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1128 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 14, NO. 4, JULY 2010

Evaluation of Low-Level Controllers for anOrthopedic Surgery Robotic System

Duygun Erol Barkana

AbstractIn this paper, a computed-torque control anddisturbance-observer-based control were evaluated for an ortho-pedic surgery robotic system called OrthoRoby, to track bone-cutting trajectory. Robust motion control is required to controla medical robotic system in an environment where model un-certainty and disturbances exist. Experiments were performed todemonstrate the performance of the tracking of the desired cuttingtrajectory when a computed-torque controller and disturbance-observer-based controller were used for OrthoRoby. It was ob-served thata computed-torquecontrollercan become unstablewithinexact cancellation due to parameter uncertainties and unmod-eled dynamics. A disturbance-observer-based control was shownto ensure stability with inexact cancellation due to parameter un-certainties and unmodeled dynamics.

Index TermsComputed-torque control, disturbance-observer-based control, orthopedic surgery robot, parallel robot.

I. INTRODUCTION

ORTHOPEDIC surgery is one of the most common oper-

ations in hospitals. Most bone-related orthopedic surg-

eries are performed to straighten bone deformities, to extend

bone length, and to remove bone regions affected by tumors

and infections. Current manual surgical techniques may result

in inaccurate placing and balancing of hip replacements, knee

components, or soft tissues. In recent years, computer-assisted

robotic systems have been developed for orthopedic surgeries,which improve the precision and accuracy of the surgery and in

turn lead to better long-term outcomes.

Various orthopedic surgery robotic systems have been devel-

oped to perform orthopedic surgeries in an accurate and safe

manner. Some of these robotic systems use serial manipulators

while others use parallel manipulators. Robodoc [1], Acrobot

[2], and Arthrobot [3] are well-known orthopedic surgical

robots that use serial manipulators. They tend to consume large

workspaces, are somewhat heavy, suffer from low stiffness and

accuracy, and possess low nominal load/weight ratio. Parallel

robots are also used for orthopedic surgery robots, which have

specific advantages over serial robots, including greater stiff-ness and precise positioning capability. Miniature robot for sur-

gical procedures (MARS) is one of the patient-mounted parallel

Manuscript received August 18, 2009; revised November 8, 2009 andJanuary 11, 2010; accepted February 22, 2010. Date of publication April 5,2010; date of current version July 9, 2010 The work was supported by theSupport Programme for Scientific and Technological Research Projects (1001)under Grant 108E092.

The author is with the Department of Electrical and Electronics Engi-neering, Yeditepe University, Istanbul 34755, Turkey (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TITB.2010.2044581

robots [4], [5]. Similar to the MARS robot, miniature bone at-

tached robotic system [6], [7] is used for machining the femur to

allow a patella implant to be positioned. Compact robot system

for image-guided orthopedic surgery is a parallel robot devel-

oped for planning surgical interventions and supervising the

robotic device [8]. Additionally, Orthdoc [9] uses parallel ma-

nipulators for orthopedic surgery. Hybrid bone-attached robot

has been developed with a parallel and serial hybrid kinematic

configuration for joint arthroplasty [10]. Parallel robots with

high stiffness and precise positioning capabilities are suitable

for orthopedic bone shaping operations [11]. Parallel robots are

significantly more prone to failure than serial devices because

in a serial device, one failure can cause the robot to move dra-

matically, whereas in a parallel structure, one failure will have

little effect on the overall position of the robot. This is important

because surgeon requires the device to maintain its last position

in the event of a catastropic failure. In our previous work an or-

thopedical surgical robotic system OrthoRoby, which consists

of a parallel robot and a cutting tool, has been developed [12].

It is desirable for an orthopedic surgical robot to complete

the bone cutting operation in an accurate manner. The low-level

controller of an orthopedic surgical robotic systemis responsible

for tracking the cutting trajectory in a desired manner. The low-

level controller of a parallel robot is still an open field. A fuzzyand PID control for a 3 degree-of-freedom (DoF) parallel robot

has been proposed [13]. A new discrete sliding mode control ap-

proach for a parallel robot is presented to achieve accurate servo

tracking in the presence of load variations, parameter variations,

and nonlinear dynamic interactions [14]. A fuzzy adaptive su-

pervisory controller is combined with the fuzzy sliding mode

control to demonstrate that the chattering of the sliding mode

controller is reduced greatly and the parallel robot realizes the

trajectory tracking in an accurate manner [15]. A model-based

adaptive back-stepping controller is also designed for a planar

parallel robot [16]. An impedance control algorithm has been

used on the control unit of the parallel robots interacting withdynamic environments prototype [17]. A detailed review of the

control of parallel systems is provided in [18]. In our previous

work, computed-torque controller has been tested for the low-

level controller of the OrthoRoby to track the desired cutting

trajectory [12].

It should be noted that the computed-torque controller can

become unstable with inexact cancellation due to parameter

uncertainties (e.g., an inexact inertia matrix) and unmodeled

dynamics, such as joint elasticity. The stability of an orthopedic

surgical robot is an important issue during a surgical operation.

Thus, in this paper, a disturbance-observer-based control method

has been evaluated as a low-level controller for the OrthoRoby

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BARKANA: EVALUATION OF LOW-LEVEL CONTROLLERS FOR AN ORTHOPEDIC SURGERY ROBOTIC SYSTEM 1129

Fig. 1. (a) Parallel robot design details. (b) Overall OrthoRoby system.

to track the cutting trajectory in a desired manner in case of

modeling errors or disturbances.

This paper introduces the OrthoRoby robotic system,

kinematic, and dynamics analysis in Section II. Low-level

controllers of the OrthoRoby are presented in Section III.

Section IV discusses experimental results that are performed to

demonstrate the feasibility of the computed-torque controller

and disturbance-observer-based controller. Possible directions

for future work and conclusions are provided in Sections V and

VI, respectively.

II. ORTHOROBY ROBOTIC SYSTEM

A well-known parallel robot manipulator called Stewart plat-

form is used for OrthoRoby robotic system. OrthoRoby parallel

robot consists of two circular plates connected by six linear

actuators [see Fig. 1(a)]. The plates are connected by six lin-

ear actuators CARE33H (SKF). Linear actuators have a stroke

length of 150 mm and a load capacity of 60 kg. We note that

CARE33Hs shaft rotates around itself when it moves forward

and backward because of its standard construction. Encoder,

which is a sensor, is attached to the actuator to measure the

rotation. The position of the actuator is determined by measur-

ing this rotation. When CARE33Hs shaft rotates around itself

then encoder measures extra rotation, which misleads accurate

position reading of the actuator. Accurate position reading from

the actuator is important to track the cutting trajectory in a de-

sired manner. The structure of the actuator has been examined to

solve this problem. The actuators shaft is made of 2-mm-wide

stainless pipe, and the head part that bears pipe is made of hard

plastic. A 3-mm-wide straight stainless-steel rod is welded to

the pipe along its mil axis and a hard plastic part that bears pipe

is manufactured using 7000 series hard aluminum. In this way

shaft rotation is prevented and the position of the actuator can

be read accurately.

Additionally, it has previously been shown that some highly

symmetrical architectures of the Stewart platform may result in

singularities, termed architecture singularities, extending over

the whole workspace or significant regions of it [19]. Singularity

of an orthopedic surgical system may cause unsafe operation

area, thus the base and moving platforms of the OrthoRoby

systemare developed in such a way that various Stewart platform

structures can be formed easily by only changing the positions

of the joints on the platforms to check the singularity. Holes are

defined on both moving and base platforms with 15 spacing

[see Fig. 1(a)]. This is one of the differences of the OrthoRoby

from other parallel surgical robots. In this paper, six spherical

joints are placed at 60 along the circumference of the base

platform and six spherical joints are placed with 75

and 45

spacing at the moving plate [see Fig. 1(a)]. The actuators are

connected to the base and moving platform by spherical joints,

which have pivot angles of 40.

The other difference of OrthoRoby compared to existing par-

allel surgical robots is the addition of a revolute joint at the

origin of the base platform. The limitation of parallel robots

in terms of orientation of the mobile platform is a well-known

problem. In this paper, a revolute joint is added to the origin of

the base platform of the OrthoRoby. The addition of a revolute

joint will help OrthoRoby to move from one part of the bone

to another part with reduced leg length changes. Note that the

addition of a revolute joint may affect the performance of the

robot. Thus, the revolute joint is activated using the intelligent

control architecture only when the OrthoRoby is required to cut

the other part of the bone [12].

A hole on the middle of the moving platform of OrthoRoby

is opened for the cutting tool. The cutting tool selected is the

Dremel 400 Digital (Dremel, Inc,). A drill is attached to the end

of this cutting tool. The cutting tool is attached on the moving

platform in such a way that the height of the tool can be easily

adjusted. The mechanical system of OrthoRoby with the cutting

tool is provided in Fig. 1(b).

The OrthoRoby is controlled via a 3.2 GHz Pentium 4 PC with

2 GB of RAM. The hardware is controlled by MATLAB Real

Time Workshop Toolbox from Mathworks, and WinCon from

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Fig. 2. OrthoRoby ADAMS model.

Quanser Consulting [see Fig. 1(b)]. All data I/O is handled by

the Quanser Q8 board. The joint angles of the robot are acquired

using encoders of CARE33H with a sampling time of 0.001 sfrom Quanser Q8 card. The torque output to the OrthoRoby is

provided with the same card and the same sampling time. A

control card is developed to drive actuators of OrthoRoby [see

Fig. 1(b)].

A. Kinematics of the OrthoRoby Robotic System

The OrthoRoby robotic system used in this study consists of

a parallel robot and a cutting tool (see Fig. 2). Fixed reference

frame N is attached to the base platform at the center O. Acoordinate system U is located at the center S of the movingplate and coordinate system T for the cutting tool is located at

the center ofE. Let each leg be a fixed right-handed coordi-nate system located at the center of mass for the ith leg withaxis directions determined by an orthonormal set of unit vectors

Li1 , Li2 , Li3 , where i = 1, . . . ,6. Li3 is along the axis of eachleg. Ai (i = 1, . . . ,6) represents spherical joint positions at thebase platform, and Bi (i = 1, . . . ,6) represents the sphericaljoint positions at the moving platform. The linear extension and

retraction of the six actuated prismatic joints gives the platform

6 DoF positioning capabilities, consisting of three translation

and three rotation. x,y,z represent the position and ,,rep-resent the orientation of the cutting tool with respect to the base

platform. Vector loop closure equations are used to derive the

inverse and forward kinematics equations of the OrthoRoby sys-tem. The details of the kinematics of the OrthoRoby system are

provided in [12].

B. Dynamics of the OrthoRoby Robotic System

Forward dynamics derivation is required to compute acceler-

ation responseof the robot legs for an applied force to control the

OrthoRoby. Existing dynamic models of the parallel robot are

derived using either the Lagrange formulation or the Newton

Euler method. The NewtonEuler method involves treating ev-

ery body as a separate free body and solves for all reaction

forces and torques. There are six equations (three translational

and three rotational) for each body. If there are n bodies, this

Fig. 3. Computed-torque control for OrthoRoby.

means that the total number of unknowns will always be six

times n. However, note that there is no need to solve equa-tions for large numbers of unwanted reaction forces and torques

for control purposes. On the other hand, Lagrange method is

based on the algorithm of virtual displacements and energy

dissipation [20]. The masses of the supporting legs often are ig-nored and, their inertia, invariably, assumed negligible when the

Lagrange formulation or the NewtonEuler method are used.

In this paper, Kanes method is selected for its relative ease of

computerization and its computational efficiency to derive the

dynamics equations of the OrthoRoby [21][23].

Kanes methodis fundamentally a projection methodand does

not require calculation of unwanted interaction forces from the

analysis. Additionally, it eliminates vagueness surrounding the

virtual work approach. The proper selection of the generalized

speeds reduces the complexity of the equations of motion and

provides a computationally efficient analysis in Kanes method.

Masses and inertia of both platforms and legs are taken into

account in Kanes method. The details of the dynamics of theOrthoRoby system are provided in [12].

III. LOW-LEVEL CONTROLLERS

A. Computed-Torque Control

Computed-torque control has been previously used to control

parallel robots [18], [24]. Computed-torque control is a model-

based method, which uses robot dynamics in the feedback loop

for linearization and decoupling. Fig. 3 shows the block diagram

of the computed-torque control used to control the parallel robot

of the OrthoRoby. Consider the control input

M(l)lr + C(l, l)lr + G(l) + dist = ctrl (1)

which consists of an inner nonlinear compensation loop and

an outer loop with an exogenous control signal lr . Substitutethis control law into the dynamical model of the robot manip-

ulator M(l)l + C(l, l)l + G(l) + dist = ctrl , where l = lr . Itis important to note that this control input converts a compli-

cated nonlinear controller design problem into a simple design

problem for a linear system consisting of n decoupled subsys-tems. One approach to the outer-loop control is proportional-

derivative feedback, as

lr = ld + Kv (ld la ) + Kp(ld la ) (2)

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Fig. 4. Disturbance-observer-based control for OrthoRoby.

where ld is the desired leg length, la is the actual leg length, andeq = (ld la ). The control input becomes

M(l)(ld + Kv (ld la ) + Kp(ld la ))

+C(l, l)l + G(l) + dist = ctrl . (3)

The resulting linear error dynamics is given in the following

equation where the convergence of the tracking error to zero is

guaranteed.

eq + Kv eq + Kpeq = 0 (4)

where Kv and Kp are the derivative and proportional gains,respectively. If the model of the robotic system is accurate,

then computed-torque controller produces good control perfor-

mance. The computed-torque controller can become unstable

with inexact cancellation due to parameter uncertainties (e.g.,

an inexact inertia matrix and unmodeled dynamics). Thus, in

the next section a disturbance-observer-based control algorithm

is evaluated for the OrthoRoby. The key idea of the disturbance-

observer-based control is to compensate modeling uncertainties

as well as external disturbance.

B. Disturbance-Observer-Based Control

Robust motion control is required to control a medical robotic

system in the environment where model uncertainty and distur-

bances exist. Disturbance-observer-based control algorithms are

used to compensate modeling uncertainties as well as external

disturbances [25][27]. Instead of explicitly designing a nonlin-

ear control law to compensate the nonlinearities in the dynamic

equations of motion of the OrthoRoby, the nonlinearities are

treated as disturbances to a linear plant. Disturbance observer

regards the difference between the actual output and output of

the nominal model as an equivalent disturbance applied to the

nominal model.

A disturbance observer is closed around each joint to estimate

and cancel the uncertainties. Therefore, when disturbance ob-

server is applied to each joint of the system, each joint dynamics

of the robot can be considered as a simple inertia system M,where M = diag(M11 , . . . , Mnn ) is a nxn diagonal matrix.Fig. 4 shows the block diagram of the disturbance-observer-

based position control used for OrthoRoby. Model-based dis-

turbance observer block attempts to cancel the disturbance by

estimating the disturbance torque, and this block cancels any

Fig. 5. OrthoRoby used for cutting of a femur bone model.

disturbance that is not canceled by model-based disturbance

observer block using the following equation

d = (M(l)

M)

lr +

C(l,

l)

lr +

G(l) (5)

where M(l), C(l, l), G(l) represent dynamic models of therobotic system. Reference acceleration generated usingthe posi-

tion controller is selected, as in (2). The disturbance is canceled

by the disturbance observer block, thus a simple proportional-

derivative control action is sufficient to track a desired trajectory.

The reference torque is calculated as

re f = Mlr . (6)

Disturbance observer in the loop cancels disturbances and

plant modeling errors, which is designed as follows:

distobs =

g

s + g (v + gM

la)

gM

la (7)

where Q(s) = g/(s + g) is generally chosen as a low-pass fil-ter [26], [27]. g/(s + g) is used to attenuate high frequencycomponents resulting from differentiation action in the sys-

tem. g is the frequency. When Q(s) is approximately equalto 1 (low frequency disturbance), then unmodeled dynamics are

cancelled. When Q(s) is approximately equal to 0, then sen-sor noise is eliminated. dist represents the external forces anddisturbances applied to the OrthoRoby during the bone cutting

operation. The torque applied to OrthoRoby is calculated using

ctrl = d + (re f distobs) + dist equation (see Fig. 4).

IV. RESULTS AND DISCUSSION

A. Experimental Setup

The use of OrthoRoby in a bone cutting operation on a fe-

mur bone model is shown in Fig. 5. The user holds OrthoRoby

to perform cutting trajectory tests. In the future, a serial robot

manipulator will be integrated into OrthoRoby to hold the robot

and to locate it near the area on the patients body that will be

cut. A bone cutting path was constructed in consultation with

an orthopedist in Yeditepe University Hospital. The surgeon de-

fined the desired cutting path using a graphical user interface

(GUI).This interface uses Digital Imaging and Communications

in Medicine (DICOM) images of the patients bone as inputs to

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Fig. 6. Position and Euler angles of the cutting trajectory.

Fig. 7. Leg lengths of the cutting trajectory.

form patient-specific bone structure in 3-D. Then surgeon deter-

mines the cutting trajectory based on the 3-D bone model. An

example of cutting trajectory was constructed with the surgeon

using GUI. Note that it is possible for the surgeon to plan other

cutting trajectories using the GUI.

OrthoRoby was initially programmed to move toward the

bone until point A with the constructed trajectory. Then the

robot was asked to move toward the inside of the bone while

cutting a part of the bone using the cutting tool (from A to B)

(see Fig. 6). When the bone was cut, OrthoRoby came back to

its starting position at point C. Then, OrthoRoby again moved

toward the other part of the bone until point D, and it kept

moving while cutting the other part of the bone (from D to

E). Finally, OrthoRoby came back to its starting position. The

position and Euler angle of the OrthoRoby throughout the bone-

cutting path were provided in Fig. 6, and the leg length changes

were provided in Fig. 7.

Fig. 8. Position and Euler angle changes with and without revolute joint.

Fig. 9. Leg length changes with and without revolute joint.

B. Evaluation of Addition of a Revolute Joint

A variety of leg lengths were observed when the revolute joint

was added to the base platform of the OrthoRoby. The position

and Euler angle changes of the robot were provided in Fig. 8 as

solid lines, and the leg length changes were provided in Fig. 9

as solid lines when the revolute joint was added.

When OrthoRoby completed cutting one part of the bone (at

point B), then the robot rotated 180 using the revolute joint

attached to its base platform so that the robot could start cutting

the other part of the bone. The robot still reached the same

desired points A(a) and D(d) to cut the required parts of the

bone with reduced leg length variations.

Note that OrthoRoby reached same desired points with and

without the revolute joint at the same time. However when the

revolute joint was used, rotated 180 to rotate OrthoRoby for

preparation to cut the other part of the bone without changing

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Fig. 10. Tracking position performance of DOBC and CTC.

leg lengths from b to d. Thus, the addition of revolute joint

would help OrthoRoby to move from one part of the bone to

another part with reduced leg length changes.

C. Evaluation of Low-Level Controllers

Two experiments were performed to demonstrate the per-

formance of the tracking of the desired cutting trajectory

when computed-torque controller (CTC) and disturbance-observer-based control (DOBC) were used for the OrthoRoby.

In the first experiment, no disturbance was applied to the input

of the OrthoRoby robotic system and the desired cutting trajec-

tory was selected as described in Section IV-A. The sampling

frequency of the simulation was selected as 500 Hz. Cuttoff

frequency of the disturbance observer filter was set at 300 Hz,

thus 300/(s + 300) was used as the low-pass filter for the dis-turbance observer block in Fig. 4. The gains proportional (Kp )and derivative (Kv ) were adjusted to 10

4 and 150, respectively,

for both the CTC and DOBC.

The trajectory tracking performances of both the CTC and

DOBC were presented in Figs. 10 and 11. Note that until

t = 3.5 s, the CTC and DOBC low-level controllers were re-sponsible to move the OrthoRoby so that the cutting operation

can be completed in a desired manner. Then the revolute joint

dc motor controller was activated to rotate the OrthoRoby so

that it started cutting the other part of the bone. As it can be seen

in Fig. 9 (between b and d), the OrthoRoby leg lengths did

not change during this operation, thus only the revolute joint dc

motor controller was activated during this period. Considering

this situation, the tracking errors of low-level controllers CTC

and DOBC were only presented until t = 3.5 s. These figuresindicated that the tracking error was approximately 104 in po-sition and 103 in orientation; thus both low-level controllers

tracked the desired cutting trajectory well.

Fig. 11. Tracking orientation performance of DOBC and CTC.

In the previous experiment, it was assumed that there was no

modeling error and disturbances. In practice, however, such

modeling errors are inevitable. So the low-level controller

should have the capability to achieve the desired objective in

spite of potential modeling errors or unknown disturbances. In

order to simulate a real surgery scenario, disturbance from exter-

nal forces such as Fex t = 16 sin(10t) that act on the moving

platform and Tex t = 8 sin(10t) that act on the moving plat-form were applied to the input of the OrthoRoby. Additionally,extra disturbances Fdist = 16 sin(10t) that act on the leg ac-tuators along the longitudinal axis were applied to the input of

the OrthoRoby, and a uniform noise between 104 was addedinside the plant of the OrthoRoby through velocities of the legs.

The same desired trajectory was selected and provided in exper-

iment 1. The trajectory tracking performances of both the CTC

and DOBC were presented in Figs. 12 and 13. These figures

indicated that DOBC tracked the desired trajectory better than

the CTC because the basic role of the disturbance observer was

to make the system behave as a nominal model in spite of the

presence of disturbance within the defined frequency range.

It can be seen that CTC can become unstable with inexactcancellation due to parameter uncertainties and unmodeled dy-

namics. Robust motion control is required to control a medical

robotic system in the environment where model uncertainty and

disturbances exist. Thus, the DOBC is shown to ensure stabil-

ity with inexact cancellation due to parameter uncertainties and

unmodeled dynamics.

V. FUTURE IMPLEMENTATIONS

In the future, OrthoRoby will be tested on bone models and

in cadaver studies. These tests will be performed in consultation

with an orthopedist at Yeditepe University.

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Fig. 12. Tracking position performance of DOBC and CTC with disturbance.

Fig. 13. Tracking orientation performance of DOBC and CTC withdisturbance.

Various parallel robot configurations of OrthoRoby will be

created to find workspace and force distribution on the joints

of the OrthoRoby. Then it will be possible to determine the

best configuration of OrthoRoby that has large workspace and

less force distribution on the joints. Note that it is difficult to

test configurations on the mechanical OrthoRoby system. Thus

ADAMS (SIMULIA) will be used to model OrthoRoby in a sim-

ulation environment. Motion and force analysis in a simulation

environment will be performed to determine the best configu-

ration for the bone cutting operation without actually changing

the physical configuration of the mechanical system.

Note that in free space, when there is no contact with the

bone, a low-level controller that satisfies motion tracking and

disturbance rejection is sufficient. However, the interaction dy-

namics of the controlled system also depend on the dynamics of

the bone. Thus, one of the interaction control strategies called

impedance controller will be tested on OrthoRoby [28], [29].

The deviation of the bone cutting tool motion from the desired

motion due to the interaction with the bone will be related to the

contact force through a mechanical impedance with adjustable

parameters using the impedance control.As a future work, a serial robot manipulator will be developed

and integrated into the OrthoRoby to locate the robot roughly

near the region of the bone that is going to be cut.

VI. CONCLUSION

In this paper, a computed-torque control and disturbance-

observer based control were evaluated for OrthoRoby to track a

desired bone-cutting trajectory. It was observed that computed-

torque controller can become unstable with inexact cancella-

tion due to parameter uncertainties and unmodeled dynamics. A

disturbance-observer-based controller was shown to ensure sta-

bility with inexact cancellation due to parameter uncertainties

and unmodeled dynamics.

ACKNOWLEDGMENT

The author would like to thank the help of Dr. Inan who

is an orthopedist in Orthopedics and Traumatics Department,

Yeditepe University Hospital.

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Duygun Erol Barkana received the B.Sc. degreefrom Eskisehir Osmangazi University, Eskisehir,Turkey, in 2001, and the M.Sc. and Ph.D. degreesfrom Vanderbilt University, Nashville, TN, in 2003and 2007, respectively.

She is currently an Assistant Professor at the De-partment of Electrical and Electronics Engineering,Yeditepe University, Istanbul, Turkey, where she di-rects the Robotics Research Laboratory. Her researchinterests include dynamics, control, hybrid systems,medical, and rehabilitation robotics.

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