Adaptive Control of Position Compensation for Cable-Conduit

Mechanisms Used in Flexible Surgical Robots

T. N. Do

, T. Tjahjowidodo

, M. W. S. Lau

and S. J. Phee

School of Mechanical and Aerospace Engineering, Nanyang Technological University, Robotic Research Centre, 50

Nanyang Avenue, Singapore, 639798, Singapore

Newcastle University International Singapore (NUIS),

180 Ang Mo Kio Avenue 8, Block P, Room 220, Singapore 569830, Singapore

Keywords:

Surgical Robot, Cable-Conduit, Nonlinear Control, Adaptive Laws, Flexible Endoscope.

Abstract:

Natural Oriﬁce Transluminal Endoscopic Surgery (NOTES) is a method that allows for performing complex

operations via natural oriﬁces without skin incisions. Its main tool is a ﬂexible endoscope. Cable-Conduit

Mechanisms (CCMs) are often used in NOTES because of its simplicity, safety in design, and easy trans-

mission. Backlash hysteresis nonlinearities between the cable and the conduit pose difﬁculties in the motion

control of the NOTES system. It is challenging to achieve the precise position of robotic arms when the slave

manipulator inside the humans body. This paper presents new approaches to model and control for pairs of

CCMs. It is known that the change of cable-conduit conﬁguration will affect the backlash hysteresis non-

linearities. To deal with such change, a new nonlinear and adaptive control scheme will be introduced. The

backlash hysteresis parameters are online estimated under the assumption of availability of output feedback

and unknown bound of nonlinear parameters. To validate the proposed approach, a prototype of single-DOF-

Master-Slave system, which consists of a master console, a telesurgical workstation, and a slave manipulator,

is also presented. The proposed compensation scheme is experimentally validated using the designed sys-

tem. The results show that the proposed control scheme efﬁciently improves the tracking performances of the

system regardless of the change of endoscope conﬁguration.

1 INTRODUCTION

Flexible endoscope is used in minimally invasive

surgery (MIS) to inspect and treat gastrointestinal

(GI) tract disorders without making any abdominal in-

cisions in the patients body (Zhang et al., 2014); (Ott

et al., 2011); (Clark et al., 2012). One of the promis-

ing surgical procedures using ﬂexible endoscopes is

the natural oriﬁce transluminal endoscopic surgery

(NOTES). The ﬂexible endoscope could reach poten-

tial surgical site via natural oriﬁces or small incisions

and perform ﬂexible tasks with the attached robotic

arms. A pair of Cable-Conduit Mechanisms (CCMs)

or tendon-sheath mechanisms is often used to actuate

the robotic joints inside the human body by control-

ling each of the degrees of freedom (DOFs) of the

robotic arms. The CCM is preferred over other trans-

mission systems because it can operate in restricted

work spaces and in long, narrow, and tortuous paths.

Compared with other mechanisms like cable-pulley or

hyper-redundant mechanism, CCM offers high pay-

load and greater ﬂexibility. However, the main draw-

back in the CCM is the presence of nonlinear fric-

tion and backlash hysteresis. Control of precise mo-

tion of the robotic arms is prominently a challenging

issue in the use of such mechanism. Recently, vari-

ous models for the CCM have been proposed and dis-

cussed to enhance performances of the CCM. Many

researchers (Kaneko et al., 1992); (Palli et al., 2012);

(Sun et al., 2014); (Chiang et al., 2009); (Phee et al.,

2010) used lumped mass model elements to charac-

terize the tendon-sheath transmission. In other ap-

proaches, some authors (Agrawal et al., 2010b) pro-

posed a set of partial differential equations to model

the tendon-sheath nonlinearity using a number of ten-

don elements. However, limitations still exist. Firstly,

if more elements of the CCM are taken into consid-

eration to improve the accuracy, the computation be-

comes more complex. Secondly, a constant preten-

tion for all tendon elements is assumed. Thirdly, the

models need the information of sheath conﬁguration

along the endoscope. Lastly, discontinuous phenom-

ena still exist in the model approaches due to the use

of Coulomb friction model. Although Do and his col-

110

Do T., Tjahjowidodo T., Lau M. and Phee S..

Adaptive Control of Position Compensation for Cable-Conduit Mechanisms Used in Flexible Surgical Robots.

DOI: 10.5220/0005114701100117

In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2014), pages 110-117

ISBN: 978-989-758-039-0

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

leagues (Do et al., 2013a), (Do et al., 2013b), (Do

et al., 2014b), and (Do et al., 2014a) introduced novel

dynamic friction model to overcome the discontinu-

ity for estimated force feedback, no motion control

schemes were introduced to compensate for the posi-

tion errors.

It has been known that the backlash hysteresis pro-

ﬁle varies with the endoscope conﬁguration (Bardou

et al., 2012),(Kesner and Howe, 2011), (Kesner and

Howe, 2014). To achieve accurate tracking control,

two approaches are usually considered. The ﬁrst one

is that feedback of the robotic joints is available and

the closed-loop control is used. Online estimation of

backlash hysteresis parameters with adaptive control

laws is applied regardless of the changes of conﬁgu-

ration. In this case, electromagnetic tracking system

or image processing methods can be considered as a

potential tool to provide the output feedback (Reilink

et al., 2013). In the absence of the position feedback

during the compensation, feedforward control scheme

should be used. To improve the tracking perfor-

mances using ofﬂine learning, a backlash hysteresis

model and compensation control scheme with higher

accuracy and degree of smoothness, and ease of im-

plementation, are desired. For the design of back-

lash compensators, some researchers (Su et al., 2000);

(Hu et al., 2013) used a very complex nonlinear and

adaptive control algorithm to deal with the nonlinear-

ities under the assumption of available output feed-

back. They indicated that the backlash model given

by authors in (Tao and Kokotovic, 1995) is not suit-

able for the system control as the backlash function is

discontinuous. Agrawal and his colleagues (Agrawal

et al., 2010a) used a smooth inverse of backlash hys-

teresis model to compensate for the error. However, a

smooth inverse model, a switching law for the veloc-

ity, and output feedback were needed. Do and his col-

leagues (Do et al., 2014c) used a direct inverse model-

based feedforward to compensate for the position er-

ror in a single CCM. The compensator uses the direct

inverse structure that does not require complex inver-

sion of backlash hysteresis model and allows for easy

implementations (Rakotondrabe, 2011); (Do et al.,

2014c), (Hassani et al., 2014); (Minh et al., 2010), and

(Vo-Minh et al., 2011). However, the change of cable-

conduit mechanism has not been considered yet. To

deal with this challenge, a direct control algorithm

is developed regardless of the construction of inverse

model (Cai et al., 2013); (Zhang et al., 2014). In this

paper, new adaptive control laws are presented with-

out using any inverse model for the compensation.

The control scheme in this paper allow for captur-

ing the backlash hysteresis nonlinearities and efﬁcacy

of enhancing tracking performances regardless of the

curvature and sheath angles. Compare to the other

approaches (Agrawal et al., 2010a); (Bardou et al.,

2012),(Kesner and Howe, 2011), (Kesner and Howe,

2014); (Do et al., 2014c), where the backlash hystere-

sis or the bound of parameters must be known in ad-

vance, in our schemes, their bounds are unknown and

online estimated during the compensation. To vali-

date the proposed approach, a dedicated single degree

of freedom of a Master-Slave system is introduced.

The system consists of a master console, actuator

housing, and a slave manipulator. This type of system

has been presented in NOTES systems like MASTER

(Phee et al., 2010), (Abbott et al., 2007). Using the

designed Master-Slave system, the proposed schemes

are experimentally carried out to validate real surgical

tasks such as gripping a determined object. The rests

of this paper are organized as follow: In section 2,

an overview of NOTES system and the transmission

property of a pair of TSM are introduced. The de-

sign of the Master-Slave system for validation, which

contains the master console, motor housing and slave

manipulator, is introduced in this section. In addi-

tion, the development of nonlinear and adaptive con-

trol laws will be given. Experimental demonstration

is presented in section 3. Finally, the conclusion is

drawn in section 4.

2 MATERIALS AND METHODS

In order to evaluate the proposed control scheme, a

human-subject platform is introduced. This section

also presents the cable-conduit transmission charac-

teristics and experimental instruments. Nonlinear and

adaptive control laws for enhancing the tracking per-

formance will be also given.

2.1 NOTES System and Cable-Conduit

Characteristics

Figure 1: Overview of a NOTES system.

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A typical Natural Oriﬁce Transluminal Endoscopic

Surgery (NOTES) system is illustrated in Fig. 1. Sur-

geons carry out the surgical tasks using a master con-

sole to control the slave manipulator (includes robotic

arms) inside the patients body. The system consists of

a master console, a slave manipulator, and a telesur-

gical workstation (motor housing). One of the main

tools of NOTES is a long and ﬂexible endoscope,

i.e. a ﬂexible shaft with an articulated bending tip

and tool channels to house the robotic arms as well

as a camera (provide visual feedback to the surgeon).

The robotic arms which possess multiple degrees of

freedom (DOFs) are ﬁxed and carried along with the

endoscope to perform demanding surgical procedures

such as suturing and cutting. Triangulation is carried

out at the distal end of the endoscope while actuation

is externally provided.

Figure 2: (Upper) Diagram for a pair of CCMs; (Lower)

Ways for connecting cables (tendons) to pulleys.

To control each of the DOFs for the robotic arms,

a pair of CCMs is often used. The pull-pull trans-

missions for the CCMs have been studied in (Kaneko

et al., 1992); (Agrawal et al., 2010b). The upper panel

of Fig. 2 shows the structure of a pair of the CCMs.

and x

out

denote the displacements at the proximal

end and at the distal end of the system, respectively.

The two cables and conduits are routed along a ﬂex-

ible tube as the endoscope. Suppose that the input

pulley initially rotates in the clockwise direction (pos-

itive velocity-see The upper panel of Fig. 2a). When

the input pulley reverses its motion, the output pulley

does not immediately rotate, which results in a cer-

tain delay. The tension decreases in the previously

tensed cable. The loss of tensions along the conduit,

which due to the gap and friction force between the

cables and the conduits, results in delay for imme-

diate transmission of motion from the input pulley

(proximal end) to the output pulley (distal end). Once

the friction between the cables and the conduit in the

outer loop of the pair of CCMs is overcome, then the

output pulley immediately rotates following the input

pulley. Similar transmission characteristics are de-

scribed for the reversal motion in counter-clockwise.

This behavior of the transmission characteristics of

the CCM is referred to as a backlash hysteresis pro-

ﬁle. Note that the dead-band is not considered in this

paper because the cables are always pre-tensed. From

aforementioned descriptions, cable-conduit transmis-

sion can be approximately modeled as the backlash

hysteresis where the nonlinear parameters of hystere-

sis proﬁle depend on the cable-conduit conﬁguration.

2.2 Experimental protocol

In this section, we introduce a dedicated experimental

setup of a single-DOF Master-Slave system. The sys-

tem consists of a master console, telesurgical work-

station (include actuator housing and dSPACE con-

troller), and a slave manipulator. For illustration, a

slave system with a single-DOF robotic arm is con-

sidered. The overview of NOTES system has been

illustrated in Fig. 1. The mechanism design of a

Figure 3: The master console and motor housing with di-

agrams and real photos:(Upper) Master console with two

DOFs; (Lower) Actuator housing with two motors.

master console with a single-DOF, denoted as Mas-

ter Gripper is presented in The upper panel of Fig.

3a. The master console, which enables the user to

control the robotic arm at the distal end, is an er-

gonomic human-machine interface. In the master

console, one encoder (Master Encoder) is mounted

to the Master Gripper to provide necessary signal

(position-reference trajectory y

) to the output pul-

ley with an attached gripper. The encoder is type

of SCA16 from SCANCON. Signal from the Mas-

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112

ter Encoder will be subsequently sent to the dSPCAE

controller where the data are processed and the cables

and conduits actuation are controlled. The users con-

trol the motions of a gripper mounted on the output

pulley via Master Gripper. The picture of the mas-

ter console is shown in right side of the upper panel

of Fig. 3. The telesurgical workstation (The lower

Figure 4: (Upper) Slave manipulator with two DOFs:

(Lower) Photo of experimental setup.

panel of Fig. 3) consists of an actuator housing and

dSPACE DS1103 controller. The controller consists

of the control board, which is programmed via MAT-

LAB Simulink from MathWorks. The signals from

the master console and the robotic arm at distal end

are also acquired to this system. The actuator hous-

ing includes a PITTMAN 8693 DC motors equipped

with high resolution encoder E30. A input pulley,

which actuates the slave joint (gripper with output

pulley) using the CCMs, is also conneted to the mo-

tor. The CCMs are from Asahi Intecc Co. where

the size of the cables is WR7x7D0.27mm with teﬂon

coated wire ropes and the conduits with a round-wire

coil and inner diameter of 0.36mm and outer diam-

eter of 0.8mm. The length of the two conduits is 2

metre. The two CCMs are routed to follow a ﬂexible

endoscope and are connected to pulleys. At the in-

put pulley, cables are ﬁxed on the pulley using crews

while at the output pulley, cables are ﬁxed on corre-

sponding holes using aluminium rings (see the lower

panel of Fig. 2). In order to record the tensions at

proximal end of the system, two load cells LW-1020-

50 from Interface Corporation are used. They are

mounted on frictionless sliders. The two cables and

two conduits, subsequently, are used to actuate one

of DOFs of the rotation joints. Noting that the ten-

sions at proximal end are used to guarantee the same

pretension when trials are repeated. Fig. 4 depicts

the slave manipulator structure. In the experimental

work, a gripper which is mounted on the tip of the en-

doscope is used as a robotic arm. The two cables are

routed along two conduits passing through a ﬂexible

endoscope. The ﬂexible endoscope, which is a type of

GIF-2T160 from Olympus, Japan, has two tool chan-

nels with a length of 135cm. At each side (proximal

end and distal end), the tendon is attached to corre-

sponding pulleys (see the lower panel of Fig. 2). To

measure the rotational displacement for the gripper

joint at proximal end, a high resolution encoder Type

SCA16 from SCANKON is utilized. The encoder is

connected to the gripper joint via a small cable. The

rotation motion of gripper is recorded by the dSPACE

controller DS1103 via MATLAB environment from

MathWorks.

2.3 Nonlinear and Adaptive Control

An adaptive control law is given in this section to

deal with the change of cable-conduit conﬁguration.

If we consider this change as an unexpected distur-

bance, the nonlinear backlash hysteresis model which

has been described in (Do et al., 2014c) can be rewrit-

ten by:

out

= cu

+ D (1)

where D denotes the change of the hysteresis curve

when the cable-conduit conﬁguration varies, u

represents for the control input, x

out

is the output

position.

Before going to the design of control law, some

assumptions are made: (i) the cables are kept at some

suitable pretension in order to avoid the cable slack,

(ii) Output position feedback is used during the com-

pensation, (iii) Uncertain parameter c is positive and

its bound is unknown. Let the positive value D

∗

be the

bound of which is assumed to be unknown. It will be

estimated using the designed adaptive law; α is a pos-

itive parameter. Deﬁne a coordinate transformation ω

and n for the system given by Eq. (1) and a tracking

error e

as follows:











n =

(y(τ) − y

(τ))dτ

(t) = y(t) − y

(t)

ω = e

(t) + α

(τ)dτ = ˙n + αn

(2)

The ﬁrst order derivative of the new variable can

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be expressed by:

ω = α(y − y

) + ˙e

= α(cu

+ D − y

) + ˙e

(3)

Denote the inverse of backlash hysteresis slope c

by χ = 1/c, then the estimate of χ and D

∗

will be

stated as

χ and

∗

, respectively. Deﬁne

∗

= D

∗

−

∗

as the error estimate bound of disturbance D

∗

. From

Eq. (2) and Eq. (3), the adaptive control law is de-

signed as follows:

= −

χ(kω + sgn(ω)

∗

− y

+ (1/α) ˙e

) (4)

χ = δ

(kω + sgn

∗

− y

+ (1/α) ˙e

)ω (5)

∗

= δ

|ω| (6)

where k, δ

,δ

are positive parameters that adjust

the controller to force the tracking errors tend to com-

pact sets.

With Eq. (3) to Eq. (6), the following theorem

holds:

Theorem 1. Consider the nonlinear system (Eq. 3)

with uncertainties and satisﬁes the assumptions (i) to

(iv). The following statements hold under the con-

troller given by Eq. (4) and the update laws given by

Eq. (5) and Eq. (6):

1. The closed loop system results in global stability.

2. The tracking errors e

and estimates

χ,

∗

are uni-

formly ultimately bounded (UUB).

Proof : We deﬁne the Lyapunov function V as fol-

lows:

V = 0.5ω

+ (0.5/µ)(

∗

)

+ (c/2δ)(

χ)

(7)

where

χ = χ −

χ is error estimate of χ; µ,δ

are positive parameters. The initial values of func-

tion V is V (0) = 0.5(ω(0))

+ (0.5/µ))(

∗

(0))

(c/2δ)(

χ(0))

with ω(0),

∗

(0),

χ(0) are initial val-

ues of ω,

∗

χ, respectively.

The derivative of the Lyapunov function given by

Eq. (7) can be obtained by:

V = ω

ω − (1/µ)

∗

− (c/δ)

χ = ω(α(cu

+ D

− y

) + ˙e

) − (1/µ)

∗

− (c/δ)

χ (8)

Note that the term u

can be expressed by:

= c

χ ¯u = c

χ ¯u + ¯u − cχ ¯u = ¯u − c

χ ¯u (9)

where ¯u = −kω − sgn(ω)

∗

+ y

− (1/α) ˙e

Replace Eq. (4) to Eq. (6) into Eq. (8), one can

obtain:

V = ω(α(cu

+ D − y

) + ˙e

) − (1/µ)

∗

− (c/δ)

χ = ω(α(−kω − sgn(ω)

∗

+ y

− (1/α) ˙e

− c

χ ¯u + D − y

) + ˙e

) − (1/µ)

∗

− (c/δ)

= −αkω

− α|ω|

∗

+ αDω − (1/µ)

∗

− (c/δ)

χ(αδ ¯uω +

χ) = −αkω

− (c/δ)

χ(αδ ¯uω +

χ)

+ (1/µ)

∗

(−

∗

+ αµ|ω|) ≤ −αkω

≤ 0 (10)

where δ

= αδ,δ

= αµ

With the inequality given by Eq. (10), one can see

that the Lyapunov function V is a decreasing function

and bounded from below by zero. From Eq. (10),

one can obtain

V ≤ 0 ⇐⇒ V ≤ V (0) where V (0) =

0.5(ω(0))

+ (0.5/µ)(

∗

(0))

+ (α/2ρ)(

χ(0))

≥ 0.

Hence, variables ω,

∗

χ are also bounded. From (7),

one can obtain 0.5ω

≤ V ≤ V (0) or |ω| ≤

2V (0).

Two cases for the solutions of n: Case(i) ω = ˙n +

nα ≤

2V (0) or n ≤ (n

− (1/α)

2V (0))e

−αt

(1/α)

2V (0). There exists t > T > 0 such that

n ≤ (1/α)

2V (0) since (n

− (1/α)

2V (0))e

−αt

→ 0 for any t > T . Case(ii) ω = ˙n + nα ≥ −

2V (0)

or n ≥ (n

+ (1/α)

2V (0))e

−αt

− (1/α)

2V (0).

There exists t > T > 0 such that n ≥ −(1/α)

2V (0)

since (n

+ (1/α)

2V (0))e

−αt

→ 0 for any t > T .

For both cases, we have:

|n| ≤ (1/α)

2V (0) (11)

With |ω| ≤

2V (0) and (11), one can obtain:

| ˙n| − α|n| ≤ |ω| = | ˙n + nα| ≤

2V (0)

or | ˙n| ≤ α(1/α)

2V (0) +

2V (0)

= 2

2V (0) (12)

Then, one can verify that the UUB tracking per-

formance for the ﬁlter ω and its components n, ˙n = e

are guaranteed. It is also demonstrated that the up-

date parameters are guaranteed to be UUB. The proof

is completed here.

Remark 1: It is recommended that relevant valid-

tions based on simulation should be carried out before

doing the practical experiments. Based on the simu-

lation results, optimal parameters can be obtained.

3 REAL-TIME EXPERIMENTAL

VALIDATIONS

For validation purpose, the motion of slave manipu-

lation is investigated by random motions prescribed

from the users movement through the master console.

Fig. 5 illustrates the experimental setup and control

schemes for validation test. In practical validation,

the grasper is required to grip an elastic object that is

controlled using the Master Gripper (see Figs. 3, 4,

and 5). A motion generated by the user via the mas-

ter console is applied to the actuator housing at the

proximal end (see Fig. 5). The Master Encoder and

Slave Encoder are used to record the input and output

motions at corresponding joints using the dSPACE

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114

Figure 5: Compensation control structure for the Master-

Slave system.

DS1103. The purpose is to control the output posi-

tion y to follow a desired reference input y

as close

as possible.

Figure 6: Compensation results: (Upper) Without com-

pensation; (Lower) With nonlinear control; (Left) Position

tracking; (Right) Tracking error.

Table 1: Quantitative measures for case of nonlinear and

adaptive control.

Position (rad)

Trials Mean squared error Standard deviation

1 0.000276 0.0166

2 0.000196 0.0140

3 0.000286 0.0169

4 0.000244 0.0156

5 0.000227 0.0159

In order to demonstrate the effectiveness of the

proposed nonlinear adaptive scheme, a set of control

parameters are established basing on relevant simula-

tions, i.e. k = 15,α = 5, δ

= 10, δ

= 10. The signum

function is approximated using sgn(ω) = ω/(|ω| +

0.01) in order to avoid chattering during the imple-

mentation of the controller. The initial values for esti-

mate variables are chosen to

χ(0) = 1 and

∗

(0) = 0.

The experimental validations are carried out ﬁve

times (ﬁve trials). For illustration purposes, one of the

ﬁve trials will be given. Fig. 6 depicts the compensa-

tion results using nonlinear adaptive control scheme

which is illustrated by the proposed structure in Fig.

5. In the case of no compensation control, the mea-

sured position output y always lags to the desired tra-

jectory y

. This phenomenon can be seen from the

upper left panel of Fig. 6. When the nonlinear con-

trol scheme is used (see Fig. 5), the measured out-

put y accurately follows the desired trajectory y

(see

the left panel of Fig. 6). The relative error under the

nonlinear control scheme is also depicted in the right

panel of Fig. 6. There is a signiﬁcant reduction from

0.2669 rad peak-to-peak error before compensation to

0.08743 rad peak-to-peak after compensation. Quan-

titative measures of the results in terms of mean error

and standard deviation for each of trials are shown in

Table 1.

Figure 7: Compensation results with disturbance: (Upper)

Random change of conﬁguration; (Lower) Results for non-

linear control; (Left) Position tracking; (Right) Tracking er-

ror.

It is known that the backlash hysteresis proﬁle will

change if the conﬁguration changes. Hence, the per-

formances of proposed control scheme based on the

change of endoscope conﬁguration during the exper-

iments are evaluated and discussed. The endoscope

conﬁguration, which is shown in the upper panel of

Fig. 7, is varied during the experiments. When the

nonlinear adaptive controller is applied (see the lower

panel of Fig. 7), the phase lag and tracking error are

almost around 0.09743 rad peak-to-peak. It can be

concluded that the proposed control can adapt to any

change of the endoscope conﬁguration.

AdaptiveControlofPositionCompensationforCable-ConduitMechanismsUsedinFlexibleSurgicalRobots

115

4 CONCLUSIONS

This paper introduces a new adaptive control scheme

to enhance the tracking performances for a ﬂexible

endoscopic system using cable-conduit mechanisms.

The proposed control laws are able to deal with non-

linearities in the presence of uncertainties and dis-

turbances. Unlike current approaches of the cable-

conduit control, our control scheme has efﬁciently

reduced the tracking error and robustness. Experi-

mental validations have been carried out using a real

master-slave system to evaluate the controller perfor-

mances. Comparisons between the proposed model

and the experimental data show a good agreement.

It has been demonstrated that the model approach

works well on a real surgical device (Master-Slave

system) in NOTES system to carry out the task of

gripping a real object. It has also been indicated

that the proposed scheme is able to track the de-

sired reference signal regardless of the conﬁguration

of the endoscope. In addition, no knowledge of exact

backlash hysteresis parameters is required. The pro-

posed control scheme has opened potential beneﬁts to

other ﬂexible endoscopic system for enhancing track-

ing performances of precise motion. Future activities

will be conducted the validations for higher degrees

of freedom of ﬂexible endoscopic systems. In addi-

tion, in-vivo on live animal and human will be carried

out for further validations.

REFERENCES

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