Enhanced Performances for Cable-Driven FlexibleRobotic Systems with Asymmetric Backlash Profile

Thanh Nho Do∗, Tegoeh Tjahjowidodo∗, Michael Wai Shing Lau†, and Soo Jay Phee∗∗School of Mechanical & Aerospace Engineering Nanyang Technological University, Singapore.

Emails: thanh4@e.ntu.edu.sg; ttegoeh@ntu.edu.sg; msjphee@ntu.edu.sg†School of Mechanical and System Engineering, Newcastle University, United Kingdom

Email: michael.lau@ncl.ac.uk

Abstract—Cable-conduit mechanism (CCM) or tendon-sheathmechanism (TSM) is widely used in many flexible roboticsystems such as prosthetic hand robots, rehabilitation robots,and surgical robots because it offers efficient transmission offorces/torques from the external actuator to the end effectorwith light weight and high flexibility. However, the accurateposition control is challenging in such mechanism due tofriction and backlash-like hysteresis between the cable and theconduit. In this paper, a new control approach is proposedto enhance the trajectory tracking performances of the CCMusing in flexible robotic systems. Unlike current approachesfor the CCM in the literature, the proposed scheme considersthe position transmission of the CCM as an approximationof backlash-like hysteresis nonlinearities without requiring theexact values of model parameters and their bounds. Onlineestimation of unknown system parameters are also established.In addition, the designed controller can adapt to any changes ofthe cable-conduit configuration and it is stable. The results of theproposed control techniques have been experimentally validatedon a real flexible robotic system using a flexible endoscope.Experimental validations show substantial improvements on theperformances of position tracking for the use of CCM regardlessof the arbitrary changes of the cable-conduit configurations.

Keywords—Flexible robotic systems; compensation control;cable-conduit mechanism; backlash.

I. INTRODUCTION

Flexible mechanisms like parallel linkage or cable-drivenactuation have been widely used in many applications likesurgical robots, robot hands, rehabilitation robots to executecomplex tasks [1], [2], [3], [4]. These mechanisms are veryuseful for driving and grasping determined objects whereactuators are placed away from the operation sites. In addition,they are able to reduce the bulkiness of actuators that are tooheavy in current robotic components. Although parallel linkagemechanism have been widely used to develop underactuatedplannar mechanism, they are limitted by rigid links that aretoo cumbersomes to work in complex environments and narrowpaths. In contrast, cable-conduit mechanism (CCM) or tendon-sheath mechanism (TSM) is a potential transmission modewhich allows for the separation between the actuator siteand the joint site. Compared to parallel linkage mechanisms,CCM offers light weight and inertia, simplified modelling ofdynamics, cost efficiency, ease of transportation and reconfig-uration, and better safety [1], [5]. Hence many applicationshave also utilized the CCM as the main mode of transmissionsuch as wearable robot [6], robot hands [7], surgical robot

[8], and exoskeleton robots [2]. Although the CCM offersmany advantages, the interactions between the cable and theconduit generally introduce large friction, deadzone, hysteresis,and backlash that degrade the accurate control of positionand system performances [9], [10], [11], [12], [13]. Due tothese limitations, the control of cable-conduit systems couldbe challenging and thereby affect the use of CCM in thedevelopments of flexible robotic systems.

The motion in the CCM is transmitted from the externalactuator to the end effector joint through a cable routedalong a conduit. It was known that the friction, backlash, andhysteresis vary with the change of cable-conduit configuration.To enhance the efficient use of CCM, mathematical modelsfor the cable-conduit transmission are desired for the analysisof nonlinear behaviors and compensation control needs [12],[14]. The characteristics of cable-conduit transmission havebeen previously discussed by various researchers and groups.There are two main discussions for the transmission problems:(i) Tension transmission analyses, and (ii) Motion analyses.The former focuses on the tension transmission of the cableacross the conduit, in which the friction between the cableand the conduit is modelled by static friction like Coulomb ordynamic friction like LuGre models. The latter concentrates onthe motion analyses and control, in which an approximationof backlash-like hysteresis or smooth inverse of backlash areused to compensate the position tracking error. For most cases,many researchers focus on the motion and tension analysesfor the CCM using lumped mass model or discontinuousbacklash profile under the assumption of known cable-conduitconfiguration and equal distribution of cable elements alongthe conduit [15], [16], [17], [18], [19]. Three major limitationsare found in these approaches. Firstly, the use of lumped massmodel parameters becomes more complex if more segmentsare used. Secondly, the assumption of uniform distributionfor pretension is impractical. Lastly, the mathematical modelsrequire the measurements of cable-conduit configurations. Inpractice, the pretension for each of segments is unequal andit is hard to obtain the configuration information. AlthoughDo and his colleagues presented novel friction models toaddress the tension transmission for the CCM, no motioncontrol schemes were introduced to compensate the trackingerror [20], [21]. Based on the system dynamics, the motioncontrol of cable-conduit transmission can be approximatelymodelled as backlash-like hysteresis profile [22]. Kaneko etal. [12] described the tension and motion transmission of theCCM as a backlash-like hysteresis profile with input dependentstability. Agrawal et al. [23] used a smooth inverse of backlash

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model to compensate the tracking error of the CCM. Forthe applications of robotic catheter and flexible endoscope,Bardou et al. [24], Kesner et al. [25], and Reilink et al.[26] used an inverse backlash model to compensate the phaselags between the output position and the desired trajectory.However, a switching function for the velocity was requiredand the slope of the backlash profile was ignored. AlthoughDo et al. [22] used a direct inverse model-based feedforwardcompensation to overcome the above limitations, the designedcontroller was not able to deal with the change of the cable-conduit configuration. In addition, the values of backlash-likehysteresis parameters must be known in advance.

Various linear and nonlinear control schemes have beenreported in the literature. Recent works on the mechanicalsystems such as magnetic devices or piezoelectric actuatorshave focused on the perfect cancellation of backlash-likehysteresis using inverse models and nonlinear adaptive al-gorithms [27], [28], [29], [30], [31], [32], [33]. However,little experimental validations have been carried out. Unlikethose aforementioned approaches for the CCM, new nonlinearand adaptive control scheme will be discussed in this paper.The motion transmission of the CCM is characterized as anapproximation of backlash-like hysteresis profile (see [22]).The proposed controller can adapt to any changes of the cable-conduit configuration. In addition, exact values of backlash-like hysteresis parameters are not required. To validate theeffectiveness of the proposed control schemes, a dedicatedexperimental platform of a single-degree of freedom (DOF)flexible robotic system will be introduced. Using the designedsystem, the proposed controller is experimentally validatedusing real-time tasks such as gripping a determined elasticobject. There are significant enhancements on the positiontracking error between the measured output position and thedesired trajectory. The rests of this paper are presented asfollow: In section II, a review of the asymmetric backlash-likehysteresis model on the CCM will be introduced. Section IIIaddresses the new control approach for the CCM. The designof the flexible robotic system and experimental validations willbe given in section IV. Finally, discussion and conclusion arepresented in section V.

II. ASYMMETRIC BACKLASH-LIKE HYSTERESIS PROFILEIN FLEXIBLE CABLE-CONDUIT MECHANISM

The tension transmission characteristics of the CCM wereinvestigated by Do et al. [13], [34]. However, in this paper, weare interested in the accurate position control for the CCM. Inour previous work [22], [35], the backlash profile for the CCMis asymmetric and it was approximated using an asymmetricform from the modified asymmetric Bouc-Wen model. Themodel was named as a backlash-like hysteresis profile and itcan be rewritten by:

ζ = Ax− ϑ|x|ζ + δ|x| (1)Φ = αx(x)x+ ζ (2)

where x and x are the input position and velocity, respectively;αx(x) = (α1e

2x+α2)/(e2x+ 1) is a continuous function thatallows for a smooth transition from the loading to unloadingphases and vice versa (see [22]); α1 > 0, α2 > 0, A, ϑ, δ areparameters that control the shape of hysteresis loops in theloading and unloading phases; ζ is the internal state variable;

and Φ is the output position; the dot at the top of variablesrepresents for the first derivative with respect to time.

The model given by (1) and (2) represents for the asym-metric backlash-like hysteresis with asymmetric slope α1, α2

in the loading and unloading phases, respectively. In addition,it is able to provide smooth transition from the loading tounloading phases and vice versa (see [22] for more details).

To use the asymmetric backlash-like hysteresis modelgiven by (1) and (2), some assumptions have been made: (i)the values of backlash hysteresis parameters such as α1, α2,A, ϑ, δ must be known in advance; (ii) the cable-conduitconfiguration must be unchanged; and (iii) the cable is alwaysmaintained at a suitable pretension in order to avoid the cableslacking. Although the direct inverse model-based feedforwardcontroller efficiently reduced the position tracking error for theCCM, the three above assumptions limit the flexibility of thecontrol approaches. In practice, these parameters are usuallyunknown because there are hardly instances for measuringand calculating the exact values of the parameters during theoperation process. In addition, the model parameters alwaysvary with respect to the change of cable-conduit configuration.

III. COMPENSATION CONTROL DESIGN

For the proposed control approach in this paper, the exactvalues of model parameters and their bounds are not requiredin advance. The cable-conduit configuration can be freelychanged during the operation. Online learning of unknownparameters will be introduced to relax these above limitations.

If we consider the change of cable-conduit configurationas an unexpected disturbance d, the asymmetric nonlinearitygiven by (2) can be rewritten by:

y = αx(u)u+ ζ + d = αx(u)u+ ∆n (3)

where ∆n = ζ+d represents the variation of the internal statevariable ζ when the configuration changes; αx(u) = (α1e

2u+α2)/(e2u + 1) denotes the asymmetric slope of the backlash-like hysteresis profile; u = x is the control input; y = Φ is theoutput position.

Some assumptions are made for the controller design: (i)The cable is kept at a suitable pretension to avoid the slack;(ii) Exact values of model parameters and their bounds arenot required.

Let the positive value ∆∗n be the bound of ∆n (|∆n| ≤ ∆∗

n)and α is a positive number. Define a new coordinate transfor-mation ω and n for the system (3) and a position tracking errorer = (y − yr) by:

n =

∫ t

0

(y(τ)− yr(τ)) dτ (4)

ω = er(t) + α

∫ t

0

er(τ) dτ (5)

The first order derivative of the new variable ω given by(5) can be expressed by:

ω = αer + er = α(αx(u)u+ ∆n − yr) + er

= α((α1e

2u + α2)/(e2u + 1)u+ ∆n − yr)

+ er (6)

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In order to simplify the controller design u in (6), a newform of u will be established with respect to new virtualcontrollers ui, (i = 1, 2). Denote the estimate of ∆∗

n as ∆∗n

and define the control input by ui = χiui where χ1 = 1/α1

and χ2 = 1/α2 be the inverse of parameters α1 and α2,respectively. χi(i = 1, 2) are estimates of χi. One canreformulate the controller u as follow:

u =2∑i=1

ui (7)

where ui(i = 1, 2) are defined as u1 = ue2u/(e2u + 1) andu2 = u/(e2u + 1). From (7), one can obtain:

(α1e2u + α2)u/(e2u + 1) = α1u1 + α2u2 (8)

Let χ1 = χ1 − χ1, χ2 = χ2 − χ2 be error estimatesof χ1, χ2, respectively. Then the term αiui(i = 1, 2) can beexpressed by:

αiui = αiχiui = ui − αiχiui (9)

Define the error tracking between ∆∗n and its estimate ∆∗

n

by ∆∗n = ∆∗

n − ∆∗n. From system (6) and its control input u

as well as its coordinate transformation (4) to (9), parameteradaptive laws and control input are designed as follow:

u =2∑i=1

χiui (10)

u1 = −k1ω − tanh(ω/ε)∆∗n + yr − (1/α)er (11)

u2 = −k2ω (12)˙χ1 = −δ1u1ω − σ1χ1 (13)˙χ2 = −δ2u2ω − σ2χ2 (14)˙∆∗n = δ3ωtanh(ω/ε)− σ3∆∗

n (15)

where σi(i = 1, 2, 3) are small positive numbers that helpto avoid the estimates χi(i = 1, 2) and ∆∗

n drift to large values;ε is a small positive value that helps to accurately control thesmoothness of the tanh function. δi(i = 1, 2, 3) are positiveparameters for the controller and update laws.

With the control laws from (10) to (15), ω in (6) can berewritten by:

ω = α(−2∑i=1

(kiω + αiχiui)− tanh(ω/ε)∆∗n + ∆n) (16)

Theorem 1: Consider the nonlinear system (6) and thedesigned adaptive laws given by (10) to (15), the followingstatements hold:

1) The tracking error er and updated parametersχ1, χ2, ∆

∗n in the closed-loop system are uniformly

ultimately bounded (UUB).2) In the presence of unknown model parameters and

their bounds, the position tracking error er = (y −yr) converges to a desired compact region Ω2 =|er|

∣∣|er| ≤ 2√

2Ψ/% and the controller u issmooth.

where Ψ = (0.2785α∆∗nε+

2∑i=1

(αiσi/2ρi)χ2i +σ3(∆∗

n)2/2µ);

% = min2α2∑i=1

ki, σ1, σ2, σ3; α, ε, αi, ρi(i = 1, 2), σj(j =

1, 2, 3), and µ are positive constants.

Proof: Define a Lyapunov candidate function V as fol-lows:

V = 0.5ω2 + (0.5/µ)(∆∗n)2 +

2∑i=1

(αi/2ρi)(χi)2 (17)

The derivative of (17) along (16) with controller and updatedlaws given by (10) to (15) can be expressed by:

V = ωω − (1/µ)∆∗n

˙∆∗n −

2∑i=1

(αi/ρi)χi ˙χi = ω(α((α1e2u

+ α2)/(e2u + 1)u+ ∆n − yr) + er)− (1/µ)∆∗n(−σ3∆∗

n

+ δ3ωtanh(ω/ε))−2∑i=1

(αi/ρi)χi(−δiuiω − σiχi)

= −α2∑i=1

(kiω2 − (αiσi/αρi)χiχi) + (σ3/µ)∆∗

n∆∗n

+ ∆nαω − αω tanh(ω/ε)∆∗n ≤ −α∆∗

nω tanh(ω/ε)

+ α∆∗n|ω|+ (σ3/µ)∆∗

n∆∗n − α

2∑i=1

(kiω2 − (αiσi/αρi)χiχi)

≤ −α2∑i=1

kiω2 + (σ3/µ)∆∗

n∆∗n +

2∑i=1

(αiσi/ρi)χiχi

+ 0.2785α∆∗nε (18)

where u1 = −k1ω − tanh(ω/ε)∆∗n + yr − (1/α)er and u2 =

−k2ω are taken from (11) and (12); δ1 = αρ1; δ2 = αρ2;δ3 = αµ.

As introduced in [36], the tanh(ω/ε) function obeys thefollowing property: |ω| − ω tanh(ω/ε) ≤ 0.2785ε. Applythe Young’s inequality for two numbers a and b, i.e. ab ≤0.5(a2 + b2), the second term and the third term in (18) canbe reformulated as:

(σ3/µ)∆∗n∆∗

n = (σ3/µ)∆∗n∆∗

n − (σ3/µ)(∆∗n)2

≤ (σ3/2µ)(∆∗n)2 − (σ3/2µ)(∆∗

n)2 (19)2∑i=1

(αiσi/ρi)χiχi =2∑i=1

((αiσi/2ρi)(χi)

2 + (αiσi/ρi)(χi)2)

≤2∑i=1

((αiσi/2ρi)(χi)

2 − (αiσi/2ρi)(χi)2)

(20)

Put (19) and (20) to (18), V becomes:

V ≤ −2α2∑i=1

0.5kiω2 − (σ3/2µ)(∆∗

n)2 −2∑i=1

(αiσi/2ρi)(χi)2

+ (0.2785α∆∗nε+

2∑i=1

(αiσi/2ρi)χ2i + σ3(∆∗

n)2/2µ)

≤ −%V + Ψ (21)

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Solving (21) and from (17), one can obtain:

0 ≤ 0.5ω2 ≤ V ≤ (V (0)−Ψ/%)e−%t + Ψ/% (22)

Eq. (22) can be obtained from (17), V = 0.5ω2 +(0.5/µ)(∆∗

n)2+∑2i=1(αi/2ρi)(χi)

2 ≥ 0.5ω2 ≥ 0. From (22),the variable ω can be expressed by:

|ω| ≤√

2(V (0)−Ψ/%)e−%t + 2Ψ/% (23)

It can be seen that there exists a time T1 such that ∀t >T1, |ω ≤

√2Ψ/% since 2(V (0) − Ψ/%)e−%t → 0 as

t > T1. From the inequality |ω| = n + αn ≤√

2Ψ/%,two cases for n exist: Case(i) ω = n + nα ≤

√2Ψ/%

or n ≤ (n0 − (1/α)√

2Ψ/%)e−αt + (1/α)√

2Ψ/%. Thereexists t > T2 > T1 > 0 such that n ≤ (1/α)

√2Ψ/%

since (n0 − (1/α)√

2Ψ/%)e−αt → 0 for any t > T2 >T1 > 0. Case(ii) ω = n + nα ≥ −

√2Ψ/% or

n ≥ (n0 + (1/α)√

2Ψ/%)e−αt − (1/α)√

2Ψ/%. There existst > T2 > T1 > 0 such that n ≥ −(1/α)

√2Ψ/% since

(n0 + (1/α)√

2Ψ/%)e−αt → 0 for any t > T2 > T1 > 0.For both cases, we have:

|n| ≤ (1/α)√

2Ψ/% (24)

With |ω| = n+ αn ≤√

2Ψ/% and (24), one can obtain:

|n| − α|n| ≤ |ω| = |n+ nα| ≤√

2Ψ/%

or |n| ≤ α(1/α)√

2Ψ/%+√

2Ψ/% = 2√

2Ψ/% (25)

Then, one can prove that the UUB tracking performance for|er| = |n| is guaranteed. From (22), one has 0 < V ≤Ψ/%,∀t > T1. From (17), it is easy to observe that allsignals ∆∗

n, χi and ∆∗n, χi are proved to be UUB. The proof

is completed here.

IV. REAL-TIME EXPERIMENTAL VALIDATIONS

A. Experimental Setup

Fig. 1. Different control schemes: (a) Without using any compensationcontroller; (b) Using feedforward compensation controller; (c) Using nonlinearcontroller

The experimental setup is shown in Fig. 2. It consists of asingle DOF of telerobotic system where the the user controlsa motion device and the slave manipulator with a single DOFgrasper is actuated by a DC-motor (Faulhaber 2642W024CR)via a CCM. The motor is controlled by a simple PI controller(P=2.8, I=2). The CCM which is provided by Asahi Intecc Co.consists of a Teflon coated wire cable with a specification ofWR7x7D0.27mm and a round wire coil conduit with an innerdiameter of 0.36mm and an outer diameter of 0.8mm. TheCCM has a length of 1.5m and is routed along a flexible en-doscope GIF-2T160 from Olympus, Japan. Necessary signalsfrom the user’s hand (desired trajectory yr) are recorded by the

(a)

(b)

Fig. 2. Experimental setup: (a) Diagram, (b) Photo

encoder SCA16 (E1) with resolution of 6000 pulses/revolutionfrom SCANCON while the position of the grasper y at the endeffector is measured by the encoder E2. At the motor side,the cable is fixed on a pulley P in which is connected to theDC-motor by a bolt screw while at the end effector side, thecable is connected to a spring via an output pulley P out (thegrasper) as shown in Fig. 2.

B. Validation Results

The nonlinear and adaptive control laws are given by (10)to (15) are used with the designed parameters k1 = 20, k2 =10, δ1 = 10, δ2 = 10, δ3 = 10, ε = 0.05, σ1 = σ2 =σ3 = 0.01, α = 5. The initial values for updated laws areχ1(0) = χ2(0) = ∆∗

n(0) = 0. These designed parameters areobtained from some simulations based trial-and-error methodusing MATLAB Simulink environment. The obtained param-eters are subsequently used in real-time experiments.

For easy comparison, a sinusoidal input signal of amplitute0.8 rad and frequency of 0.3 Hz is applied to the systemunder the change of cable-conduit configuration during theoperation and the grasper is contacted with the elastic object.Fig. 3 presents the experimental result for the CCM usingour previous compensation control scheme (see compensa-tion structure from Fig. 1b) [22]. There is a large error ofRMSE = 0.0755 rad ∼ 4.326o compared to the case of pro-posed adaptive control with RMSE = 0.0156 rad ∼ 0.894o

(see Fig. 4).

The effectiveness of the proposed nonlinear controller willbe also validated with random input signal from the control

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0 5 10 15 20 25 30−1

−0.5

0

0.5

1

Time (s)

Pos

ition

(ra

d)

0 5 10 15 20 25 30−0.5

−0.25

0

0.25

0.5

Time (s)

Err

or (

rad)

Desired trajectory Measured output

Fig. 3. Tracking result using sine signal under disturbance with compensationcontrol from [22] (see Fig. 1b): (Upper) Time history of desired trajectory andmeasured output; (Lower) Time history of corresponding error

0 5 10 15 20 25 30−1

0

1

Time (s)

Pos

ition

(ra

d)

0 5 10 15 20 25 30−0.5

−0.25

0

0.25

0.5

Time (s)

Err

or (

rad)

Desired trajectory Measured output

Fig. 4. Reference sine signal under disturbance with proposed nonlinearcompensation (see Fig. 1c): (Upper) Time history of desired trajectory andmeasured output; (Lower) Time history of corresponding error

motion device. For all cases, five trials will be carried out.For illustration purposes, one of the trials will be presentedonly as shown in Fig. 5. The upper panel of Fig. 5 showsthe time history of the desired trajectory and measured outputwithout using the designed control scheme. It can be seen thaty always lags yr with a high error values of root mean squareerror (RMSE = 0.1327 rad ∼ 7.6o) without using the com-pensation scheme (see scheme in Fig. 1a). The correspondingerror between y and yr can be seen from the lower panel ofthis figure. To reduce the tracking error under the change ofthe configuration, the proposed nonlinear control is appliedto the system. It can be seen from Fig. 6 that the proposedcontrol scheme is able to deal with any change in the endo-scope configuration. The tracking performances between thedesired trajectory yr and measured output y are good. Thereis a significant decrease of the tracking error when the newcontrol scheme is used. It seems that the change of endoscopeconfiguration does not affect the tracking results significantly.As shown in the Fig. 6, the RMSE = 0.0447 rad ∼ 2.56o.The quantitative measures of trials are illustrated in Table I.

V. CONCLUSION

This paper introduces a new adaptive control scheme toenhance the tracking performances for flexible robotic systemusing cable-conduit mechanisms. The proposed control lawsare able to deal with nonlinearities in the presence of time vary-ing configuration of the conduit. Unlike current approachesof the cable-conduit control, our control scheme has effi-ciently reduced the tracking error regardless of the change ofthe cable-conduit configuration. Experimental validations havebeen carried out using a real flexible robotic system to evaluate

0 10 20 30 400

0.5

1

Time (s)

Pos

ition

(ra

d)

0 10 20 30 40−0.5

−0.25

0

0.25

0.5

Time (s)

Err

or (

rad)

Desired trajectory Measured output

Fig. 5. Tracking performance of the system without using the proposed con-troller (see Fig. 1a):(Upper) Time history of desired trajectory and measuredoutput; (Lower) Time history of corresponding error

0 5 10 15 20 25 300

0.5

1

1.5

Time (s)

Pos

ition

(ra

d)

0 5 10 15 20 25 30−0.5

−0.25

0

0.25

0.5

Time (s)

Err

or (

rad)

Desired trajectory Measured output

Fig. 6. Tracking performance of the system using the proposed nonlinearcontroller (see Fig. 1c): (Upper) Time history of desired trajectory andmeasured output; (Lower) Time history of corresponding error

the controller performances. It has been demonstrated that themodel approach works well on a real flexible system to carryout the task of gripping a real object and/or in free motion. Inaddition, no exact values of backlash-like hysteresis parametersare required. The proposed control scheme provides potentialbenefits to any flexible robotic system for enhancing trackingperformances of precise motion. The approaches in this paperhave used traditional encoders to get the position feedbackfrom the distal end. In the case of no output position feedback,our previous approach [22] can help to reduce the trackingerror. However, they are not able to deal with the changeof conduit configuration. For the use in surgical robots, it isknown that some applications can utilize advanced techniquessuch as 3D ultrasound probe or image-based methods toachieve the position output feedback [24], [25], [26], [37].Hence, these non-conventional methods should be applied tofulfill the needs for the real applications. Future activities willbe conducted to validate the designed controllers for higherDOFs of flexible robotic systems.

REFERENCES

[1] R. Ozawa, H. Kobayashi, and K. Hashirii, “Analysis, classification, anddesign of tendon-driven mechanisms,” IEEE Transactions on Robotics,vol. 30, no. 2, pp. 396–410, April 2014.

[2] C. Jones, F. Wang, R. Morrison, N. Sarkar, and D. Kamper, “Designand development of the cable actuated finger exoskeleton for hand reha-bilitation following stroke,” IEEE/ASME Transactions on Mechatronics,vol. 19, no. 1, pp. 131–140, Feb 2014.

[3] L. U. Odhner, L. P. Jentoft, M. R. Claffee, N. Corson, Y. Tenzer, R. R.Ma, M. Buehler, R. Kohout, R. D. Howe, and A. M. Dollar, “A com-pliant, underactuated hand for robust manipulation,” The InternationalJournal of Robotics Research, vol. 33, no. 5, pp. 736–752, 2014.

978-1-4799-8757-3/15/$31.00 ©2015 IEEE

TABLE I. QUANTITATIVE MEASURES OF THE ERROR RMSE USINGTHE DESIGNED CONTROLLER WITH VARYING CONFIGURATION OF THE

ENDOSCOPE

Trials (Tracking results-RMSE)

1 0.045 rad ∼ 2.56o

2 0.0374 rad ∼ 2.144o

3 0.0316 rad ∼ 1.81o

4 0.0424 rad ∼ 2.43o

5 0.0458 rad ∼ 2.625o

[4] S. Kim, C. Laschi, and B. Trimmer, “Soft robotics: A bioinspiredevolution in robotics,” Trends in Biotechnology, vol. 31, no. 5, pp. 287–294, 2013.

[5] M. Controzzi, C. Cipriani, and M. C. Carrozza, “Design of artificialhands: A review,” in The Human Hand as an Inspiration for RobotHand Development. Springer, 2014, pp. 219–246.

[6] M. S. Cherry, S. Kota, and D. P. Ferris, “An elastic exoskeletonfor assisting human running,” in ASME 2009 International DesignEngineering Technical Conferences and Computers and Information inEngineering Conference. American Society of Mechanical Engineers,2009, pp. 727–738.

[7] G. Palli, C. Melchiorri, G. Vassura, U. Scarcia, L. Moriello, G. Berselli,A. Cavallo, G. De Maria, C. Natale, S. Pirozzi et al., “The dexmarthand: Mechatronic design and experimental evaluation of synergy-basedcontrol for human-like grasping,” The International Journal of RoboticsResearch, vol. 33, no. 5, pp. 799–824, 2014.

[8] S. B. Kesner and R. D. Howe, “Robotic catheter cardiac ablationcombining ultrasound guidance and force control,” The InternationalJournal of Robotics Research, vol. 33, no. 4, pp. 631–644, 2014.

[9] T. N. Do, T. Tjahjowidodo, M. W. S. Lau, and S. J. Phee,“Nonlinear friction modelling and compensation control of hys-teresis phenomena for a pair of tendon-sheath actuated surgi-cal robots,” Mechanical Systems and Signal Processing, 2015,http://dx.doi.org/10.1016/j.ymssp.2015.01.001.

[10] M. Kaneko, T. Yamashita, and K. Tanie, “Basic considerations ontransmission characteristics for tendon drive robots,” in ’Robots inUnstructured Environments’, 91 ICAR., Fifth International Conferenceon Advanced Robotics, vol. 1, Pisa, Italy, 1991, pp. 827–832.

[11] T. N. Do, T. Tjahjowidodo, M. W. S. Lau, and S. J. Phee, “Dynamicfriction model for tendon-sheath actuated surgical robots: modelling andstability analysis,” in ISRM 2013-Proceedings of the 3rd InternationalSymposium on Robotics and Mechatronics. Singapore, 2013, pp. 302–311.

[12] M. Kaneko, W. Paetsch, and H. Tolle, “Input-dependent stability ofjoint torque control of tendon-driven robot hands,” IEEE Transactionson Industrial Electronics, vol. 39, no. 2, pp. 96–104, 1992.

[13] T. N. Do, T. Tjahjowidodo, M. W. S. Lau, and S. J. Phee, “Aninvestigation of friction-based tendon sheath model appropriate forcontrol purposes,” Mechanical Systems and Signal Processing, vol. 42,no. 1-2, pp. 97–114, 2014.

[14] ——, “Adaptive control of position compensation for cable-conduitmechanisms used in flexible surgical robots,” in ICINCO 2014-Proceedings of the 11th International Conference on Informatics inControl, Automation and Robotics. Vienna, Austria, 2014, pp. 110–117.

[15] G. Palli and C. Melchiorri, “Model and control of tendon-sheath trans-mission systems,” in ICRA 2006. Proceedings 2006 IEEE InternationalConference on Robotics and Automation. Orlando, FL, 2006, pp. 988–993.

[16] G. Palli, G. Borghesan, and C. Melchiorri, “Modeling, identification,and control of tendon-based actuation systems,” IEEE Transactions onRobotics, vol. 28, no. 2, pp. 277–290, 2012.

[17] V. Agrawal, W. J. Peine, and B. Yao, “Modeling of transmissioncharacteristics across a cable-conduit system,” IEEE Transactions onRobotics, vol. 26, no. 5, pp. 914–924, 2010.

[18] Z. Sun, Z. Wang, and S. J. Phee, “Elongation modeling and compensa-tion for the flexible tendon–sheath system,” IEEE/ASME Transactionson Mechatronics, vol. 19, no. 4, pp. 1243–1250, 2014.

[19] L. Chen, X. Wang, and W. Xu, “Inverse transmission model and com-pensation control of a single-tendon sheath actuator,” IEEE Transactionson Industrial Electronics,, vol. 61, no. 3, pp. 1424–1433, 2014.

[20] T. N. Do, T. Tjahjowidodo, M. W. S. Lau, and S. J. Phee, “Dynamicfriction-based force feedback for tendon-sheath mechanism in notessystem,” International Journal of Computer and Electrical Engineering,vol. 6, no. 3, pp. 252–258, 2014.

[21] ——, “Nonlinear modeling and parameter identification of dynamicfriction model in tendon sheath for flexible endoscopic systems,” inICINCO 2013-Proceedings of the 10th International Conference onInformatics in Control, Automation and Robotics. Reykjavik, Iceland,2013, pp. 5–10.

[22] T. N. Do, T. Tjahjowidodo, M. W. S. Lau, T. Yamamoto, and S. J. Phee,“Hysteresis modeling and position control of tendon-sheath mechanismin flexible endoscopic systems,” Mechatronics, vol. 24, no. 1, pp. 12 –22, 2014.

[23] V. Agrawal, W. Peine, B. Yao, and S. Choi, “Control of cable actuateddevices using smooth backlash inverse,” in IEEE International Confer-ence on Robotics and Automation (ICRA). Anchorage, AK, 2010, pp.1074–1079.

[24] B. Bardou, F. Nageotte, P. Zanne, and M. De Mathelin, “Improvementsin the control of a flexible endoscopic system,” in IEEE InternationalConference on Robotics and Automation (ICRA). Saint Paul, MN, May2012, pp. 3725–3732.

[25] S. Kesner and R. Howe, “Position control of motion compensationcardiac catheters,” IEEE Transactions on Robotics, vol. 27, no. 6, pp.1045–1055, Dec 2011.

[26] R. Reilink, S. Stramigioli, and S. Misra, “Image-based hysteresis reduc-tion for the control of flexible endoscopic instruments,” Mechatronics,vol. 23, no. 6, pp. 652–658, 2013.

[27] C.-Y. Su, Y. Stepanenko, J. Svoboda, and T. Leung, “Robust adaptivecontrol of a class of nonlinear systems with unknown backlash-likehysteresis,” IEEE Transactions on Automatic Control, vol. 45, no. 12,pp. 2427–2432, 2000.

[28] X.-S. Wang, C.-Y. Su, and H. Hong, “Robust adaptive control of a classof nonlinear systems with unknown dead-zone,” Automatica, vol. 40,no. 3, pp. 407–413, 2004.

[29] C. Hu, B. Yao, and Q. Wang, “Performance-oriented adaptive robustcontrol of a class of nonlinear systems preceded by unknown deadzone with comparative experimental results,” IEEE/ASME Transactionson Mechatronics, vol. 18, no. 1, pp. 178–189, 2013.

[30] T. Nguyen, T. N. Do, M. W. S. Lau, and S. J. Phee, “Modelling,design, and control of a robotic running foot for footwear testing withflexible actuator,” in the 1th International Conference in Sports ScienceTechnology (ICSST). Singapore, 2014, pp. 505–514.

[31] T. V. Minh, T. Tjahjowidodo, H. Ramon, and H. Van Brussel, “Controlof a pneumatic artificial muscle (pam) with model-based hysteresis com-pensation,” in The Proceedings of IEEE/ASME Int. Conf. on AdvancedIntelligent Mechatronics, Singapore, 2009, pp. 1082–1087.

[32] T. Tjahjowidodo, “Theoretical analysis of the dynamic behavior ofpresliding rolling friction,” Mechanical Systems and Signal Processing,vol. 29, pp. 296–309, 2012.

[33] T. V. Minh, T. Tjahjowidodo, H. Ramon, and H. Van Brussel, “Non-local memory hysteresis in a pneumatic artificial muscle (pam),” in17th Mediterranean Conference on Control and Automation (MED ’09),2009, pp. 640–645.

[34] T. N. Do, T. Tjahjowidodo, M. W. S. Lau, and S. J. Phee, “A novelapproach of friction model for tendon-sheath actuated surgical systems:Modeling and parameter identification,” Mechanism and Machine The-ory, vol. 85, no. 2015, pp. 14–24, 2015.

[35] V. Hassani, T. Tjahjowidodo, and T. N. Do, “A survey on hysteresismodeling, identification and control,” Mechanical Systems and SignalProcessing, vol. 49, no. 1, pp. 209–233, 2014.

[36] Y. Feng, Y.-M. Hu, C. A. Rabbath, and C.-Y. Su, “Robust adaptivecontrol for a class of perturbed strict-feedback non-linear systems withunknown prandtl-ishlinskii hysteresis,” International Journal of Control,vol. 81, no. 11, pp. 1699–1708, 2008.

[37] C. Di Natali, M. Beccani, and P. Valdastri, “Real-time pose detection formagnetic medical devices,” IEEE Transactions on Magnetics, vol. 49,no. 7, pp. 3524–3527, 2013.

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