*Corr. Author’s Address: Department of Computer Science and Technology, Faculty of Science and Engineering, University of Hull, HU6 7RX, UK, j.iqbal@hull.ac.uk 401
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 401-410 Received for review: 2021-05-28
© 2021 Journal of Mechanical Engineering. All rights reserved.  Received revised form: 2021-08-17
DOI:10.5545/sv-jme.2021.7258 Original Scientific Paper Accepted for publication: 2021-08-18
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© 2021 Journal of Mechanical Engineering. All rights reserved.
Original Scientific Paper, 1.01 — DOI: 10.5545/sv-jme.2021.0000
Received for review: 2021-05-28
Received revised form: 2021-08-17
Accepted for publication: 2021-08-18
ControlofanAnthropomorphicManipulatorusingLuGre
FrictionModel-DesignandExperimentalValidation
Khurram Ali
1
- Adeel Mehmood
1
- Israr Muhammad
1
- Sohail Razzaq
2
- Jamshed Iqbal
3,*
1
COMSATS University Islamabad, Department of Electrical and Computer Engineering, Islamabad, Pakistan
2
COMSATS University Islamabad, Department of Electrical and Computer Engineering, Abbottabad, Pakistan
3
University of Hull, Faculty of Science and Engineering, Department of Computer Science and Technology, Hull, UK
Automation technology has been extensively recognized as an emerging field in various industrial applications. Recent breakthrough in flexible automation is
primarilyduetodeploymentofroboticarmsormanipulators. Autonomyinthesemanipulatorsisessentiallylinkedwiththeadvancementsinnon-linearcontrol
systems. Theobjectiveofthisresearchistoproposearobustcontrolalgorithmforafivedegreeoffreedom(DOF)roboticarmtoachievesuperiorperformance
and reliability in the presence of friction. A friction compensation-based non-linear control has been proposed and realized for the robotic manipulator. The
dynamic model of the robot has been derived by considering the dynamic friction model. The proposed three-state model is validated for all the joints of the
manipulator. The integral sliding mode control (ISMC) methodology has been designed; the trajectories of system every time begin from the sliding surface
and it eliminates the reaching phase with assistance of integral term in the sliding surface manifold. The designed control law has been first simulated in
Matlab/Simulink environment to characterize the control performance in terms of tracking of various trajectories. The results confirm the effectiveness of the
proposed control law with model-based friction compensation. The transient parameters like settling and peak time have improvement as well have better
results with friction than without considering the friction. The proposed control law is then realized on an in-house developed autonomous articulated robotic
rducational platform (AUTAREP) and NI myRIO hardware interfaced with LabVIEW. Experimental results also witnessed the trajectory tracking by the robotic
platform.
Keywords: robotic manipulator, lugre friction model, sliding mode control
Highlights
• A dynamic model of robot manipulator is presented in this work by considering the friction between the joints.
• DynamicLuGremodelisusedforfrictionwhichreflectstherealfrictionphenomenonbyconsideringstick-slipmotionandstribeckeffect.
• Sliding mode control technique is used to design the control law using Lyapunov stability theorem.
• Controller performance is evaluated with and without friction compensation in Matlab.
• Proposed controller is also tested on experimental test bench using NI myRio 1900 and AUTAREP robot system.
0 INTRODUCTION
Robotic arms are playing a pivotal role in today’s
industrial world [1]. The industrial automation
methods are majorally affected by the development
in the field of robotics. Robotic arms are basically
the mechanical replication of the human body arm.
Research shows that they can outperform the humans
intermsofstrength,precision,speedandrepeatability,
thus, they can save time with improved performance
[2]. Owing to these concrete reasons, robotic arms
have acquired an invaluable place in industry [3]. To
achievehighprecisioninroboticmanipulators,friction
in joints is the major limitation [4]. A manipulator,
being inherently non-linear in nature, can demonstrate
steady-state error and limit cycles and hence may
suffer from degraded performance [5]. It affects both
dynamic and static performances and can results in
instability due to coupling effects. Henceforth, joint
friction compensation in robot has been one of the
major research problem in control design throughout
the years. Friction is one of the main reasons of
unwanted effects and system performance degradation
[6]. Friction is a force which mostly occurs in moving
systemsexhibitingacomplexphenomenonandcanbe
dividedintotwotypes. Thefirsttypeisknownasstatic
frictionF
s
whichisoftendefinedforthebodiesatrest.
The other type is known as dynamic friction which
occurs when one body is moving with respect to some
other body in contact. It is further divided into three
components. One component is recognized as sliding
friction and others are rolling and pivot friction [7].
Static friction models like Karnopp model are
difficult to implement while simulating the dynamic
systems [8]. The dynamic friction models established
so far cover majority of non-linear phenomena and
they exhibit continuous behavior when the velocity
is zero. These characteristics make the dynamic
models more useful and convenient for software
simulations and analysis of control algorithms. It is
knownthatsomeoftheforemostrestrictionstorealize
*Corr. Author’s Address: Department of Computer Science and Technology, Faculty of Science and Engineering, University of Hull, HU6 7RX, UK, j.iqbal@hull.ac.uk 1

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admirable breakthrough in mechanical frameworks
is the presence of friction, which is a non-linear
phenomenon and hard to depict analytically [9].
Friction should be taken into account at an early
stage throughout the system design by reducing it
at probable minimum limit through careful design.
Moreover, research shows that most of the dynamic
models developed so far are incapable to capture the
real friction phenomenon experienced by surfaces in
contact [10]. The LuGre friction model is used in the
current research since it describes important friction
behaviourandcharacteristicssuchasstick-slipmotion
and stribeck effect etc. [11]. While demonstrating
advantages of friction modelling, the LuGre friction
modelcanresultinnumericallystiffandtoughsystem
dynamics. Moreover, the LuGre model performs like
a linear spring pair when it is linearized for small
motions. For a control engineer, it is suitable to
analyse the impact of friction on the feedback system
in order to design a control law that reduces the effect
offriction.
In robotics, non-linear, centralized trajectory
tracking refers to the input torque computation which
guaranteesprecisetrackingofreferencetrajectory. The
research community has suggested numerous control
approaches varying from simple linear feedback
control to sophisticated algorithms. Sliding mode
control (SMC) is one of the robust non-linear control
techniques based on principle of the variable structure
control theory. The key features of SMC include
systemrobustness[12]anditsstabilityagainstmatched
uncertainties [13]. The dynamics of a robotic
manipulator having multi-DOF is complicated and
highly non-linear [14]. The position of a single joint
and its two higher derivatives have a strong impact on
all joints of robotic manipulator. Moreover, gravity,
external forces, modelling uncertainties, and friction
can impact the robot motion. The state-of-the-art
research works have been reported in the literature on
robotic manipulator that uses friction models instead
of a disturbance. An adaptive robust control (ARC)
algorithm has been proposed for an electric cylinder
withtheLuGrefrictionmodelin[15]andtheLyapunov
approach has been suggested for system stability and
ARC handles external disturbances. In [16], to lessen
the impact of estimation errors the robust sliding
mode controller with an adaptive block compensation
controller is proposed. The inverted pendulum and
planar multi-joint robot with friction model are used
tovalidatethecontroller. Authorsin[17]usedadaptive
ISMCwithtime-delayestimation.
In this paper, an ISMC for anthropomorphic
manipulator based on modified LuGre model with
friction compensation is proposed. The following is
abriefdescriptionofthemaincontribution:
• Mathematical model of AUTAREP robotic
manipulator is centered on a five DOF has
been derived by considering the kinematics and
dynamics of the robot manipulator, as well as the
LuGrefrictionmodel.
• Robust controller has been designed to
compensate the dynamic friction behaviors
and drive the position and speed to track the
desired trajectories. The integral sliding mode
control (ISMC) law, which is based on the
Lyapunov function, is used to compensate
for the system’s parametric and load torque
uncertainties.
• The proposed control law is then implemented
on a custom developed platform using LabVIEW
interfacewithNImyRIOhardwarehavingmotors
drivingcircuits.
This article is organised as follows; Section 1
derives the mathematical model of a single joint along
with LuGre friction model. In Section 2, SMC
based control law is designed. After the control
design, in section 3, outcomes of control design have
been analysed and experimental results are discussed.
Section4concludesthearticle.
1 MATHEMATICALMODELLING
A robotic manipulator usually consists of servo
motors, optical encoders, and one or more controllers.
Theroboticmanipulatorusedforresearchandanalysis
in the current research is AUTAREP ED-7220C [18]
shown in Fig. 1. The robotic manipulator has five
degrees of movement actuated with DC servo motors.
A single motor is used to move each joint except the
wrist joint where pitch and roll motions are controlled
by two motors. The model characterizes an extremely
non-linear system since velocities as well as positions
of links are coupled dynamically. For feedback from
joints, the robotic arm has optical encoders mounted
on each joint servo motor axis, which provides
information about its position. An adequate motion
control algorithm could be accomplished through
mathematical modelling by considering the dynamics
oftherobotmanipulator.
Kinematics of a robot gives the relationship
between joint angles/translations and the location
(position and orientation) of its end-effector [19]. The
kinematic model of the manipulator established on
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Fig. 1. AUTAREP Manipulator ED-7220C with joints corresponding range
of motions
Denavit-Hartenberg (D-H) parameters is reported in
[20]. The process of modelling the robot dynamics
involves derivation of velocities and inertia matrices,
computation of kinetic and potential energies and final
formulation of torque equation [21]. Each link of
the manipulator is considered as a set of number
of elements for which potential and kinetic energies
are developed. In the present research work, the
Lagrangean approach is used for the formulation of
dynamics [22]. Fig. 2 illustrates the kinematic
representation of AUTAREP manipulator. In order to
function motors, the model should be able to evaluate
the joint torques which are system control input [23].
The manipulator’s dynamic equation is given by Eq.
(1):
τ
f
=M(q
i
) ¨ q
i
+C
c
(q
i
, ˙ q
i
) ˙ q
i
+G(q
i
)+T
f
(˙ q
i
), (1)
where for n joints, M(q
i
)∈ R
n×n
is the mass/inertial
matrix, C
c
(q
i
) ∈ R
n×n
represents the coriolis and
centripetal forces, G(q
i
) ∈ R
n×1
is the gravitational
matrix, T
f
(˙ q
i
)∈R
n×1
represents friction torques. The
termτ
f
∈R
n×1
isthevectorofinputtorquesappliedto
the joints of the robot. Friction is one of the major
causes of undesirable effects. Numerous dynamic
models for friction have been suggested in literature,
including the Dahl model and LuGre model [24], etc.
ThedynamicDahlfrictionmodelformstheorigin
of the LuGre friction model and is an integrated
dynamic model of friction. However, it does not
Fig. 2. Kinematic representation of the robotic arm where (L
1
= 385
mm,L
2
= 220 mm,L
3
= 220 mm,L
4
= 155 mm )
consider all the non-linear phenomena caused by
friction. In the literature, it has been shown that
static models cannot capture certain characteristics of
true frictional phenomena that are experimentally seen
in high friction systems. Therefore, LuGre model
of friction is a dynamic friction model related to
the bristle interpretation of friction and the average
deflection force of elastic springs is used to model
friction. The velocity determines the average bristle
deflection for a steady state motion. It is lower
at low speeds, implying that steady-state deflection
decreases with increasing velocity. Rate dependent
friction phenomena such as varying break-away force
and frictional lag are also included in the model.
Therefore, the LuGre model is used here for friction
modeling and is given as
T
f
=σ
0
z+σ
1
˙ z+ f(ν), (2)
where f(ν)=σ
2
ν, z is internal friction state and the
termT
f
is predicted friction torque.
T
f
=σ
0
z+σ
1
˙ z+σ
2
ν. (3)
The dynamics of friction statez can be defined as:
˙ z=ν−σ
0
|ν|
g(ν)
z, (4)
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where g(ν) is given by:
g(ν)=F
c
+(F
s
−F
c
)exp
−(|ν/ν
s
|)
. (5)
The LuGre model can illustrate several
properties of real friction, for example the limit
cycle displacement in stick-slip motion. For
steady-state friction measurement the functions
f(ν) and g(ν) can be used. The model has a
significant drawback in that, this does not take into
account the dwell time effect, which implies that it
cannot model variations in friction force when two
surfaces are maintained in contact at rest for a set
period. The LuGre model is a dynamical system with
the following properties: internal state dissipativity,
boundedness, I/O dissipativity with constant σ
1
and velocity-dependent σ
1
(ν) [25]. Most of these
are reasonable characteristics of a model illustrating
friction. Parameters of LuGre friction model are
obtained from literature [26] and are given in Table 1.
Table 1. Parameters of LuGre friction model
Parameter Value Unit Description
σ
0
2750 Nm/rad Stiffness coefficient
F
s
8.875 Nm Static friction torque
F
c
6.975275 Nm Coulomb friction torque
σ
1
45.2 Nm·s/rad Damping coefficient
σ
2
1.819 Nm·s/rad Viscous friction coefficients
ν
s
6.109·10
−2
rad/s Velocity
Let q
1
is the position vector, q
2
is the velocity
vector and z
3
is internal friction state. Thus the
state-space model of a single joint can be represented
by Eq. (6):
˙ q
1
=q
2
˙ q
2
=M
−1

τ
f
−C
c
q
2
+Gq
1
+σ
0
z
3
+σ
2
q
2
+σ
1
˙ z
3

˙ z
3
=q
2
−σ
0
|q
2
|
g(q
2
)
z
3
.
(6)
2 CONTROLDESIGN
SMCtechniquepermitscontrolofnon-linearprocesses
subjected to high model uncertainties and external
disturbances [27]. In present research, SMC based
law with friction compensation is implemented on
AUTAREP manipulator. SMC law is divided into two
phases i.e. the sliding phase and the reaching phase
[28]. The system trajectories achieve the required
sliding surface in the case of reaching phase, defined
as:
˙ q
i
= f (q
i
)+g(q
i
)u+Δ(q
i
,t). (7)
The vector fields f (q
i
) and g(q
i
) are the non
linear functions representing the system with matched
uncertainties Δ(q
i
,t). For the control design, the first
stepistodefineaslidingsurfaceandthewholesystem
states are forced in such a way that the sliding surface
converges to zero in a finite time and remains there
as long as there is no change in reference input [29].
The control objective in this work is to make sure that
the robot should track the predefined trajectory q
di
. To
accomplish this aim, a sliding surface based on error
signal for each link is described in Eq. (8):
S
si
=C
s
˙ e
s
i+λ
si
e
si
+I
si

e
si
dt, (8)
where C
s
, λ
si
and I
si
are positive constants. The
trackingfunctionisestablishedforwell-definedsliding
surface in Eq. (8). Thus, the sliding surface will
converge to zero with the applied control effort. This
will ensure the tracking error e
si
converges to the
origin. The control input of SMC law comprises of
two parts. The first part is equivalent control law
(u
seq
) and it is a continuous term. The second part
is discontinuous control law (u
sdis
) with the signum
function.
u=u
seq
+u
sdis
. (9)
The equivalent control input (u
seq
) is acquired
through sliding surface by considering
˙
S
si
= 0 which
is obtained after taking the time derivative of Eq. (8):
˙
S
si
=C
s
¨ e
si
+λ
si
˙ e
si
+I
si
e
si
. (10)
In SMC, the objective is accomplished by setting
˙
S
si
=0. Substituting this value in Eq. (10):
0=C
s
¨ e
si
+λ
si
˙ e
si
+I
si
e
si
, (11)
where ˙ e
si
= ˙ q
di
− ˙ q
i
and ¨ e
si
= ¨ q
di
− ¨ q
i
are the first and
second time derivatives of error function respectively.
Substituting error dynamics, we get:
0=C
s
(¨ q
di
− ¨ q
i
)+λ
si
(˙ q
di
− ˙ q
i
)+I
si
(q
di
−q
i
), (12)
¨ q
i
=( C
s
)
−1
[(λ
si
(˙ q
di
− ˙ q
i
)+I
si
(q
di
−q
i
)]+ ¨ q
di
. (13)
The equivalent control effort u
seq
is chosen as:
u
seq
=M(q
i
)(C
s
)
−1
[(λ
si
(˙ q
di
− ˙ q
i
)+I
si
(q
di
−q
i
)]
+ ¨ q
d
+(C
c
)(q
i
, ˙ q
i
)+G(q
i
)+T
f
(˙ q
i
).
(14)
In order to compensate the dynamic model
uncertainties, the discontinuous function u
sdis
is
defined as given in Eq. (15):
u
sdis
= −k
si
sign(S
si
)−ζS
si
, (15)
where k
si
and ζ are positive constants. The equivelant
control input u
seq
drives the system from initial
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state to sliding surface and ensures that
˙
S = 0.
However, due to different uncertainties and external
disturbances the sliding surface may not converge
to zero. Lyapunov stability-based method is used
for analysis and control design which guarantees the
system stability. For stability analysis, a positive
definite Lyapunov energy-function for SMC is chosen
asEq. (16):
V =
1
2
S
2
si
. (16)
TakingderivativeofEq. (16),weobtain:
˙
V =S
si
˙
S
si
. (17)
By substituting the value of
˙
S
si
given in Eq. (12)
andsubstituting u
seq
aswell u
sdis
inEq. (17),weget:
˙
V =S
si
(−k
si
sign(S
si
)−ζS
si
), (18)
˙
V ≤−k
si
|S
si
|−ζ(S
si
)
2
. (19)
The derivative of Lyapunov function
˙
V, turns
out to be negative semi-definite function which is
sufficient condition for Lyapunov stability. Therefore,
thedynamicsofsystemwillconvergeinfinitetimeand
the error will converge to zero for the applied input
giveninEq. (20):
τ
f
=M(q
i
)C
s
−1
[(λ
si
(˙ q
di
− ˙ q
i
)+I
si
(q
di
−q
i
)]
+¨ q
di
+C
c
(q
i
, ˙ q
i
)+G(q
i
)+T
f
(˙ q
i
)
−ksignS
si
−ζS
si
.
(20)
2.1 Experimental Setup
The proposed control algorithm is also tested on
the experimental setup using LabView environment
and NI myRIO-1900 hardware. The experimental
setup is shown in Fig. 3. The myRIO-1900 is
a tool used to implement multiple design concepts
with one reconfigurable input/output (I/O) device. It
is a portable device that can be used to design and
develop various applications in robotics as well in
mechatronic systems. It consists of a Xilinx Field
Programmable Gate Arrays (FGPA), digital I/O lines
and analog inputs as well as analog outputs. It
has a built-in accelerometer with distinct features
such as Universal asynchronous receiver-transmitter
(UART), audio input and output terminals and a pulse
width modulator. The myRIO-1900 is a WiFi-enabled
edition which allows for speedy integration into
remotely control embedded applications. The
myRIO-1900 is programmed with LabVIEW using
graphical programming language (G-Programming)
Fig. 3. Hardware setup
(a) Motor driving board (b) Main board
Fig. 4. Motors driver board for robotic manipulator
with a high data flow and a building block that can be
used for link data acquisition, logical operations, and
analysis.
In the proposed solution, digital outputs are
used for controlling the actuators that are interfaced
through indigenously designed H-bridges by using
power transistors TIP147 and TIP142 as shown in
Fig. 4a with current rating of five Amperes. The
movement of rotary joints in a robot manipulator is
controlled by using motor driver circuitry and the
Fig. 4b presents the main board which connects
the robotic manipulator with motor driving board.
The desired speed of the motor is accomplished by
controlling the voltage via pulse width modulation
of the corresponding duty cycle. The actuators are
integrated with optical encoders to determine the joint
positions and their signals are sent to the myRIO for
data processing.
3 RESULTSANDDISCUSSIONS
Matlab/Simulink is used for simulation. To validate
the model, simulations are conducted using Matlab
R2016a installed on a core i5 processor system having
6 GB random access memory. Step response is
presented for the elbow joint of the robot manipulator
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asshowninFig. 5whilesinusoidalresponseisplotted
for the base joint as presented in Fig. 6.
The desired step input signal of amplitude of
0.1 rad is given to the closed loop system and Fig.
5a shows simulation results for a control law that is
designedtotrackaunitstepfunctionwithandwithout
friction compensation. Although there is no overshoot
inFig. 5a,butitshowsanimprovementinsettlingtime
inthecaseofthecontrollerwithfrictioncompensation.
The controller with friction compensation has settling
time of 1 second as compared to 2 second settling
time without considering the friction. The results
show that the response of ISMC is better for friction
taking into account in terms of steady-state error. The
Fig. 5b demonstrates the control effort in elbow joint
of robotic manipulator. The results clearly indicate
that the more control effort is required for controller
withoutfrictionandcontrolinputexhibitsanunwanted
chatteringphenomenon,whichcanbedamagingtothe
system’s mechanical and electrical components. The
trajectories of system begin from the sliding surface
and the reaching phase is removed with the help of
integraltermintheslidingsurfacemanifold. However,
a discontinuous term of the switching control appears
in the resulting joint torque. The chattering impact
is the main hurdle in the practical realization of the
sliding mode control. An integral term of SMC
improves the outcomes by simplifying the higher
order derivatives of the system. In the figure, it can be
observed from the result that the control effort with
friction compensation-based SMC allows the system
totracktherequiredtrajectorywithmoreprecisionand
accuracy as compared to SMC without considering
the friction model. Fig. 5c demonstrates the tracking
error signal with and without friction compensation.
As figure shows that at time of one second the error
signal is zero with friction compensation as compared
to 0.15 with out considering friction. The internal
state of friction in elbow joint of robotic manipulator
is illustrated in 5d.
In Fig. 6, to test the closed loop tracking
performance of the robot manipulator system, the
desired differentiable sinusoidal input signal is
generated with an amplitude and frequency of 0.1
rad and 0.016 Hz, respectively. The simulation
results are generated with and without friction
compensation. 6a illustrates the sinusoidal response
of base. At some point actual position attains the
required trajectory then it follows the desired path
for remaining time. In the figure, It can be observed
from the results that the control effort with friction
compensation-based control allows the system to
track the required trajectory with more precision and
accuracy as compared to SMC without considering
thefrictionmodel. Fig. 6billustratesthecontroleffect
in the form of applied torque to the base. The control
effort is calculated using the control law defined in
Eq. (19). The SMC based law reduces the chattering
effect, when the dynamics of the system are weak
against the uncertainties. Fig. 6c shows the error
signal between actual and desired positions of the
base. These results show that SMC with friction
compensation demonstrates better performance with
nearly zero error signal compared to SMC without
frictioncompensation. Inthefigure,itcanbeobserved
that without friction compensation error signal has
greater amplitude of error in comparison to friction
compensation error signal. Fig. 6d shows the internal
state of LuGre friction model in base joint of the
AUTAREP robot manipulator.
Figs. 7a and b present the experimental results of
joints of the robot manipulator. Fig. 7a demonstrates
the step input response for base joint of the robot
manipulator and shows that the joint reaches the
desired position in 0.6 sec with overshoot. It can be
seen that both transient and steady-state parameters
are within acceptable limits. Sinusoidal response
of base joint is also shown in Fig. 7b. The results
demonstrate the well-known chattering phenomenon.
This behavior of the system is undesirable and it may
cause heat and energy dissipation and wear and tear
of various components in the system. The chattering
phenomenon can be reduced by implementing other
variants of SMC such as higher order SMC.
The proposed ISMC technique and the
adaptive sliding mode control (ASMC) methodology
implemented in [30] are compared in Fig. 7c.
By employing SMC’s reaching condition, these
trajectories approach zero and provide asymptotic
stability to the system. Fig. 7c demonstrates the
tracking behavior between both the current and
desired positions which does not exceed 1.5 s for
both techniques. The ISMC method has settling time
of 1.25 s with friction compensation in comparison
to 1.45 s for control law proposed in [30]. It has
rise time of 214.9 milli second with overshoot of
0.792 % in comparison to ASMC technique having
270.63 milli-second rise time and overshoot of 0.658
%. The passivity based adaptive control of a
serial robotic manipulator is implemented in [31]
using joint frictions depending upon temperature.
The position tracking of said technique along with
the method implemented in this paper is shown in
Fig. 7d. The position tracking in ISMC has better
convergenceperformanceandasymptoticconvergence
in comparison to method proposed in [31]. The
6 Ali, K. - Mehmood, A. - Muhammad, I.- Razzaq, S. - Iqbal, J.

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(a) Angular position of elbow joint
(b) Control effort
(c) Error signal
(d) Friction state z
Fig. 5. Step response obtained by the elbow joint of the robotic manipulator
negative aspect in the proposed technique ISMC with
friction compensation is that the temperature effect of
joints are not considered as well high control gains
and high control efforts related to chattering issues.
As robotic manipulators are often used in various
applications where the joints get warmer due to the
friction after the manipulator operates for some time.
They may also be used when the temperature varies
from very low to very hot degrees. The temperature
effectsmustthereforebeconsidered.
4 CONCLUSIONS
In this research work, a sliding mode control with
an integral term is proposed for the desired trajectory
tracking and robotic manipulator is modeled using
dynamic LuGre friction model. The effectiveness of
the proposed ISMC technique is initially validated in
Matlab and simulation findings are shown to illustrate
theeffectivenessofthedesignedrobustcontrollerwith
and without considering the friction. The proposed
control scheme is then evaluated by comparing with
the other sliding mode control techniques. The ISMC
techniqueperformssuperiorintermsofsystemcontrol
efforts and transient parameters involving percentage
overshoot, rise time and settling time etc. have been
witnessed to be within certain bounds as anticipated.
The proposed control law is also being tested on
the custom developed experimental test bench using
LabVIEWandNI-myRIO.
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(a) Angular position of base joint
(b) Control effort
(c) Error signal
(d) Friction statez
Fig. 6. Sinusoidal input signal response obtained by the base joint of the robotic manipulator
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