New condition for tofu stable grasping with fluid fingertips
Toshihiro NISHIMURA, Yoshinori FUJIHIRA, Member, IEEE, Ryota ADACHI and Tetsuyou
WATANABE, Member, IEEE

Abstract— Tofu shows the following compression behavior.
First, the behavior is non-linear; subsequently, the behavior
becomes elastic/linear, followed by yielding and fracture. A
linear behavior indicates that there is no fracture, but further
increase of compression can cause yielding or fracture. The
compression in the region of linear behavior then can be
regarded as maximum. With this in mind, this paper presented
a grasping condition of controlling the amount of compression
so that the compression behavior can be linear. This condition isapplied to the previously proposed fluid fingertip that utilizes arubber bag filled with a viscoelastic fluid and having a rigid layer
inside the fluid. In addition, this paper presents a methodology
for checking whether the grasping condition is held, based on
our previously developed phase change detection method ofcomparing the fitting accuracies of different approximation
models. Additionally, this paper presents the reason behind the
behavioral change of fluid pressure. Before phase change, thefluid fingertip behaves like a rigid fingertip, while after phasechange, the contact pressure is transmitted to the fluid pressure
and can be observed by the fluid pressure. The validity of theapproach was shown through experiments.

I. INTRODUCTION
Robotic systems that can work in a human environment are
required. Robotic hands play an important role as endeffectors for such robotic systems, and many types of robotic
hands have been developed [1]–[16]. In a human environment,a collision between humans and robots cannot be avoided, andthus, the surfaces of robots should be soft. With this in mind,
we previously developed a robotic hand with a soft surface byfilling a rubber bag with a viscoelastic fluid, and showed thatthe hand can grasp a wide variety of fragile objects [1]–[3].
Because of incompressibility, a uniform contact pressure
distribution is obtained. Uncertainties in object shape can beabsorbed by fluid deformation. These are benefits for delicate
grasping of fragile objects. Additionally, a rigid layer was set
inside of fluid that helped in grasping heavy rigid objects. We
presented a methodology especially for grasping (Kinugoshi)
tofu, which is one of the softest and most fragile objects,
without using any advanced knowledge related to fracture
stress. We focused on the pressure profile of the filled fluid
because it corresponds to stress. If the pushing distance isincreased, the rate of increase of fluid pressure decreases justbefore fracture. By detecting this decrease, a tofu can be
grasped without fracture [1], [2]. The success rate was 4/5.
The problem was too close to total fracture, and local fracture*Research supported by NSK Advanced Mechatronics Foundation and
JSPS KAKENHI Grant Number 16H04298.
T. Nishimura and R. Adachi are with the Graduated school of Naturalscience and Technology, Kanazawa University, Kakuma-machi, Kanazawa,
9201192 Japan (e-mail: to.nishimura@stu.kanazawa-u.ac.jp). Y. Fujihira iscould not be avoided. We then performed a detailed
investigation of the pressure profile, and presented a new
method was presented [3]. We showed that tofu could begrasped without fracturing at the point where the behavior of
fluid pressure changed. The drawbacks of the method are as
follows.
1) Which change should be the grasping point was unclear.
The strategy varied based on the filling rate of fluid in thefingertips.
2) Why the behavioral change of fluid pressure happened
was unclear.
Therefore, it was not a reasonable grasping strategy,
although the tofu could be grasped.
In order to overcome these drawbacks, this paper provides
a novel condition for stable grasping of soft and fragile objects
whose compression behavior is qualitatively similar to that of
tofu. Tofu shows the following compression behavior. At thefirst stage of compression, the pressure exponentially
increases. Subsequently the behavior becomes elastic/linear.
Finally, yielding and total fracture occurs. Elastic/linear
behavior indicates that the contact between an object and thefingertip can be modeled using a linear spring, and the applied
force can be transmitted to the object without any loss.
Fracture does not occur in the region of linear behavior. The
applied force is large because linear behavior is observed
before yielding, and nominal grasping conditions of frictionaland equilibrium conditions can be satisfied with highpossibility. The failure in the region of linear behavior
indicates impossibility of grasping; required force forgrasping cannot be applied. Larger grasping force causes
yielding or fracture. Therefore, the grasping in this region(alternatively saying, to control the amount of compression sothat the compression behavior can be elastic/linear) is acondition for tofu grasping. The condition remains the sameirrespective of the filling rate of fluid. This paper also presents
a methodology for detecting the elastic behavior ofcompressed objects. The proposed methodology is based on
the phase change detection method [3] of comparing fitting
accuracies of different approximation models. Additionally,
this paper presents the reason behind the behavioral change of
fluid pressure.
The rest of this paper is arranged as follows. The next
subsection provides related works. Section 2 presents thewith the Muroran Institute of Technology (e-mail: yfuji@mmm.muroranit.ac.jp). T. Watanabe is with the Faculty of Mechanical Engineering,
Institute of Science and Engineering, Kanazawa University, Kakuma-machi,
Kanazawa, 9201192 Japan (e-mail: te-watanabe@ieee.org).

basic concept of grasping conditions and applicable objects.
Section 3 presents the methodology for detecting whether thegrasping condition can be held. Section 4 presents theexperimental results for observing the working of thegrasping condition.
Related works
Anthropoid robotic hands have been developed inconsideration of human affinity [4]–[10]. Normally, thesurface of a finger is rigid at factories and not suitable foradaptation to human environment. Simoga and Goldenberg
claimed that gel is effective for constructing the surfaces offingertips because it can reduce contact impact and strainenergy, and fit according to the shape of the object [17]. In
addition to these advantages, we observed other benefits in
our previous studies, i.e., a uniform contact pressure
distribution and an automatic stiffness increase [1], [2]. The
main drawback of using gel for fingertips is the limitation on
the maximum applicable forces. Thus, a two-layer structure
where a rigid component was installed inside the gel waspresented in[1], [2].
To fit the target object is key for obtaining universal
grasping (a wide variety of objects can be grasped by one
robotic hand). A pioneer work in this regard might be thesnake like gripper presented by Hirose and Umetani [11]. Kim
and Song developed a gripper that included hybrid variable
stiffness actuators [12]. The actuators could control contact
stiffness. Brown et al. [13] developed a universal gripper forgrasping objects having a wide variety of shapes. It was basedon the jamming phenomenon [18], [19]. Choi and Koc
developed a design of inflatable rubber pockets on thegripping sides [14] for the same purpose of grasping objects
having a wide variety of shapes. Pettersson et al. utilized
magnetorheological (MR) fluid for constructing a gripper thatcan fit to the shape of the object and provide a space for
confining objects [15]. The space was formed by molding the
MR fluid. Kim et al. [16] presented a soft skin for safeinteraction between children and robots. The research showedthat a robotic hand with soft skin could grasp several objects,
including a plastic cup and a roll of paper. In the above studies,
several fragile objects, including eggs and fruits, weresuccessfully grasped. However, studies on grasping soft andfragile objects, such as tofu, are still limited.
The next step in enhancing the function of robotic handsfrom the viewpoint of universal grasping would be to grasp
soft and fragile objects. Thus, this paper focuses on grasping
soft and fragile objects, and presents a grasping strategy forsuch objects.
II. BASIC CONCEPT FOR GRASPING CONDITION AND
APPLICABLE OBJECTSSoft (Kinugoshi) tofu, which is a typical example of afragile and soft object in a human environment, was used as
the target object. In order to observe the compression
behavior of tofu, a compression test was conducted. Fig. 1
shows the experimental setup. An indenter was attached to an
automatic poisoning stage. The tofu (Topvalue, Silken tofu,

size: 25 25 30 mm ) was pushed against a duralumin
plate at a low speed of 1.0 [mm/s] to minimize the influenceof speed.

Figure 1. Experimental setup for compression test of soft (Kinugoshi) tofu

Figure 2. Results of compression test; pushing distancecompression force[mm] versus

Fig. 2 shows the result of the compression test. At first, thetofu showed a curve behavior; subsequently, a linear behavior
was observed with the increase of pushing distance, followedby yielding and fracture. The curve behavior is considered tobe due to the increase of density. The increase of density intofu corresponds to consolidation [20] which is a process ofdecrease in volume with the decrease of water inside theobject (tofu). Consolidation indicates the increase in fillingrate of the solid part. An evidence that supports thisassumption is the existence of water around the tofu after thecompression test. The process of increase of density is nonlinear. Therefore, linear behavior is not considered as theprocess, i.e., the increase of density stops in the region of
linear behavior. Linear behavior is helpful for grasping
because it indicates that the contact can be modeled using alinear spring, and compliance control can be obtained. The
force applied by the robot/finger can be transmitted to the tofu
without any loss in the region of linear behavior. In addition,
it should be noted that linear behavior is observed before
yielding and subsequent fracture. Forces in the region can be
regarded as maximum applicable grasping forces without
fracture. Hence, if stable grasping of tofu cannot be realized
in the region of linear behavior, tofu cannot be grasped
without fracture. Grasping when the compression behavior islinear is then the proposed grasping condition. Then, the only
problem that remains to be solved is detecting the region of
linear behavior It should be noted that frictional andequilibrium conditions (balancing of object weight) are
additionally required for realizing grasping [21]. If the weightof an object is small, it is expected that these conditions canbe satisfied because of the large grasping force in the regionof linear behavior.

Although the target object is tofu, the grasping strategy canbe applied to all objects whose compression behavior isqualitatively similar tofu (i.e., linear behavior after non-linear
behavior). It should be noted that the presented condition does
not depend on size or weight of objects because it isassociatedwithnotgravitycompensationbut
fracture/yielding avoidance.

Figure 5. Pushing distance versus fluid pressure in compression test of
tofu using fluid fingertip (initial fluid pressures (the pressure when there isno contact) were 1.5, 2.7, 4.0, and 6.0 [kPa])
Figure 3. Schematic view of fluid fingertip

III. METHODOLOGY FOR DETECTING WHETHER GRASPINGCONDITION CAN BE HELD

A. Fluid fingertips
We developed deformable fingertips having a two-layer
structure, i.e., a fluid layer and a rigid layer. Fragile objects
can be handled using the fluid layer, and normal rigid objects
can be handled using the rigid layer [1], [2]. For realizing
universal grasping, we will try to grasp tofu with the fingertips.
Because this study focuses on grasping soft and fragile objects(tofu), we will consider only the fluid layer. For this purpose,
we constructed deformable fingertips by using a rubber bag
filled with a viscoelastic fluid, as shown in Fig. 3. The
structure, sensors, and materials are similar to those used tofabricate the fluid fingertip in our previous study [3].

Figure 4. Experimental setup for compression test of tofu using fluid
fingertip

B. Overview of methodology
The area where the grasping condition can be heldcorresponds to the area where the compression behavior of
the object is linear. An overview of the methodology for
detecting the area is presented below.
Step 1. Detect the point where the fluid pressure inside thefingertip corresponds to the contact pressure of theobject. After detecting the point, the contact pressureof the object can be observed via the fluid pressure.
Step 2. Detect points where the compression behavior islinear through the fluid pressure.
As described later, at the first stage of compressing the tofu,
the fluid pressure does not correspond to the contact pressureof the object, and we cannot observe the state of tofu via thefluid pressure. This is the reason why step 1 is conducted
before step 2.
The detection method is based on the phase change
detection method [3] of comparing the fitting accuracies ofdifferent approximation models.

C. Compression test of tofu by fluid fingertips
Fig. 4 shows the experimental setup. The fluid fingertip
was attached to a handmade load cell (allowable load: 20 [N];resolution: 0.01 [N]) that was fixed on an automatic
positioning stage. The tofu was pushed by the fluid fingertip
at a low speed of 1.0 [mm/s] to minimize the influence of
speed. The experiment was conducted until the tofu wascompletely broken. The experiment was conducted at initial
fluid pressures (the pressure when there is no contact) of 1.5,
2.7, 4.0, and 6.0 [kPa]. The initial pressures were chosen byconsidering allowable maximum and minimum tensions ofrubber surface. It should be noted that the filling rate of thefluid was 1.5, 2.7, 4.0, and 6.0 [kPa]. The experiments wereconducted three times for each condition.
Fig. 5 shows the results where mean values are displayedfor convenience. When the initial fluid pressure was 1.5, 2.7,
and 4.0 [kPa], the curve converged to one line. When theinitial fluid pressure was 6.0 [kPa], linear behavior wasobserved, but it was different from those observed under otherconditions. The presented methodology is to detect the regionof linear behavior.

Figure 6. Schematic views of phase 1 (fluid fingertip behaves like rigid
fingertip) and phase 2 (Contact pressure of the object can be transmitted to
the fluid in the fingertip)

Figure 7. Model of interaction between the fluid fingertip and soft object(tofu).

D. Step 1: detection of the point where the fluid pressure
inside the fingertips becomes to correspond to thecontact pressure of the object
As shown in Fig. 5, if the pushing distance is small, thevalue of the fluid pressure does not change significantly. Here,
we focused on the interaction between the fluid fingertip andthe tofu, and defined two phases, as shown in Fig. 6. At phase
1, the fluid fingertip does not deform while the object deforms.
The fluid fingertip behaves like a rigid fingertip. Phase 1 canbe observed when the pushing distance is small. If thepushing distance is increased, phase 2 can be observed. At
phase 2, both the fluid fingertip and object deform; thisphenomenon is called phase change. Note that here, only twophases were used for explanation, but there could be morethan two phases. In that case, there could be more than one
phase change.
Here, we constructed a simple model for describing thephenomenon (Fig. 7). For easy understanding, a spring model
was used, and viscosity was neglected (because of the low
speed of the test). Letandbe the stiffnesses of thefingertip and the object, respectively;anddenote thedisplacements of the fingertip and the object,→
be the force applied to the fingertip by the object, andbe the force applied to the object by the→fingertip. Then, we obtain
(1)
→
(2)
→
, we have
From
→
→
1

(3)

Figure 8. Experimental setup for pushing the fluid fingertip with an initial
fluid pressure of 4.0 [kPa] by the fluid fingertip with an initial fluid pressureof 6.0 [kPa]

Figure 9. Results of the experiment shown in Fig. 8; pushing distancefor the fluid[mm] versus fluid pressures with the ∆RMSE
fingertip with the an initial fluid pressure of 6.0 [kPa]It should be noted that and changes with the change
in displacements and , as shown in Figs. 2, 5. Here, we
suppose the case when the stiffness of the fluid fingertip isgreater than that of the object initially (when there is nocontact). In this case, ≫ . Then, (3) becomes
1

≅

(4)

It indicates that the fingertip displacement corresponds
to the deformation of the tofu , i.e., there is no deformationin the fingertip, and the fingertip behaves like a rigid fingertip.
This state corresponds to phase 1. We observed the captured
image at phase 1, and found that there was no deformation of
the fingertip at phase 1 (Note that only visible parts were
examined), as shown in Fig. 6. A slight increase in fluidpressure (see Fig. 5) is also an evidence. It should be notedthat at phase 1, the fluid pressure does not correspond to thecontact pressure of the object. Therefore, the fluid pressurecannot be used for observing the contact pressure at phase 1.
At phase 2, the deformation of the fingertip was observed,
as shown in Fig. 6, although the deformation was small. Thus,
the contact pressure can be observed via the fluid pressure at
the fingertip in phase 2.
In order to verify it, we conducted experiments where a
fluid fingertip was used instead of the tofu, as shown in Fig.
8. A direct measurement of the internal pressure of the tofu
was not possible; thus, we conducted this experiment tosimulate the pushing of tofu by the fluid fingertip. For thesimulation, the fluid fingertip having an initial fluid pressureof 4.0 [kPa] was pushed by the fluid fingertip having an initial
fluid pressure of 6.0 [kPa]. Fig. 9 shows the results of theexperiment; the behavior of fluid pressure of the fingertip
with an initial fluid pressure of 6.0 [kPa] was very close to thecase when the tofu was pushed, as shown in Fig. 5. At first,
the fluid pressure of the fluid fingertip with an initial fluidpressure of 4.0 [kPa] increased. When the pushing distance
was increased, phase change occurred, and the fluid pressureof both the fingertips increased. The value of fluid pressure
for both the fingertips became similar. Phase 2 corresponds tothe state where the fluid pressure of both the fingertips
increased, while phase 1 corresponds to the state when thefluid pressure of the fluid fingertip with a larger initial fluidpressure of 6.0 [kPa] did not increase. It should be noted thatphasechangewasdetectedbychecking
exceeded the threshold value
whether ∆RMSE(more detail will be described later). Although the structureof the fluid fingertip was different from that of the tofu, theresults support the findings; the fluid fingertip behaves like arigid fingertip at phase 1, while the contact pressure can betransmitted to the fluid and can be observed via the fluidpressure at phase 2. Therefore, in order to detect the area
where the presented grasping condition can be held via fluidpressure, we need to stay at phase 2. Hence, as a first step, we
need to detect (first) phase change (Recall that there could be
more than one phase change).
The methodology is based on our previous one [3], which
compared the fitting accuracies of different approximation

models. Simple and complex fitting models were prepared forthe approximation. For easy understanding, two- and threedimensional polynomial functions were assumed to represent
simple and complex fitting models, respectively. The
regression started from the point where the pushing distance
was 0.1 [mm] (the number of data points was 10).
Regression was performed each time new data were available,
and the root mean squared error (RMSE) was calculated foreach model. Let RMSEpoly2 and RMSEpoly3 be the RMSE fortwo- (simple) and three-dimensional (complex) polynomial
functions. Then, the RMSE difference was computed asfollows:
∆RMSE

RMSE

RMSE

(5)

Figure 10. Phase change detection method

Suppose the simple and complex models describe data wellbefore phase change, because of a simple data arrangement.
is small (see Fig. 10 left).
In this case, ∆RMSE
During phase change, the data is rearranged, and new data
deviates from the original data arrangement. In this case, thesimple model might not be able to describe the data
adequately, while the complex model can do so. Then, thecould become large (see Fig. 10 right).
∆RMSE
Hence, by checking whether the value of ∆RMSE
exceeds a threshold value (0.001), phase change can bedetected. It should be noted that in our previous paper,∆RMSE
was continuously calculated after (first)
phase change, and an attempt was made to obtain anotherphase change. However, the change of ∆RMSE
after (first) phase change lost physical meaning. Thus, we
stopped the regression after (first) phase change in this paper.
The regression was restarted, and the starting point was
selected as the point just after phase change.

Fig. 11 shows the calculated ∆RMSE
fordetecting the first phase change for the data shown in Fig. 5.
It can be seen that phase change was successfully detected. It
should be noted that when the number of data is small, RMSE
0.9 (R
does not work well. We then ignored cases when R
is coefficient of determination), which corresponds to the casewhen the pushing distance was close to zero.
Step2: Detect the points where compression behavior islinear.
Suppose the number of data is increased in increments of
one when conducting linear regression. The keys for detecting
linear/elastic behavior are determining a method tocontinuously obtain the same slope of the regression line, andappropriate setting of the starting point for regression.
A one-dimensional polynomial function was prepared for
regression. Regression was performed each time new data
were available, and the coefficient of determination (R ) andthe slope ( of
) of the regression line were
derived. The coefficient of determination ( R ) and thedeviation of the slope were evaluated. The deviation of theslope ( ) was determined using
|
1
|
(6)
10
is the th point of , andis theat . If
where
the deviation of the slope ( ) was less than the thresholdvalue (0.92), and the coefficient of determination ( R )exceeded the threshold value (0.9), we judged that the data
arrangement showed a linear/elastic behavior.
For setting the starting point for regression, we used thephase change detection method. We subsequently checkedphase change after the first phase change was detected, andthe data were split into several phases. Linear regression wasapplied to split phases. The point just after phase change wasset as the starting point for regression. Phase change indicatesthe change of the fitting model. Therefore, this strategy was
suitable for detecting linear behavior.
Table 1 shows the points where linear behavior wasobserved, and grasping condition was satisfied. Recall that thecompression test was conducted three times for eachcondition. Small deviations showed the stability of the
proposed detection methodology. The points are also shownin Fig. 5, where it can be seen that the detection method
worked well.
Fig. 12 summarizes the procedure for detecting points
where linear behavior was observed, and grasping condition
was satisfied.
TABLE I.

THE POINTS WHERE LINEAR BEHAVIOR WAS OBSERVED,AND GRASPING CONDITION WAS SATISFIED

Initial fluid pressure[kPa]
The (grasping)
points [mm]Standard deviationof [mm]Figure 11. Pushing distance[mm] versus ∆RMSE

1.5

2.7

4.0

6.0

11.6

13.8

12.6

10.4

0.5

0.3

0.1

0.4

Figure 12. Procedure for detecting the points where linear behavior wasobserved, and grasping condition was satisfied

experiments were conducted three times for each condition.
Table 2 summarizes the results of the experiment. It can beseen that if the pushing distance during the experiment ( ) islarger than the pushing distance at the point where thecompression behavior becomes linear (Table 1), the grasping
was successful for each case and the grasping was stable. It
indicates that the proposed grasping condition is valid. It
should be noted that the proposed condition is not a necessary
condition, but a sufficient and conservative condition. Linear
behavior is observed before yielding, and corresponds to thecase when a relatively large grasping force is applied to theobject. If the weight of an object is small, the magnitudes of
the grasping force is sufficient to satisfy frictional andequilibrium conditions. In this case, grasping is guaranteed tosucceed if only the proposed condition is satisfied. This is thereason why grasping succeeded for each case listed in Table
2. If the proposed condition is not satisfied, it cannot be
confirmed whether grasping was successful (therefore, there
could be cases when grasping succeeded even if the proposed
condition is not satisfied).

Figure 13. Experimental procedure for grasping soft (Kinugoshi) tofu

IV. EXPERIMENTAL CONFIRMATION OF HOW THE PROPOSEDGRASPING CONDITION WORKED

In order to observe how the proposed grasping strategy
works, we conducted experiments for grasping a tofu. The
experimental setup is shown in Fig. 4. The procedure of
performing the experiments is shown in Fig. 13. The
dimensions and weight (22.7 [g]) of all the tofus were same.
The fluid fingertip was pushed against the tofu at a speed of
1.0 mm/s. We stopped when the pushing distance was
4,6, 8, 10, 12, and 14 [mm], and the Z-axis of the stage on which
the tofu was placed was moved in the lower direction forgrasping. After checking whether the tofu was grasped (falldown), a disturbing force was exerted in the direction ofgravitational force manually, in order to observe the stabilityof grasping. If the tofu did not fall down, the grasping was
judged to be stable. If the tofu fell down, the grasping was
judged to be unstable. The manual disturbance was notquantitative. Then, we measured the amplitude of fluidpressure in the fingertip when the disturbing force was applied,
as shown in Fig. 14. Table 2 lists the measured mean
amplitude for each condition. The magnitude of the disturbing
force when the grasping was stable was lower than or equal
to that when the grasping was unstable, except for one or twocases. Thus, it can be concluded that the evaluation/judgment
was valid. The initial fluid pressure in the fingertip (whenthere is no contact) was set as 1.5, 2.7, 4.0, and 6.0 [kPa]. The

Figure 14. Time series data of the fluid pressure P (initial fluid pressure: 6
kPa, pushing distance : 14 mm). The first peak (indicated by the arrow)denote the point when the pushing distance was 14mm. The second peakdenotes the point when the tofu was grasped.

V. CONCLUSION
This paper presented a novel condition for grasping objects
whose compression behavior is qualitatively similar to that of
tofu. We applied the condition to the fluid fingertip thatutilizes a rubber bag filled with a viscoelastic fluid [1]–[3].
The compression behavior of tofu shows the following trend:
at first, the behavior is non-linear, followed by linear behavior.
Finally, yielding and fracture occurs. The grasping condition
is to control the amount of compression so that thecompression behavior can be elastic/linear. When thegrasping condition is satisfied, it indicates that there is no
fracture, and the contact between the fluid fingertips and theobject can be modeled using a liner spring, and contact force
by the fingertip can be transmitted without any loss. Therefore,
stable grasping can be easily obtained (by a simple controller).
Contact pressure can be observed through the fluid pressureof the fingertips (because linear behavior is observed in phase2, as shown in Figs. 7 and 10). Linear behavior is observed
before yielding, and corresponds to the case when thegrasping force is relatively large. Thus, if the weight of an
object small, the grasping force is sufficient to satisfy

frictional and equilibrium conditions. In this case, grasping
succeeds only if the proposed condition is satisfied.

will be discussed in a future study.
REFERENCESTABLE II.

EXPERIMENTAL RESULTS FOR GRASPING TOFU AT AN
INITIAL FLUID PRESSURE OF 1.5, 2.7, 4.0, AND 6.0 [KPA]. THE CONDITIONSWHEN THE PUSHING DISTANCE EXCEED THE GRASPING POINTS ARE
INDICATED IN BOLD.

Initialfluid
pressure
[kPa]

1.5

2.7

4.0

6.0

Pushing
distace[mm]

Success rate)(

Stability

Measuredmean
amplitudeofdisturbanc
e [kPa]-4 [mm]

0/3-

6 [mm]

0/3--

8 [mm]

3/3

Unstable

0.633

10 [mm]3/3

Stable0.674

12 [mm]3/3

Stable0.502

14[mm]

3/3

Stable0.477

4 [mm]

0/3--

6 [mm]

3/3

Unstable

0.207

8 [mm]

3/3

Unstable

0.439

10 [mm]3/3

Unstable

0.518

12 [mm]3/3

Stable0.514

14[mm]

3/3

Stable4 [mm]

0/3

-

0.456
-

6 [mm]

0/3--

8 [mm]

3/3

Unstable

0.351

10 [mm]3/3

Unstable

0.600

12 [mm]3/3

Stable0.822

14[mm]

3/3

Stable4 [mm]

0/3

-

0.658
-

6 [mm]

0/3--

8 [mm]

3/3

Unstable

0.165

10 [mm]3/3

Stable0.307

12 [mm]3/3

Stable0.581

14[mm]

3/3

Stable0.497

This paper also presented a methodology for detecting
whether the proposed grasping condition was satisfied. The
methodology was based on the phase change detection
method [3] of comparing the fitting accuracies of different
approximation models. Phase change indicates the change offitting/approximation model. By using the phase change
detection method, the starting point of each phase was
detected. By applying linear regression to the data from theobtained starting point, we determined the points where theslope of the regression line was constant under the conditionof good fitting accuracy. The obtained points correspond topoints where the compression behavior is linear.
We also presented the reason behind (first) phase change,
which was unclear in the previous study [3]. In the phase justbefore phase change, there was a slight increase in fluidpressure, and the fingertip behaves like a rigid fingertip. In thephase after phase change, the internal pressure of the object(contact pressure) is transmitted to the fluid pressure, and thecontact pressure can be observed through the fluid pressure.
The linear behavior of compression suggests the possibilityof construction of a controller for (tofu) manipulation. This

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