Control Strategy of Vibrational Capsubot in Viscoelastic Environment

doi:10.4236/eng.2013.510B087

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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

Email: *[email protected]

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

and a purely elas-

tic sprin g whose elastic constant is

connected in series.

The constitutive equation is

( )( )( )

σσ

εη

= +



(1)

Where

is time,

is strain and

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

εε

(2)

Where

is frequency,

is strain amplitude

We substitute (2) to (1)

() it

ie E

ωσσ

ωε η

= +



(3)

Equation (3) is solved to yield the stress response. The

stress response must contain factor

under steady-

state condition because

and

are both real. Define

( )

*it

σσ

(4)

Where

is stress amplitude

We substitute (4) to (3)

( )( )

()

ηω

σε

ηω

(5 )

Define

*12

()

( )()()()

Y iYiYiE

ηω

ωω ω

ηω

=+=

(6)

Where

()Yi

is complex dynamic modulus, then

we have

22 2

2 222 22

(), ()

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

, sectional

area is

. The displacement of the capsubot is

Kinetic equation

0Mu A



(8)

Where

Mmm= +

is the stress of the material

Geometric equation

(9)

The constitutive equation of the viscoelastic material

σε

(10)

Substitute (9) and (10) to (8)

MuY u



(11)

Define the plural solution of the free vibration

0it

u ue

(12)

Then we have the frequency equation of the free vi-

bration

Md Y

− +=

(1 3)

Substitute (6) to (13), we have

E EA

iMd

ωω

− −=

(1 4)

The solution of

EAE E

iMd

ωηη

=±−

(15 )

We assume that the radical is real and it is defined as

. Then we have

ωβ

= +

(16)

The solution of the distance is

( )

212

cos sin

ue CtCt

ηββ

−

= +

(17)

Where

and

are determined by initial distance

and velocity.

Now the system is periodic damped oscillation. The

peak time is

(18)

When

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

+−− =

 

(19)

( )

2222 1

sgnmxmgxxF

+ −=−

 

(20)

From the principle of mechanics, we have

= ⋅

(21)

Where

is the absolute displacement of the shell,

is the absolute displacement of the mass,

is the

friction coefficient between the sliding mass and the shell,

is the out put force of the driver,

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.

[

)

0,tt∈

: Fast backward accelerated motion of m2

( )

0, 0xx<< <

 

leads to forward accelerated motion of

( )

0, 0xx>>

 

[

)

,t tt∈

: Fast backward decelerated motion of m2

Figuer 8. The sliding mass velocity.

C. ZHANG ET AL.

427

( )

0, 0xx>> <

 

lead to forward decelerated motion of

( )

0, 0xx<>

 

[

)

,t tt∈

is driven by the inner friction

( )

0x<



moves ba c kward by

( )

0x<



0F=

[

)

,t tt∈

: Fast forward accelerated motion of

( )

0, 0xx>>>

 

leads to backward accelerated motion

( )

0, 0xx<<

 

[

)

,t tt∈

: Fast forward decelerated motion of

( )

0, 0xx<< >

 

lead to backward decelerated motion

( )

0, 0xx><

 

[

)

,t tt∈

is driven by the inner friction

( )

0x>



moves forward by

( )

0x>



0F=

[

)

,t tt∈

and

[

)

,t tt∈

are the same as

[

)

0,tt∈

and

[

)

,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

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.

REFERENCES

[1] “Principles and Clinical Application of Capsule Endos-

copy System,” Science Press, 2010, pp. 144-154.

[2] J.-Y. Zuo and G.-Z. Yan, “A Multi2unit Creeping Robot

Based on Earthworm Principle,” ROBOT, Vol. 7, 2004,

pp. 320-324.

[3] P. Dario, M. C. Carrozza, Lencioni, et al., “A Micro Ro-

botic System for Colonoscopy,” IEEE International Con-

ference on Robotics and Automation, Albupuerque, New

Mexico, 1997, pp. 1567-1572.

http://dx.doi.org/10.1109/ROBOT.1997.614363

[4] D. Peir s Jreynaerts and H. Van Brussel, “Design of Mini-

ature Parallel Manipulators for Intergration in a Self-Pro-

pelling Endoscope,” Sensors and Actuators, Vol. B85, pp.

409-417.

C. ZHANG ET AL.

428

[5] X.-Y. Jian, T. Mei, X.-H. Wang, “Driving Method of an

Endoscopic Robot Capsule by External Magnetic Field,”

ROBOT, Vol. 27, No. 4, 2005, pp. 367-372.

[6] Olympus Medical System Corporation, “Development of

Capsule Endoscope and Peripheral Technologies for Fur-

ther Expansion and Progress in Endoscope Applications.”

[7] Y. S. Zhang, Z. G. Li, S. P. Jing, et al., “Characteristics of

Magnetic Tensile Force along Axial Direction of a Cap-

sule Micro Robot Applied in Intestine,” Chinese Mecha-

nical Engineering, Vol. 18, No. 14, 2007, pp. 1709-1713.

[8] M. Sendoh, K. Ishiyama and K. I. Arai, “Fabrication of

Magnetics Actuator for Use in a Capsule Endoscope,”

IEEE Transactions on Magnetics, Vol. 39, 2003, pp.

3232-3234.

http://dx.doi.org/10.1109/TMAG.2003.816731

[9] A. Moglia, A. Menciassi, M. Schurr and P. Dario, “Wir e-

less Capsu le Endosco py: From Diagnostic Decices to Mul-

tipurpose Robotic System,” Biomed Microdevis, Vol. 9,

2007, pp. 235-243.

http://dx.doi.org/10.1007/s10544-006-9025-3

[10] M. Quirini, R. J. Webster III, A. Menciassi and P. Dario,

“Design of A Pill-Sized 12-Legged Endoscopic Capsule

Robot,” IEEE International Conference on Robotics and

Automation, Roma, 2007, pp. 1856-1862.

[11] G. Su, C. Zhang, R. J. Tan and H. Y. Li, “A Design of the

Electromagnetic Driver for the “Internal Force-Static Fri-

ction,” Capsubot, IEEE/RSJ International Conference on

Intelligent Robots and Systems, 2009, pp. 613-617.

[12] H. Y. Li, K. Furuta and F. L. Chernousko, “Motion Gene-

ration of the Capsubot Using Internal Force and Static

Friction,” IEEE Conference on Decision and Control,

2006, pp. 6575-6580.

http://dx.doi.org/10.1109/CDC.2006.377472

[13] “Principles of Polymer Engineering ,” 2nd Edition, Ox-

ford University Press, 1997, pp. 117-176.