changed
to the virtual object frame.
4) The real frame is available again.
5) Return to 1).

In this method, basically a real object frame which isavailable from visual sensors is manipulated to a desired

The flow chart of these steps is shown in Fig. 4. Each stepof the procedure is explained in the following sections.

4203

Eventually, a desired attitude of the object can be realized byadding the moment torque to the grasped object from eachfingertip around this desired instantaneous rotational axis.

Start

Controlled target : real frame

1)

B. Step 2)
In the case that the position and attitude informationof the grasped object is unavailable, the control target isswitched from the real object frame to the virtual object
frame, immediately. At this moment, the last real informationof the grasped object acquired from some visual sensors isstored. Then, we configure the desired virtual frame xdvir ,Rdvir using the last obtained object information. It is given
as follows:(15)
xdvir = xclast + (xd − xlast )Calculation of input torqueYes
4)

Object information
is available
No2)

Controlled target : virtual frame

3)

Rdvir = Rd RT
Rvirlast ,last

Calculation of input torqueFig. 4.

Flow chart of the switching control scheme

A. Step 1)
In this step, an accurate position and attitude of the object
is given from some visual sensors. The input torque u isgiven as(11)u = us + u p + u o ,where us is for stable object grasping, up is for position
control of the object, and uo is for attitude control of theobject, respectively. The control input for stable grasping us
is designed so that the center of each fingertip approaches
each other [7]. It is given as

where xclast is the position of the virtual object frame at
the last moment, and xlast is the position of the real object
frame at the last moment. Similarly, Rvirlast is the rotational
matrix which expresses the virtual frame at the last moment,
and Rlast is the real object frame at the last moment. Namely,
the desired virtual frame, which reflects a relative position
and attitude of the object between the real object frame andthe desired real object frame, is designed. Eventually, thismethod can avoid a discontinuity of an input torque to eachjoint which may be induced by the switching operation.
C. Step 3)
The grasped object is manipulated by the use of the virtualframe and the desired virtual frame. The control input u isswitched to the following form that is using the virtual frame.

N

fd
us =  N

i=1 ri j=1

JT
0j (xc − x0j ) − C q̇,N

where C ∈ R(Na + i=1 Ni )×(Na + i=1 Ni ) > 0 is a positive
definite diagonal matrix that expresses the damping gain foreach joint, and fd is the nominal desired grasping force. The
control input for the object position control up is given asN

up = KpJT
0j (xd − x),u = us + upvir + uovir

(12)

N

(13)

j=1

uo = Ko

N

upvir

=

Kp

JT
0j (xdvir − xc ).

(18)

j=1

The control input for attitude control of the virtual frame
uovir is expressed as
N

uovir

= Ko

JT
Ωi {(r xvir × r xdvir )i=1+ (r yvir × r ydvir ) + (r zvir × r zdvir )} .(19)
D. Step 4)JTΩj {(r x × r xd )j=1

+ (r y × r yd ) + (r z × r zd )} ,(17)

The control input for position control of the virtual frame
upvir is designed aswhere Kp is a positive scalar constant and xd is a desired
position of the object. The control input for attitude controlof the object uo [8] is given as
N

(16)

(14)

where Ko > 0 is a positive scalar constant. A desired
real object frame is expressed by a rotational matrix Rd =(r xd , r yd , r zd ). Each cross product in the right-hand sideof (14), e.g. r x × r xd , signifies an attitude error for eachaxis between the present attitude and the disired attitude of
the object. Namely, the summation of each cross productindicates a desired instantaneous rotational axis of the object.

If the real object frame is available again, the control input
is return to the initial one. In that case, a small discontinuityof the control input may be induced. However, we canassume that in this case the virtual frame has already been
regulated to the desired one sufficiently, and then the real
object frame is assumed to be near the desired one. Therefore, its torque jump might be small enough. In addition,
this state can be regarded as another initial condition of themanipulation, and the stability of the closed-loop system has
already been verified theoretically by our previous reports

4204

TABLE I
P HYSICAL PARAMETERSTABLE IIII NITIAL CONDITION
q̇
qa
q 01
q 02
q 03
ẋ
x
ω

Triple-fingered hand-arm systemst

1 link length
la11.300[m]li10.300[m]la2
1.000[m]li20.200[m]2nd link length
3rd link lengthla30.175[m]li30.140[m]1st mass center
lga1
0.650[m]lgi10.150[m]2nd mass center
lga20.500[m]lgi20.100[m]rdlga3
0.0875[m]lgi30.070[m]3 mass centerst
1 massma1
1.300[kg]mi1
0.250[kg]2nd mass
ma2
1.000[kg]mi2
0.150[kg]ma3
0.400[kg]mi3
0.100[kg]3rd mass
1st Inertia I a1
diag(7.453, 7.453, 0.260)×10−1 [kg·m2 ]nd−1diag(3.397, 3.397, 0.128)×10 [kg·m2 ]2 Inertia I a2
3rd Inertia I a3
diag(0.291, 0.291, 0.500)×10−1 [kg·m2 ]1st Inertia I i1
diag(7.725, 7.725, 0.450)×10−3 [kg·m2 ]diag(2.060, 2.060, 0.120)×10−3 [kg·m2 ]2nd Inertia I i2
diag(0.538, 0.538, 0.031)×10−3 [kg·m2 ]3rd Inertia I i3
Radius of fingertip ri
0.070[m]52
Stiffness coefficient ki
1.000×10
[N/m
]

 2
Damping function ξi
1.000× ri − Δri2 π[Ns/m2 ]R

0[rad/s](−0.183, −1.369, 1.898, 1.343, −0.787)T [rad](1.007, 0.235, −0.771, 1.338, 0.328)T [rad](0.242, −0.733, 1.122, 0.754)T [rad](2.019, −0.924, 0.912, 1.088)T [rad]0 [m/s](0.158, 0.501, 0.681)T [m]0 [rad/s]⎡⎤
1.00 0.00 0.00
⎣ 0.00 1.00 0.00 ⎦0.00 0.00 1.00

V. N UMERICAL S IMULATION

is lacked from 1.5[s] to 5[s], and it is acquired in otherperiods. The column of “Control Target” indicates the present
control target at that moment, the real object frame or thevirtual object frame. Several solid lines in this figure meantransient responses of the control targets and the desired
values. In particular in this figure, only values with respect
to r x from the rotational matrix R are shown. We can see
from this figure that all elements of R converge to eachdesired value. Figure 6 shows snapshots of the simulation. In
this figure, each image includes two contents. The left-handside of each image shows the overall view, and a translucent
red object indicates the desired object position and attitude,
and a solid blue object indicates the real object position
and attitude. The right-hand side of each image shows all
frames which are available at that moment. During 1.5 [s]to 5.0 [s], the virtual frame is utilized for the control target,
and therefore, the real object position and attitude converge
not to the desired real object position and attitude, but thedesired virutal object position and attitude. Of course, thereis the difference between the desired real object frame andthe desired virtual object frame. However, they are quite
near each other and the stability of the overall system isheld during this period. After the real object information
is available again, both the real position and attitude of theobject converge to each desired value respectively at the final
state.
From these figures, we can conclude that the object grasping and manipulation can be realized well by our proposed
method.

In this section, we report the simulation result. The robotic
hand-arm system used in this simulation is a triple-fingered
hand-arm system. It consists of an arm part which has
5 DOFs and a triple-fingered hand part which has one 5
DOFs finger and two 4 DOFs fingers. The grasped object
is triangular prism. Specific parameters of the triple-fingered
hand-arm system and the grasped object are shown in Table
I. In this Table, Yi is a perpendicular distance from the centerof the object mass Oc.m. to each surface of the object, andθti is the external angle of a cross-sectional triangle of theobject. Table II shows the desired nominal grasping force
and gains. An initial condition of the overall system is shownin Table III. Figure 5 shows the transient responses of thereal object frame and the virtual object frame. The columnof “Object Information” indicates whether the position andattitude information of the grasped object is available or not.
Namely, in this simulation, the real information of the object

This paper presented a robust object grasping and manipulation method against the temporary lack of geometrical information of the grasped object during manipulation.
Firstly, the overall system dynamics was modeled. Next, thenew virtual frame in which its attitude is defined based on
the attitude of each fingertip was introduced. After that, therobust object manipulation scheme, which utilizes the realframe and the virtual frame of the object effectively, wasdesigned. This method was designed so that the hand-arm
system works well even if the geometrical object informationis completely unavailable during manipulation. Finally, we
confirmed through the numerical simulation result that our
proposed method realized desired position and attitude of thegrasped object in stable, even though the geometrical object
information is suddenly lacked during manipulation.
In our future works, we have to consider what is the

ObjectMass m
Y1
Y2
Y3
θt1
θt2
θt3
Inertia I

0.037[kg]0.092[m]0.048[m]0.048[m]1.833[rad]1.833[rad]2.618[rad]diag (1.273, 0.193, 1.148) × 10−3 [kg · m2 ]TABLE IID ESIRED GRASPING FORCE AND GAINS
fd
Kp
Ko
Ca
C1
C2
C3
xd
Rd

10.0[N]
4.762
0.238
diag(1.003, 0.651, 0.735, 0.278, 0.177)×10−1 [Ns·m/rad]diag(0.606, 0.687, 0.786, 0.642, 0.198)×10−2 [Ns·m/rad]diag(0.468, 0.780, 0.318, 0.099)×10−2 [Ns·m/rad]diag(0.648, 0.780, 0.318, 0.099)×10−2 [Ns·m/rad]T⎡(0.100, 0.500, 0.700) [m]⎤0.88 −0.32 −0.34⎣ 0.340.94
0.00 ⎦
0.32 −0.120.94[7], [8]. Therefore, the stability of the overall system canbe ensured in all likelihood, but it must be analyzed more
carefully in the next work.

VI. C ONCLUSION

4205

Object Information
Available

Unavailable

Available

Real
Frame

Virtual Frame

Real Frame

Real Position x and Virtual Position xC [m]Control Target

0.2

0.0[s]

4.9[s]

1.4[s]

5.1[s]

1.6[s]

6.0[s]

2.5[s]

8.0[s]

4.0[s]

10.0[s]

xd
0.1

xC

0

xdvir
x

-0.1
1.2

rx [0]

rxd [0]rxdvir [1]rx vir [1]rrReal Frame x and Virtual Frame x vir

0.8

0.4

rxdvir [0]rx vir [0]rx [2]

0rx vir [2]rxd [2]rx [1]-0.4

rxdvir [2]
-0.6
0

1.5 2

rxd [1]
4

5

6

8

10

Time[s]Fig. 5.

Real frame

Desired real frame

Virtual frame

Desired virtual frame

Transient responses of the real frame and the virtual frameFig. 6.

best timing to switch the real frame and virtual frame forthe manipulation task. We also have to analyze the stabilityof the overall system including switching the controllers.
In addition, we would like to conduct experiments using a
prototype to confirm the usefulness of our proposed method.
ACKNOWLEDGMENT
This work was partially supported by ”the Kyushu University Research Superstar Program (SSP)”, based on the budgetof Kyushu University allocated under President’s initiativeand Grant-in-Aid for JSPS Fellows.
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