Engineering, 2013, 5, 424-428
http://dx.doi.org/10.4236/eng.2013.510B087 Published Online October 2013 (http://www.scirp.org/journal/eng)
Contr ol Strategy of Vi brational Capsubot in Vi scoelastic
Environment
Cheng Zhang*, Renjia Tan, Hao Liu, Hongyi Li
Shenyang Institute of Automation (SIA),
Graduate School of the Chinese Academy of Sciences, Shenyang, China
Received 2013
ABSTRACT
Active capsule endoscopy is becoming a research hotspot in recent years. We design an active capsule robot (capsubot)
with the vibrational mode. The internal force-static friction control strategy which is used in the capsubot is effective in
rigid environment but not in viscoelastic environment. A particular viscoelastic material whose parameters are con-
firmed is set to the viscoelastic environment. We suppose th at it is a periodic damped oscillation system when the cap-
subot make a free vibration in the environment. We propose a new control strategy whose principle is similar to a swing
in the environment. The simulation results show that the new str ategy is effective.
Keywords: Control Strategy; Capsubot; Viscoelastic Environment; Swing
1. Introduction
Recently, the incidence of diseases in gastro-intestinal
(GI) tract has increased annually. Endoscopy has been
widely used in clinical as the main diagnostic method of
GI diseases. Although the passive capsule endoscopy is
widely used in clinical, the disa dvantages such as missed
diagnosis and ileus are inevitable. In order to overcome
the difficulties, the motion mechanism of the capsule
endoscopy is very important [1].
The driving mode of the capsule robot contains bionic
driving, screw driving, foot driving and many others. Bio-
nic driving is mainly based on the motion mechanism of
earthworm and inchworm [2-4]. Screw driving is that
capsule is rotated by a certain method, and then the cap-
sule moves with the thrust caused by the rotation of the
thread in the grume [5-8]. Foot driving is that capsule
moves using its feet to seize the wall of the intestine,
which has a high efficiency [9,10].
In the paper, we design the capsubot with the vibra-
tional mode. The internal force-static friction control strat-
egy is proposed to make the capsubot move on the rigid
environment efficiently. But the motion efficiency is not
good if the capsubot moves in viscoelastic environment.
Therefore, we propose a new control strategy for a par-
ticular viscoelastic environment. According to the simu-
lation results, the movement of the capsubot will be
shown.
2. The Overview of the Capsubot
1) Structure of t he Ca psubot
The capsubot can be divided into two parts: a shell and
a sliding mass. The driver contains four parts: magnetic
conductor, magnetic conductive gasket, coil and magnet.
The same poles of the three magnets are placed face to
face. Three magnets are connected by magnetic conduc-
tive gaskets. The whole is used as the sliding mass. The
coils connect with the magnetic conductor. The whole is
regarded as the shell. The magnetic paths of the magnet
are shown in Figure 1. The structure with magnetic coa-
gulation effect is used for getting larger output force.
There are three slots on the magnetic conductor for in-
stalling and moving (see Figure 2). We choose NdFeB
as hard magnet and pure iron as soft magnet [11].
2) Internal Force-Static Friction Control Strategy
To move the capsubot forward, the required motion
consists of four s te ps (see Figure 3):
a) Large backward accelerated motion of the sliding
mass. Forward accelerated motion of the shell (0 − t1).
b) Small backward decelerated motion of the sliding
mass. Forward decelerated motion of the shell (t1 − t2).
Figure 1. Inside structure and magne t ic paths of the driver.
*Corresponding a uthor.

C. ZHANG ET AL.
425
Figure 2. Outside structure of the driver.
Figure 3. Steps of the internal force-static friction motion.
c) Small backward decelerated motion of the sliding
mass. The shell remains stationary (t2 − t3).
d) Forward slow motion of the sliding mass. The shell
remains stationary (t3 − t4).
The actuator is controlled by Pulse-Width Modulation
(PWM) signal. The velocity curve of the sliding mass in
two periods is shown in Figure 4 for the purpose of
making the actuator have the highest efficiency and the
lowest ene rgy cons umption [12].
Now the speed of the capsubot can reach 30 mm/s on
hard plane. The average power dissipation is 70 mW.
However, if the capsubot moves in viscoelastic environ-
ment, the internal force-static friction control strategy
fails. In step2, 3 and 4, the capsubot remains stationary
relying on the static friction. There is not only static fri c-
tion, but also reverse pull in viscoelastic environment.
3. Viscoelastic Environment Definition
We assume that the viscoelastic environment in which
the capsubot moves is in line with the Maxwell model
[13] (see Figure 5).
The Maxwell model can be represented by a purely
viscous damper whose viscosity is
η
and a purely elas-
tic sprin g whose elastic constant is
E
connected in series.
The constitutive equation is
( )( )( )
tt
tE
σσ
εη = +


(1)
Where
t
is time,
ε
is strain and
σ
is stress
According to the driving principle of the capsubot, we
need to focus on the dynamic modulus of the Maxwell
material. That is to say, we have to know the change of
dynamic stress response under the strain change. As-
Figure 4. Diagram of the velocity profile of m2.
Figure 5. Maxwell model.
suming the strain changes harmonically with time
( )
0it
te
ω
εε =
(2)
Where
ω
is frequency,
0
ε
is strain amplitude
We substitute (2) to (1)
0
() it ie E
ωσσ
ωε η = +

(3)
Equation (3) is solved to yield the stress response. The
stress response must contain factor
it
e
ω
under steady-
state condition because
E
and
η
are both real. Define
( )
*it
te
ω
σσ =
(4)
Where
*
σ
is stress amplitude
We substitute (4) to (3)
( )( )
()
()
Ei
tt
iE
ηω
σε
ηω
=+
(5 )
Define
*12
()
( )()()()
Ei
Y iYiYiE
ηω
ωω ω
ηω
=+=
+
(6)
Where
*
()Yi ω
is complex dynamic modulus, then
we have
22 2
12
2 222 22
(), ()
EE
YY
EE
η ωηω
ωω
ηω ηω
= =
++
(7)
4. Motion Analysis and Control Strategy
The capsubot makes shearing motion on the viscoelastic
environment (see Figure 6). We hope that the capsubot
can break the bondage of the environment. However,
there is no relative motion between the capsubot and the
environment because of the viscoelasticity. The abstract
model of the system is shown in Figure 7.

C. ZHANG ET AL.
426
Figure 6. Motion system.
Figure 7. Abstract model.
1) Interaction between Capsubot and Environment
First we consider the free vibration of the capsubot.
The thickness of the viscoelastic material is
d
, sectional
area is
A
. The displacement of the capsubot is
u
.
Kinetic equation
0Mu A σ +=

(8)
Where
12
Mmm= +
,
σ
is the stress of the material
Geometric equation
ud ε =
(9)
The constitutive equation of the viscoelastic material
*
Y σε =
(10)
Substitute (9) and (10) to (8)
*
0
A
MuY u
d
+= 
(11)
Define the plural solution of the free vibration
0it
u ue
ω
=
(12)
Then we have the frequency equation of the free vi-
bration
2*
0
Md Y
A
ω − +=
(1 3)
Substitute (6) to (13), we have
2
0
E EA
iMd ωω
η
− −=
(1 4)
The solution of
ω
is
2
2
24
EAE E
iMd ωηη =±−
(15 )
We assume that the radical is real and it is defined as
β
. Then we have
2
E
i ωβ
η
= +
(16)
The solution of the distance is
( )
212
cos sin
Et
ue CtCt
ηββ
−
= +
(17)
Where
1
C
and
2
C
are determined by initial distance
and velocity.
Now the system is periodic damped oscillation. The
peak time is
π
p
t β =
(18)
When
u
get to the peak, we give the next exciting
force to the system in order to make emanative vibration.
2) Capsubot’s Control Strategy
Next we consider the control strategy of the capsubot.
Using Newton’s second law, the following two relations
can be found
( )
1122 1
sgnmxfmgx xF
µ +−− =
 
(19)
( )
2222 1
sgnmxmgxxF µ + −=−
 
(20)
From the principle of mechanics, we have
fA σ = ⋅
(21)
Where
1
x
is the absolute displacement of the shell,
2
x
is the absolute displacement of the mass,
µ
is the
friction coefficient between the sliding mass and the shell,
F
is the out put force of the driver,
f
is the force from
the environment.
By using the analysis above, the sliding mass velocity
profile can be generated as shown in Figure 8. A detailed
description of the seven steps of the procedure corres-
ponding to the diagram is presented below.
a)
[
)
1
0,tt∈
: Fast backward accelerated motion of m2
( )
22
0, 0xx<< <
 
leads to forward accelerated motion of
1
m
( )
11
0, 0xx>>
 
.
b)
[
)
12
,t tt∈
: Fast backward decelerated motion of m2
Figuer 8. The sliding mass velocity.

C. ZHANG ET AL.
427
( )
22
0, 0xx>> <
 
lead to forward decelerated motion of
1
m
( )
11
0, 0xx<>
 
.
c)
[
)
23
,t tt∈
:
2
m
is driven by the inner friction
( )
2
0x<

,
1
m
moves ba c kward by
f
( )
1
0x<

,
0F=
.
d)
[
)
34
,t tt∈
: Fast forward accelerated motion of
2
m
( )
22
0, 0xx>>>
 
leads to backward accelerated motion
of
1
m
( )
11
0, 0xx<<
 
.
e)
[
)
45
,t tt∈
: Fast forward decelerated motion of
2
m
( )
22
0, 0xx<< >
 
lead to backward decelerated motion
of
1
m
( )
11
0, 0xx><
 
.
f)
[
)
56
,t tt∈
:
2
m
is driven by the inner friction
( )
2
0x>

,
1
m
moves forward by
f
( )
1
0x>

,
0F=
.
g)
[
)
67
,t tt∈
and
[
)
78
,t tt∈
are the same as
[
)
1
0,tt∈
and
[
)
12
,t tt∈
separately.
The amplitude of the vibration becomes larger by
energy accumulation. If the amplitude is larger than the
maximum extension of the viscoelastic material, the cap-
subot can break the bondage of the environment. If not,
repeat. In other word, we make the capsubot resonate
with the environment for the maximum amplitude. The
system is similar to a swing.
5. Simulation and Result
The simulation is carried out using MATLAB/SIMU-
LINK with the sampling interval
25
s
T ns=
. All of the
parameters used in the simulation are given in Table 1.
Figure 9 shows the distance of the shell. From the
figure, we can see that the first peak value (A) is 2.062
mm, the second peak value (B) is −2.258 mm and (C) is
2.377 mm. That is to say, the vibrational amplitude in-
creases by energy accumulation.
When the vibration reaches to peak, the exciting force
makes the shell move to surpass the peak. Then the max-
imum amplitude becomes larger. The force from the en-
vironment is confirmed by the material’s own characte-
ristic. Figure 10 shows the force from the environment.
6. Conclusion
In the paper, we raise a new control strategy which is
similar to a swing for the vibrational capsubot in viscoe-
lastic environment. When the capsubot make a free vi-
bration in the environment whose parameters are con-
firmed, the whole system is an underd amped system. It is
Table 1. Parameters of the motion system.
m1(kg)
0.00321 m2(kg) 0.00794 d(m) 0.002 A(m2) 0.000378
E(N/m2)
6 η(N/m2) 0.5 g(m/ s2) 9.81 μ 0.07
Fmax(N)
0.5 j(m) 0.003
Where m1 and m2 are the weight of the shell and the sliding mass of the
capsubot; j is the sliding journey; Fmax is the maximum output force of the
driver.
Figure 9. The distance of the shell.
Figure 10. The force from the environment.
proved that the strategy is effective for the movement of
the capsubot according to the simulation result. If the
capsubot can break the bondage of the environment, fric-
tional characteristic need to be considered. The strategy
broadens the application environment of the capsubot.
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