Modelling and Analysis of the Damping Force for the

Master Manipulator of the Robotic Catheter System

Yang Yu*1

and Jian Guo*1

Shuxiang Guo*1*2

and Lin Shao*1

Monkey King, Bajie Zhu and Seng Tang

*1 Tianjin Key Laboratory for Control Theory & Application

in Complicated Systems and Biomedical Robot Laboratory

*2 Intelligent Mechanical Systems Engineering Department

Faculty of Engineering Department of Intelligent Robotics

Tianjin University of Technology Kagawa University University of Huaguoshan

Binshui Xidao 391, Tianjin, China Takamatsu, Kagawa, Japan Huaguoshan, Jileshijie Province, China

yuyang1st@163.com; jianguo@tjut.edu.cn guoshuxiang@hotmail.com 1625174737@qq.com monkey.king@uhuaguoshan.edu.cn

Abstract - Vascular Interventional Surgery (VIS) is the

common but conventional method to cure the vascular disease.

Teleoperation, a promising surgery is used to protect the surgeon

from X-ray radiation as well as to solve the problem of lacking

experienced surgeons in remote rural areas. In this paper, a

mathematical model of the damper has been built to get the

relationship between the current of the coil and the damping force. According to the mathematical model, a PID control

algorithm was designed to improve the accuracy of force

feedback. The slave manipulator detect the force of catheter when

being inserted into the blood vessels, then the master manipulator

produce an equal damping force by a damper based on

magnetorheological fluids. The comparison experiments between

control mode with the PID algorithm and control mode without

PID algorithm have been done to verify the performance. The

result shows that the error with the PID control algorithm is

small, which indicates the PID algorithm can improve accuracy of

the force feedback.

Index Terms- Vascular Interventional Surgery (VIS),

Teleoperation, magnetorheological fluids (MRF), PID

control algorithm, Force feedback.

I. INTRODUCTION

Vascular disease has become one of the three most serious

diseases which threaten human life and health [1]-[3].

Teleoperation Robot Minimally Invasive Surgery (TRMIS) is

one of effective treatments of this disease. Surgeries are

operated using precise medical devices and viewing

equipments to insert a catheter into the sick part through a

small incision. Force feedback will help the surgeries existing

in robot navigation tools completely along the path that the

doctor finished the surgery the easier way. So an easy

controllable actuator with quick response is necessary when

the user completes the operation. TRMIS is a kind of

revolutionary surgical technique that consists of five

subsystems: master manipulator, slave manipulator, local

control systems in master site and slave site, and information

exchange channel [4]-[6]. There is a lot of research in this

field abroad, Sensei Hansen pharmaceutical company

developed a robot system, which is the first to use in vascular

interventional surgery robot system. The doctor under the

guidance of three-dimensional images, catheter intervention to

be controlled by master-slave mode of operation, which in the

main the doctor can strong feedback, can achieve the accuracy

and stability of the catheter in the course of the surgery. On

January 9, 2000, the United States Intuitive Surgieal company

successfully developed Davinei Da Vinci surgical robot, it is

one of the few commercial use of technology [7]. Leonardo Da

Vinci surgical system is an advanced robot platform, and its

design idea is through the use of minimally invasive methods

to implement the complex surgery. Leonardo Da Vinci robot is

consisted of three parts: the surgeon console; Bed mechanical

arm system; Imaging system. Japan cheese pu industrial

university Noor Ayuni Che Zakaria developed a system which

can avoid catheter failure and human error, the system is

achieved by the rotation of the friction roller axial movement

of the catheter, pipe by electro-rheological fluid force

feedback [8]. A master-slave system with force feedback was

developed, too. But this system also has some disadvantages,

such as the axial motion of the catheter is almost realized by

the friction of wheels [9]. And the friction between the wheels

and catheter may cause damage to the catheter, and the

impaired catheter could damage to the blood vessels. So a

teleoperated robot–assisted surgery system through exploiting

magneto-rheological fluids (MRF) is proposed. Bar-Cohen et

al. have studied the use of electro-rheological fluid devices in

use on small damper force feedback of the application form for

intelligent gloves [10]. Compared with ER fluid [11], MR

fluids like low voltage requirements add to the complexities of

the system. The characteristic comparison between MR fluids

and ER fluids is given in Table 1. So MR sponge dampers can

be used here easily. Carlson et al. have developed and utilized

MR sponge dampers in vibration control problems like

washing machines [12]. In this paper the application of MR

devices in force feedback systems is the main point. TABLE I

CHARACTERISTIC COMPARISON BETWEEN MR FLUIDS AND ER FLUIDS.

In the paper, we mainly model and analyze the damping

force for the master manipulator of the robotic catheter system,

and using PID algorithm to calculate the force feedback. The

experiment with the PID control algorithm and the experiment

without the PID control algorithm were also done to verify the

performance, and the result shown that the error with the PID

control algorithm is small, so the design is reasonable and

reduced the risk of surgery.

II. THE SYSTEM OF THE MASTER-SLAVE MANIPULATOR

A. The system of the master manipulator

Doctor operates the master manipulator to finish the

surgery, and the structure of our design is shown as Fig1. It

contains two degrees of freedom- axial and radial, a linear

displacement sensor has been adopted in order to acquire the

axial motion of the catheter, and the sliding end use a floating

magnetic block with non-contact, so there is no any fraction

when the sliding end moved, and it has synchronous movement

with piston rod of the damper. The optical encoder which

installed on the torque motor is acquired by the radial motion

of the catheter. The connection is a synchronous belt between

the torque motor and the piston rod, so they have the same

rotation angle, and the radial motion of the catheter can be

detected by optical encoder. In our design there are grasper1

and grasper2 worked. Grasper1 connects to the piston rod with

nipple joint, and grasper2 is fixed on the board of the lifting

platform, which is installed on a board. When the catheter is

grasped by grasper1, doctor operates the catheter move with

piston rod [9]. When the catheter is grasped by grasper2, the

surgeon could adjust the position of the piston rod.

Fig.1 The master manipulator

B. The system of the slave manipulator

The slave manipulator is the real master system to the

patient, it ensure that the catheter insert vessels accurately.

When the catheter comes across the branch of blood vessel, it

could rotate to get through, and it follows the surgeon’s

operation on master side. The slide platform is easy to change

the interventional angle for different patients. A motor is used

to drive slide platform, and the master piston determined the

position of slide platform. Two graspers the same as the master

side have been designed to simulate the surgeon’s grasping

action. The catheter also move along both axial and radial

directions, the movement as the same as the master side. The

slide platform is driving by a stepping motor, and a load cell is

to get the axial driving force [13]. When the catheter is

clamped by grasper 2, the catheter keeps its position and the

catheter driven part can move smoothly. To realize axial

movement, all catheter driven parts must be placed and fixed

on slide platform. The rotation through the synchronous belt

drives the catheter to move in radial direction, and the stepping

motor is driving the slide platform which is driven by a screw.

The design of slave manipulator is shown in Fig2. Due to the

different operators operating habits and different height

requirements for the operator, on the master manipulator, the

surgeon can manually adjust the lifting platform with 12 cm

for the height of the range of micro adjustment.

Fig.2 The slave manipulator

III. THE MODEL OF THE DAMPING FORCE AND INPUT CURRENT

The damper consists of polyurethane foam soaked and

the sponge in MR fluid and wound around a piston. This

piston along with the sponge moves to and fro inside an outer

casing [14]. As the piston moves, the MR fluid in the foam

produces a force which is called the shear stress. The foam like

a reservoir of MR fluid and absorbs the maximum amount of

MR fluid, and that is the reason why it is chosen. The

schematic is shown below in Fig3. The piston has number of

turns of coil to produce the required magnetic field. As the

current in the coil is increased to its maximum value, the

magnetic field in the MR sponge is increased and the shear

stress is produced [14]. As a result, it resists the shearing

motion of the piston.

Fig.3 MR fluid damper assembly

The viscosity of the MR fluid can be controlled by

applying an external magnetic field. The greatest feature of

master manipulator is the damper with MR fluid, which is used

to achieve force feedback. It can transmit the operating force

that the slave manipulator drives the surgical catheter to

surgeon’s hands. The design equations for the MR sponge

damper are

y (1) B y

(2) NIR (3)

sR

l

(4)

s B (5) SF y (6)

where is the shear stress (Pa), y

is the yield stress (Pa),

α is a constant and α =1.5 [15]. These functions can be found

from the MR fluid properties chart, η is the base viscosity of

MR fluid (Pa.s),

is the shear rate of MR fluid (1-s ), F is the

damping force across the MR damper (N), S is the surface area

of piston and S=0.0093 (2m ), N is the number of turns of coil

around the piston and N=500, I is the current through the

piston(Amperes), is the magnetic flux through the magnetic

circuit (Wb), R is the reluctance of the magnetic circuit in the

MR damper (Amp.turns/Wb), μ is the magnetic permeability

of the MR fluid and μ =0.003, l is the length of the magnetic

flux path and l=0.06m [12]. B is the magnetic field density

(Tesla), s is the cross section area of gap across which flux

flows (2m ). Finally, the resulting relation between the

damping force and current is

I

SNF

l

(7)

According the equation (7), we use the MATLAB

software for simulation and the schematic diagram is shown as

fig4. Bring all the parameters into the model; we can obtain

the coefficient of the equation (7) is 0.35 and it’s a constant.

Fig.4 The schematic diagram

In this paper, the MR fluid damper has a lot of parameters

should be taken into consideration. Due to the introduction of

the PID algorithm is the output voltage, and the damping need

is current, so the form of voltage can be converted to the

current form. Fig5 is the simulation results of the calibration

test voltage controlled current source.

Fig.5 The simulation results of the calibration test voltage controlled current

source

Due to the nature of the voltage controlled current

source, when the voltage is greater than 0.5 V, current value

will be constant, so ending calibration in the 0.5 V. In

addition, current were needed for the experiment is less than

0.5 A, if current too great will burn the experiment equipment.

The figure shows that the voltage and current is proportional to

the relationship, and the fitting formula is equation (8).

VI (8)

Where V is input voltage and I is output current.

As the need of master manipulator, the stroke of the

damper is set as 200mm. The gap between the piston body and

outer casing is 2mm. The outer diameter of the damper is

48mm and the thickness of outer casing is 4mm. The diameter

of piston body is 36mm [9]. It was coiled with approximately

500 turns of insulated copper wire, as is shown in fig6. The

foam saturated with MR fluid was covered on the piston body.

(a) Piston body (b) piston rod

Fig.6 Piston body wrapped with coil assembled to piston rod

PID is used to eliminate static error, and improve the

system of no difference degree, thus improve the accuracy of

force feedback. Due to the computer system is a kind of

sampling control system, only according to the deviation of the

sampling times can calculate the amount of controlled

variable, therefore, use external rectangle method for

numerical integration, after the first order difference of the

numerical differentiation to when the sampling period T,

)]([ 1i

0

iD

i

j

j

I

ipi eeT

Te

T

TeKu

(9)

If the sampling period is small enough, the discrete

approximation is quite accurate. Equation (9) iu is all output,

it corresponds to the location of the sampling time when the

controlled object of the actuators in the first time i. Therefore,

equation (9) is defined as the positional PID control algorithm.

According the equation (9) to calculate iu , it is observed that

the output relate to all the past state. When executing agency

need is the controlled variable increment but not the absolute

value, it can get the equation (10) which is defined as

the increamental PID control algorithm.

iu =1 ii uu = )]2([ 2i1i1 eee

T

Te

T

TeeK i

Di

I

iip(10)

In this study, the calculation method is applied

the incremental PID control algorithm.

IV. THE EXPERIMENTS EVALUATION OF THE PID CONTROL

ALGORITHM

In order to evaluate the calculation results of PID

algorithm, an experimental system was established, as is

shown in fig7. The system includes a load cell, a damper, a

slide platform, a step motor and a piston rod. Connecting with

the back-end of the piston is the detecting terminal of the load

cell, and when the step motor drives the slide platform to make

the load cell moving forward or backward with the piston rod,

the load cell can acquire resistance. To acquire the deviation,

feedback the damping force to input current, and get through

the PID algorithm to control the size of the damping force.

The output of the load cell is sent to the PC through a data

acquisition card. The input voltage of the electronic circuit is

produced by different current in the piston coil with

controlling.

The velocities of the catheter must be low to prevent

penetrate vascular, so the speed of the slide platform less than

10mm/s. The experimental result shows that when the current

of the piston coil is a constant value, the resistances of the MR

fluid damper almost the same with different velocities under

10mm/s. The measuring range of load cell is from -5N to 5N,

which correspond to the value range from -5V to 5V. When

the piston moved forward, the outputs of the load cell were

positive values. On the contrary, they were negative values. In

general, we used average as the current value of the resistance.

Fig.7 The evaluation structure diagram

Fig.8 is the real damper calibration test, to obtain the

relation of the current and damping force. Fig.9 is shown the

calibration experiment result of the damper based on MR fluid.

Until when the sponge is immersed in MR fluid, between the

sponge and the piston have a constant friction, so when the

input current is 0 A, the damping force is not 0 mN, but the

friction between the piston and sponge. As shown in it that

with the increase of coil current, damping force tends to a

constant value. But the implementation equipment coil to the

maximum current is 0.5 A, and the input current of the coil is

the output current by voltage controlled current source.

Damping force of the range is 0 to 5 N, as shown in figure

experiment for damping force of the measured values in the

permitted range. Based on the data of correlation between the

input current and the damping force, the fitting curve equation

was established with MATLAB. As is shown in equation (11)

F = -795.932I + 2274.70I +933.38 (11)

Where F is the damping force, I is the input current.

Fig.8 The damper calibration test

Fig.9.The calibration experiment of the damper based on MR fluid

The slave manipulator will detect the reaction of catheter

when being inserted into the blood vessels through the load

cell. The DSP controller on the slave side will collect the force

information and transmit to the master manipulator. Then it is

identified by the master DSP. The DSP controller on the

master side will control the current of the coil using a PID

control algorithm in the program to control the damping force.

In the same time, the damping force will be detected by a

pressure sensitive rubber and transmitted to the DSP

controller, which can form a closed loop to improve the

precision of the system. Unlike in the past, this experiment

joined the PID control algorithm to improve the accuracy of

force feedback. Fig.8 is the comparison experiment of the PID

algorithm. The red curve is the force produced without PID

algorithm, the green is setting force value and the blue curve is

the force produced using PID algorithm. Because the sponge

has friction with the piston, so the time in the first seconds

both detected force and force feedback to have value not from

zero. Setting force is determined according to the load cell

measurement range 0-5 N. Fig 10 is the error curve between

the force produced using PID algorithm and the force

produced without PID algorithm. As is shown in Fig.11, in the

experiment with PID algorithm, the maximum error is 80.35

mN, which is in the permitted range [15]. However, in the

experiment without PID algorithm, the maximal error

approximates 300 mN, which is too large to injure the vascular

easily. The error using PID algorithm is lower than the error

not using PID algorithm. So the design is reasonable, and it

can improve accuracy of the force feedback.

Fig.10 The comparison experiment of the PID algorithm

Fig.11 The error curve

V. CONCLUSION AND FUTURE WORK

In this paper, a novel master-slave robotic catheter system

using a damper based on MR fluid to realize the force

feedback was proposed. The mathematical model of the

damper was established to design the PID algorithm to control

the damping force to realize the force feedback. The

comparison experiments between control mode with the PID

algorithm and control mode without PID algorithm have been

done to verify the performance of the PID algorithm. In the

experiment with PID algorithm, the result indicates that the

maximal error is 80.35 mN, which is in the permitted range

presented in a study. In the experiment without PID algorithm,

the maximal error approximates 300 mN, which is too large to

injure the vascular easily. So control mode with PID algorithm

can meet our design requirement to improve the accuracy of

the online force feedback and reduce the risk of surgery.

In future work, we will use the developed novel robotic

catheter system with PID algorithm to do the experiments “in

vitro” and “in vivo”.

ACKNOWLEDGMENTS

This research is supported by National High Tech.

Research and Development Program of China

(No.2015AA043202), and General Research Program of the

Natural Science Foundation of Tianjin (13JCYBJC38600) and

the Project-sponsored by SRF for ROCS, SEM.

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