chapter 5 experimentation and test resultsdocinsa.insa-lyon.fr/these/2005/chen/10_chapter_5.pdf ·...

Chapter 5 Experimentation and test results

Gang CHEN 133

Thèse INSA de Lyon, LAI 2005

Chapter 5

Experimentation and test results


Gang CHEN Thèse INSA de Lyon, LAI 2005 134

5

CHAPTER 5 EXPERIMENTATION AND TEST RESULTS .................................................................... 133

5.1 Introduction..................................................................................................................................... 135

5.2 Optical fiber sensors and their calibrations ..................................................................................... 135

5.3 Dynamic performance analysis of one chamber subsystem............................................................ 138

5.4 Controller design with disturbance of insertion .............................................................................. 139

5.4.1 Manipulation context and controller specifications ................................................................................. 139

5.4.2 Controller design using sensitivity function ............................................................................................ 140

5.4.3 Implementation of a lag compensator...................................................................................................... 141

5.4.4 Experiment setup ..................................................................................................................................... 142

5.4.5 Set point response with disturbance rejection.......................................................................................... 143

5.5 Exploration in a tube ....................................................................................................................... 145

5.6 Conclusion ...................................................................................................................................... 150



5.1 Introduction

In the previous chapters, we have built the experimental dynamic model and identified

its corresponding parameters for EDORA II. In this chapter, we will focus on the closed-loop

control of EDORA II. During the operation of colonoscopy, EDORA II needs to be kept as far

as possible from the colon wall. Furthermore, the manipulator’s position requires adjustment in

order for surgeons to have a good view of the colon. The EDORA II, which is designed to

replicate these functions of the steering by physician, will pay much more attention to avoiding

the difficult bends. So this chapter will address the close-loop control and testing in the colon-

like tube by using parameters obtained from the previous chapter.

5.2 Optical fiber sensors and their calibration

The miniBIRD 3-D sensor was used for validation of forward kinematics and dynamics

in the previous chapter. However, it can’t be used in order for EDORA II to explore the colon-

like tube. For this reason other position sensors are required to integrate into EDORA II.

Because of the flexibility of the optical fibers, of their small size and of their light resolution,

we have decided to use optical fibers [PRELLE 01] to measure the distance between the

EDORA II and the colon wall. Three sensors are borrowed from the laboratory of ROBERVAL,

Université Technologique of Compiègne.

As for the principle of the sensor, the light of optical fiber sensor is emitted from a cold

source of light, and is transferred by fiber. The light reflected by the mirror is then injected in

the reception fibers placed around the emission fiber, shown in figure 5.1.

Figure 5.1 Schema of the principle optical fiber sensor

The amount of reflected light detected is a function of the distance between the sensor

and the surface of the objet. The typical sensor response is shown in the figure 5.2. It is divided

into four working areas. The first one is the dead zone where the receiving fibers cannot collect

light because of the limited space between the emission and reception fibers. Area 2 is strongly

non linear and with a small range. Area 4 is non linear but useful for a millimetric range



measurement. Area 3 is the highest sensitivity zone. The range of area 3 is variable according to

the chosen linearity criterion – the smaller the criterion, the smaller the range. For example, in

the common use, a resolution of 1 nm on a 100 µm range can be achieved. It is always possible

to use the sensor in the area 4 to measure a linear displacement on a long range but the

resolution is less than the one in area 3 and it decreases along the range.

Figure 5.2 Fiber optic probe sensitivity [PRELLE 05]

As for our application, the goal is to avoid the contact of EDORA II with the colon wall,

so the measurement range of optical fiber sensors should be from more than 0 mm to about

20mm which is the distance between the manipulator and the colon wall. Thus the area 4 is a

good choice for our application. From figure 5.2, it is noticed that that there is a voltage peak

for low values of the distance. Since the objective is always to keep EDORA II far from the

colon wall, small values of distance don’t have any significance for our application. Thus, the

start point of the sensor is chosen from the point of the voltage peak for easier measurement.

By using a pipe emulating the intestinal walls, the relationship between the distance id

and the voltage iu (where i = 1,2,3 is the number of the optical fiber sensors )are obtained from

calibration as the following ( iu in V and id in mm):

1 21

40u3.2d 3

−=+ (5.1)

2 22

50u1.6d 2.2

−=+ (5.2)

3 23

38u1.7d 2.3

−=+ (5.3)



Figure 5.3 shows the model obtained for the third optical fiber sensor, which has a good

measurement precision for distances from 2 mm to 10 mm. As the diameter of the tube used for

the test is 35 mm and that of EDORA II is 17 mm, then the maximum value will be 18mm. So

this model is satisfactory for testing the performance of EDORA II in the tube.

0 2 4 6 8 10 12 -10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

Distance (mm)

Vol

tage

(mV

) Characteristics of optical fiber sensor 3

Model Measurement

Figure 5.3 Characteristics of the third optical fiber sensor

Three optical fibers can then be easily integrated into EDORA II. As has been shown in

chapter 3, EDORA II has 6 chambers at its circumference. Three chambers are used for the

power supply, and the other three chambers are reserved for optical fiber sensor placement.

However, for the preliminary experiments, we have just attached them on the surface of

EDORA II, shown in figure 5.4.

Figure 5.4 EDORA II with integration of optical fiber sensors



5.3 Dynamic performance analysis of one chamber subsystem

Before testing the performance of EDORA II in the colon-like tube, it is necessary to

design a controller to control the position of the top-end of the EDORA II in the tube. Thus the

dynamic performances of the EDORA II are firstly analyzed in this section based on a linear

transfer function and the controller design will be discussed in the following section. The model

for the linear part of the one chamber system of the EDORA II is obtained in the precedent

chapter and is represented by the transfer function 2H (s) of zone 2 for all the working area. It is

shown as:

2 3 2

2341G(s) H (s)s 3.6s 452s 1012

= =+ + +

(5.4)

Figure 5.5 shows the root locus of the open-loop system.

-80 -60 -40 -20 0 20 40 -80

-60

-40

-20

0

20

40

60

80

System: f2 Gain: 0.0577

Pole: -0.524 - 21.2i Damping: 0.0247

Overshoot (%): 92.5 Frequency (rad/sec): 21.2

System: f2 Gain: 0.0639 Pole: -0.508 + 21.2i Damping: 0.0239 Overshoot (%): 92.8 Frequency (rad/sec): 21.2

System: f2 Gain: 0.0498

Pole: -2.51 Damping: 1

Overshoot (%): 0 Frequency (rad/sec): 2.51

Root Locus

Real Axis

Imag

inar

y Ax

is

Figure 5.5 Root locus of open-loop system for one chamber of EDORA II

The poles of transfer function shown in figure 5.5 show that the system is stable but has

a very low damping ration, which will make the response of the system oscillatory. At the same

time, it can be seen that the system has a small variation of gain before it becomes unstable.

Figure 5.6 shows the step response of one chamber system with a gain of 0.1-0.4. With a

very small gain from 0.1 to 0.3, the system is stable but there is a very big steady-state error,

from 60 % to 80 %. But when the gain is augmented to 0.4, the system becomes oscillatory. Due

to the low damping ratio, the system shows some degrees of oscillation for all the gain from 0.1

to 0.4 and thus generates a long adjustment time. Therefore, using only proportional control

methods is not sufficient for the EDORA II to adjust its position relating to the environment.

Thus, a controller should be conceived to insure that the system has a good margin of stability,



accuracy and robustness with respect to modeling errors. Thus section 5.4 will be concerned

with the requirement of the controller and its design.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0

0.2

0.4

0.6

0.8

1

Time (s)

Dis

plac

emen

t of t

op-e

nd (m

m)

Simulation of step response of one chamber without controller Reference input G=0.4 G =0.3 G = 0.2 G = 0.1

Figure 5.6 Step response of one chamber of EDORA II with different gains

5.4 Controller design with disturbance of insertion

As analyzed in 5.3, the dynamic response of the system presented big steady-state errors

and a weak stability margin. So it’s necessary to design a controller to improve the dynamic

performance to meet the desired specifications. In addition, the diagnostic procedure is not a

normal manipulation as the one used in industry, but a special manipulation of minimal contact

with the colon tissue. Our automatic manipulator EDORA II, which attempts to replicate the

function of the steering by the physician, will pay much more attention to avoiding the difficult

bends.

5.4.1 Manipulation context and controller specifications

Our resolution to improve the performance of a traditional colonoscopy is to replace the

distal end of traditional colonoscopy by designing a new automatic manipulator-EDORA II

while the progression of the colonoscope is kept for the endoscopist. Then, the bendable

manipulator will automatically find the advance direction by controlling the movement of the

EDORA II. During the process of insertion, as described in chapter 1, the colonoscope is



advanced by a variety of “in-and-out” maneuver action to “accordion” the colon [KASSIM 03].

So these movements of the colonoscope exert much disturbance for the control of the position

of the robotic tip. In addition to this, the casual motion due to breathing movements will also

affect the instrument’s position in the colon and the corresponding measurement results.

As far as these problems are concerned, the objective of designing a controller is to let

the manipulator not touch the colon wall under the circumstance of strong disturbance.

However, the contact between the instrument and the colon may take place due to the

disturbance discussed previously. This aspect is not desirable because strong contact forces can

become apparent if the stiffness is too great, which can bring more pain to patients. In the event

of contact, positioning accuracy will no longer be the only primary concern and the compliance

of the instrument should be treated to lessen harm to the colon tissue.

5.4.2 Controller design using sensitivity function

To satisfy these specifications: disturbance rejection and some kind of compliance, a

position-based manipulation control strategy is needed. PI controller is a good choice because it

can be readily implemented and has zero steady-state errors. However, the stiffness will become

infinitive when there is no steady-state errors [PRELLE 01]. This case is not allowed for our

operation conditions due to the consideration of safety. So a lag compensator is chosen as a

compromise between the performance and compliance. Let the loop transfer function be L(s) =

D(s)G(s) where D(s) is the transfer function of the controller to be designed, the maximum

sensitivity is then given by Ms = Max|S(jw)|. As is shown in [FRANKLIN 94], the quantity Ms

is the inverse of the shortest distance from the Nyquist plot of the loop transfer function to the

critical point (-1, j0). Typical values of Ms are in the range of 1.2 –2.0 [ASTROM 98]. If the

value of maximum sensitivity is given, the gain margin (GM) and phase margin (PM) can be

estimated in a conservative way [FRANKLIN 94], as showed in Equation (5.5) and (5.6).

1GM = 20log1⎛ ⎞⎜ ⎟− α⎝ ⎠

(5.5)

And :

PM = 2arcsin( / 2)α (5.6)

where 1/ Msα = and α <1.



5.4.3 Implementation of a lag compensator

In our case, we take Ms = 1.2 with the least sensitivity to the modeling errors. The

corresponding gain margin and phase margin for the transfer function (equation 5.4 ) in zone 2

are obtained as 11 dB and 64 degree by using Equation (5.5) and (5.6). With the phase margin

as described in the specification of the lag compensation, the lag compensator is given by:

0.13s 1D(s) 44s 1

+⎛ ⎞= ⎜ ⎟+⎝ ⎠ (5.7)

-1 0 1 2 3 4 5 6 7 8 0

1

2

3

4

5

6Comparison of the step response for lag controller

Time ( s )

Ste

p in

put a

nd it

s re

pons

e (m

m)

Experimental Expected Simulation

Figure 5.7 Comparison of step response between simulation and the experiment

After the lag controller is designed, it has been implemented with hardware for real

experiments. An experiment is first done in the zone 2 where the dynamic model was identified

(chapter 4.3.3). In order to be in accordance with the condition where the model is obtained, a

step of position of 6mm, which will fall into the zone 2, is applied for one chamber system.

Figure 5.7 is the comparison of step response between the experimental result and the

simulation of the model. The dash-doted line is the simulation result and the solid line is the

experimental result. It can be seen that experimental result is well in accordance with the

simulation result. This fact also proved that the dynamic model obtained in chapter 4 gives a

good modeling of the behavior into the zone 2 (figure 4.4). As it has been explained in chapter

4, since the system is a nonlinear system, other experiments with different conditions are carried

out to check the robustness of this controller within all the working zones of EDORA II.

Experimental results and their comparison of 4 different cases are shown in figure 5.8. Figure

5.8 shows that one chamber of EDORA II has the same dynamic response for the entire working

zone, except that there is a difference for the steady-state value. The reason for this result is



explained as due to the fact that the EDORA II is a nonlinear system with different static gain

when it works in the different zones (Chapter 4.1.2). Therefore, under the assumption of small

displacements of top-end of EDORA II, this controller can work well within the entire working

zone of EDORA II and it ensures the availability of the test of EDORA II in the tube.

-1 0 1 2 3 4 5 6 7 8 -1

0

1

2

3

4

5

6

7

Time (s)

Pos

ition

of t

op-e

nd o

f ED

OR

A II

(mm

)

Step response of lag controller from different working zone

Zone 2expected valueSimulationZone 1Zone 3Zone 4

Figure 5.8 Comparison of step response between simulation and the experiment

5.4.4 Experiment setup

Since the insertion disturbance of the colonoscope is an important factor to test the

performances of EDORA II, a platform is designed and built to emulate the insertion process of

a colonoscope in the colon. The platform is shown in figure 5.9, which can manually move in

two directions (X, Y).

The bottom of EDORA II is fixed on that platform, EDORA II can thus move in the

same way as does the platform. A tube with the diameter of 35mm is placed in a circle

emulating the colon. Three optical fiber sensors are used for measuring the distance between

EDORA II and the wall of the tube. Figure 5.10 shows the simplified block diagram for

feedback control of one chamber of EDORA II.



Figure 5.9 Top view of the experiment setup

5.4.5 Set point response with disturbance rejection

Figure 5.10 shows the control structure for the whole system. The path planner is used to

determine the reference point of three chambers. The first experiment is done to verify the

controller performance for one single chamber in a single direction. The platform for emulating

the insertion movement is moved in the X direction between 2 mm to 26 mm, which is the

disturbance for the reference input.

Path Planner

Controller 1

-Servovalve + Chamber 3+ Controller 3

-Servovalve + Chamber 2Controller 2+

-Servovalve + Chamber 1+

Position In the plate

Optical fiber sensor 1



Figure 5.10 the structure of the whole control system

X

Y

The base



Figure 5.11 shows the measurements of the position of the top-end with respect to the

tube, the reference position. The dashed line is the movement of the base along the axis X and

the solid line represents the real position of the top-end of EDORA II with respect to the tube. It

is clear that the system has drastically rejected the disturbance brought from the movement of

the platform. This result shows that the designed controller has a good performance record of

keeping the top-end of EDORA II to stay near the expected position while there exists a

continuous disturbance.

0 1 2 3 4 5 6 7 8 9 10 -10

-5

0

5

10

15

20

25

30

35

40

45

Time ( s )

Pos

ition

of t

op-e

nd in

the

sim

ulat

or (

mm

)

Disturbance rejection of the controllerthe movement of Xposition of top-end of EDORA II desired position The Wall of the tube

Figure 5.11 The performance of disturbance rejection of the lag compensator

The second experiment is to test if three controllers can work well at the same time for

three chambers of the EDORA II in the entire plane. Thus the platform will move stochastically

in X and Y directions in order to emulate the movement of a colonoscope in the colon. In this

case, the expected position of the top-end of the EDORA II is chosen as the center of the tube

far from the wall of the tube and the reference values for three controllers are then 17.5mm.

Measurements of three sensors are shown in figure 5.12. The values of the measurements of

three sensors are around 17.5 mm with a minimal value of 11mm and a maximal value of

23mm. That is to say, the top-end of the EDORA II can stay around the center of tube under the

disturbance. This result supported the hypothesis that three controllers can work well at the

same time and have good disturbance rejection ability.



0 1 2 3 4 5 6 7 8 9 10 -5

0

5

10

15

20

25

30

35

40 Experimental results for three controllers in the same time

Time (s)

Thre

e m

easu

rem

ents

of d

1, d

2, d

3 (m

m)

Distance 1Distance 2Distance 3The wall of the tube

Figure 5.12 Experimental result of three controller together with the insertion disturbance

5.5 Exploration in a tube

Figure 5.13 Test tube with a bend of 100°

For the validation of the conception of EDORA II, the most effective test is that if

EDORA II can easily cross the tube with a very big bend. So a suitable experiment is necessary

to test its movements in the colon-like tube. In our preliminary experiment, we use a transparent



tube with a 100° bend shown in figure 5.13. The diameter of the tube is 26 mm which is less

than the average diameter of the colon (50mm) and its length is 50 cm.

Figure 5.14 EDORA II with a covering tube for easier insertion

For the purpose of easier insertion, a soft tube 50 cm in length is used to put the entire

tube inside it, as shown in figure 5.14. During the experiment, EDORA II is inserted into the

test tube manually with the help of this covering tube. The designed controllers of EDOAR II

will adjust the position of EDORA II in the tube in order to cross the big bend minimizing the

touch with the inner wall of the tube. As it has been described, small displacement of top-end of

EDORA II is assumed to obtain the dynamic model. This assumption is suitable to the way that

EDORA II traverses the big bend. EDORA II accumulates a great deformation in accord with

the tube bend by small displacement step by step during its progression in the tube. So it is

assumed that the top-end end of EDORA II is always orthogonal to the axis of the tube. Thus

the optical fiber sensors can work the same way as they are calibrated. The schema in figure

5.15 shows the distances from three optical fibers d1, d2 and d3 and the position of the top-end

of EDORA II in the tube (O' is the center point of top-end of EDORA II).

Figure 5.15 Schema of distances d1, d2 and d3 and the position of top-end of EDORA II in the tube.

d1

d2

d3

x

y

O'

Inner wall of the tube

Top-end of EDORA II



During this process, EDORA II is inserted manually into the test tube with a velocity

about 4 cm/sec. A simple path planing algorithm is used and easily implemented to get the

reference point of three controllers: the center of the tube. At each place, there is always one

distance from three sensors that will be shortest. When one distance becomes too small beyond

the limit, the controller will command EDORA II to move to the opposite direction in order to

avoid touching of the wall of the tube.

Figure 5.16 shows different bending angles of EDORA II at the two special positions

when EDORA II crosses a tube of 100°. Figure 5.16a shows the position of EDORA II during

the start stage of the crossing. It can be seen that EDORA II bend by very few degrees in the

tube. Then when EDORA II reaches the position with the big bend, EDORA II bends itself in

accordance with the bend of the tube so that it can cross this bend, shown in figure 5.16b. From

this experiment, the assumption proved to be correct that the EDORA II crosses the big bend

through accumulating small bending movements along the path of the tube.

(a) (b)

Figure 5.16 Evolution of bending angle of EDORA II during the cross of a tube with 100°

The measurements of three optical fiber sensors d1, d2 and d3 allow us to see the

evolution of the position of the top-end of EDORA II with respect to the wall of the tube

represented in figure 5.17. Three distances varied with the position in the tube, but these

distances are never less than 0.8 mm. The reaction of EDORA II under the influence of the

controllers thus fulfilled our expectations.



0 5 10 15 20 25 30 35 40 0

1

2

3

4

5

6

7

8

9

Length of the tube (cm)

Mea

sure

men

ts o

f thr

ee s

enso

rs (m

m)

Evolution of measurements of three sensors

Sensor 1Sensor 2Sensor 3

Figure 5.17 Evolution of the measurements of three sensors

For a better representation and visualization, the position limit of the top-end of EDORA

II in the tube along the progression of 40 cm is drawn in XOY plan, shown in figure 5.18.

30

210

60

240

90

270

120

300

150

330

180 0X

Y

8mm

8 m

m

The wall the tube (Inner diameter 26mm)

Envelope of the position limit of EDAR II in the tube

Top-end of EDORA II in the middle of thu tube (diameter of 17mm)

Figure 5.18 Extreme position of top-end of EDORA II in the tube.



0 5 10 15 20 25 30 35 40 -25

-20

-15

-10

-5

0

5

10

15

20

25

Length of the tube (cm )

Dia

met

er o

f the

tube

(mm

)

Positon of EDORA II in the linear tube ((X,Z) plan)

The wall of the tube

8.5mm

8.5mm

Figure 5.19 Position of EDORA II on the (X, Z) plan

0 5 10 15 20 25 30 35 40 -25

-20

-15

-10

-5

0

5

10

15

20

25

Length of the tube (cm)

Dia

met

er o

f the

tube

(mm

)

Positon of EDORA II in the linear tube ((Y,Z) plan)

The wall of the tube

8.5mm

8.5mm

Figure 5.20 Position of EDORA II on the (Y, Z) plan

We can also represent the evolution of the position of the contours of the top end of

EDORA II along the entire length of the tube. Figure 5.19 and 5.20 demonstrate the projection

of these positions on the (X, Z) plan and (Y,Z) plan which are all bounded with the tube.

All of these figures demonstrate that three controllers for three chamber systems of

EDORA II (diameter of 26 mm) make its top-end keep a constant distance of 0.8mm from the

wall. Thus, experimental results have proved to meet the requirements in order to control the



position with respect to the wall of the tube and also proved the capability of the EDORA II to

cross a tube with a big bend of 100° without touching the wall.

5.6 Conclusion

In this chapter, we have shown that the feasibility of our design of EDORA II fulfils our

expectations. Firstly, the optical fiber sensors are chosen for measuring the distance between

EDORA II and the test tube. The integration of optical fiber sensors into EDORA II allows us to

test the performances of this micro-robot when it’s guided through a colon-like tube

automatically. Then, its physical characteristics were calibrated and the static model was built

for feedback control. After that, the dynamic performances of closed-loop system of EDORA II

are analyzed by applying a step position input. Experimental results show that there are many

steady-state errors and a small stability margin. In order to improve the dynamic performance, a

lag controller that considers the manipulation disturbance is designed. The validation

experiments are carried out on a simulation platform which can move in X and Y directions.

This platform is designed to emulate the insertion movement of the colonoscope in the colon.

Two potentiometers are installed to read the distances along the axe X and Y. Results from one

chamber system moving only in one direction and three chamber systems moving in a plane

together show that this controller has good disturbance rejection ability. By using the same

controllers, a test experiment was done in a tube with a bend of 100°. A simple path planing

algorithm is used to generate the desired position for three controllers: the center of the tube. At

each place, there is always one distance from three sensors that will be smallest. When one

distance becomes too small beyond the limit, the controller will command the EDORA II to

move in the opposite direction in order to avoid touching the wall of the tube. So every time,

there is only one controller that will react according to the priority. Experimental results show

that the EDORA II can easily cross a bend of 100° without touching the wall of the tube. At the

same time, it also verified the assumption that the EDORA II accumulates a great deformation

in accordance with the great bend by small step by step displacement with its progression in the

tube. More precisely, it justified the validity of the EDORA II design and also the feasibility to

improve the performances of the traditional colonoscopy in view of the purpose of this

dissertation.

chapter 5 experimentation and test resultsdocinsa.insa-lyon.fr/these/2005/chen/10_chapter_5.pdf ·...

Documents