Intelligent swarm algorithms for optimizing nonlinear sliding mode controller for robot manipulator

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 11, No. 5, October 2021, pp. 3943~3955
ISSN: 2088-8708, DOI: 10.11591/ijece.v11i5.pp3943-3955  3943
Journal homepage: http://ijece.iaescore.com
Intelligent swarm algorithms for optimizing nonlinear sliding
mode controller for robot manipulator
Suhad Qasim G. Haddad1
, Hanan A. R. Akkar2
1
Department of Computer Engineering, University of Technology, Iraq, Baghdad, Baghdad, Iraq
2
Department of Electrical Engineering, University of Technology, Iraq, Baghdad, Baghdad, Iraq
Article Info ABSTRACT
Article history:
Received Nov 28, 2020
Revised Mar 17, 2021
Accepted Mar 27, 2021
This work introduces an accurate and fast approach for optimizing the
parameters of robot manipulator controller. The approach of sliding mode
control (SMC) was proposed as it documented an effective tool for designing
robust controllers for complex high-order linear and nonlinear dynamic
systems operating under uncertain conditions. In this work Intelligent particle
swarm optimization (PSO) and social spider optimization (SSO) were used
for obtaining the best values for the parameters of sliding mode control
(SMC) to achieve consistency, stability and robustness. Additional design of
integral sliding mode control (ISMC) was implemented to the dynamic
system to achieve the high control theory of sliding mode controller. For
designing particle swarm optimizer (PSO) and social spider optimization
(SSO) processes, mean square error performances index was considered. The
effectiveness of the proposed system was tested with six degrees of freedom
robot manipulator by using (PUMA) robot. The iteration of SSO and PSO
algorithms with mean square error and objective function were obtained,
with best fitness for (SSO =4.4876 𝑒−6 and (PSO)=3.4948 𝑒−4.
Keywords:
Artificial intelligence
Particle swarm optimizer
Sliding mode control
Social spider optimizer
Swarm intelligence
This is an open access article under the CC BY-SA license.
Corresponding Author:
Suhad Qasim G. Haddad
Department of Computer Engineering
University of Technology, Al Sinaa Street, Baghdad, Iraq
Email: suhadhadad.sh@gmail.com
1. INTRODUCTION
Programming the multi degrees of freedom (DOF) of robot arms in order to maximize their
functionality has recently remained a challenging job, time-consuming and costly operation in particular.
Indeed, the coupling effects of multiple joints must be taken into account by controlling robot manipulator
parameters [1]. In this work, programmable universal manipulation arm (PUMA) robot, which has six
degrees of freedom (6-DOF), all are rotary joints with serial connections, was used as a study case. The first
three joints are used to control the robot's handle position. The second three joints are to obtain the
orientation of the robot's wrist locus. PUMA robot manipulator is widely used in medical, automotive,
education and other important applications. The parameters and dimensions of this robot were all known and
documented in different literatures [2]. Figure 1 illustrates the global model of PUMA robot the 6-DOF
manipulator.
Designing a stable and strong controller is an important part for sensitive and various applications
for robot manipulator. The most common nonlinear model-based controller is sliding mode controller (SMC)
which has been properly applied in various applications such as motor control, space system, automatic flight
control and finally robot control. It is considered as a powerful advance stable robotic manipulator control
system that can achieve and solve the most important tasks in control systems, which are robustness and

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Int J Elec & Comp Eng, Vol. 11, No. 5, October 2021 : 3943 - 3955
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stability [3]. Integral sliding mode controller (ISMC) was suggested in this work to boost the manipulator
output to accomplish the desired tasks with high stability.
Figure 1. The global model of puma 560 robot manipulator
The essential benefits of the SMC method are achieving of asymptotic reactivity and stability in
implementation regarding to all notched internal and external uncertainties and disturbances. The SMC can
be split into two key components, which are the discontinuous part (𝜏𝑑𝑖𝑠) that’s used to design appropriate
tracking performance centered on linear methodology requiring identical fast switching. But it is caused to
system instability and the occurrence of chatter. The second part is equivalent controller (𝜏𝑒𝑞) which is the
effect of nonlinear terms that induced reliability and used to fine-tune the sliding surface slopes [4]. In
addition, SMC has two major disadvantages, namely are chattering phenomenon in control response, and
nonlinear equivalent analogous functional formulation in indeterminate and uncertain dynamic parameters [5].
The rising in switching frequency of the control in discontinuous issue happened due to a phenomenon called
(chattering), which can be considered as an unwanted feature that appear in the control behavior of SMC. It is
a limited value with restricted frequency of oscillation that can cause some severe mechanical problems, such
as distortion and heating of robot manipulator mechanical components. This chattering influences on the
stability of the system, due to this reason chattering effect should be cancelled or minimized. So, adjusting
the sliding mode control parameters is an important part to reduce the chattering disadvantage and
developing a stable coefficient for nonlinear controllers [6]. In recent times, artificial intelligence (AI)
techniques have been implemented to overcome the disadvantage in conventional controller design, which is
an effective tool for solving many applications with intelligent techniques. These innovative approaches are
methods of biological inspired optimization, which can randomly transfer a solution of one candidate into a
new one with better fitness function [7]. Researchers have been obsessed with insect or animal species'
collective intelligent actions in nature, such as bird flocks, ant colonies, fish schools, bee swarms, where the
relation between the collection of insects or animals is referred to as swarm behaviour. This division of AI is
often referred to as swarm intelligence (SI), which deals with the mutual behavior of swarms by the active
coordination and interaction of individuals without supervision. SI provides a benefits that including
scalability, fault tolerance, flexibility, speed, mobility, autonomy, parallelism, and adaptation [8]. In this
work, particle swarm optimization (PSO), and social spider optimization (SSO), which are an efficient
algorithms of SI, were suggested to adjust the nonlinear coefficients and optimizing the parameters of the
proposed controllers. These algorithms can create the perfect solution, with a high quality and a lower
computing time than other techniques, with progressively stable assembly characteristics, they efficiently
change the parameters with sufficient convergence to achieve impressive acceleration of the system [9].
This paper has been arranged accordingly. Some related works are presented in the second section.
The third section deals with the analysis, modelling and simulation of the dynamic model of PUMA robot.
Section four concentrates on the strategy of controller model, and the method that used in designing SMC
and ISMC for controlling the dynamic part of the robot. Section 5 discusses the method of PSO and SSO

Int J Elec & Comp Eng ISSN: 2088-8708 
Intelligent swarm algorithms for optimizing nonlinear sliding mode … (Suhad Qasim G. Haddad)
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algorithms. The outcome of the debate and simulation is shown in the sixth section. The last section in the
paper introduces the conclusion and future work.
2. LITERATURE REVIEW
Researchers have been working hard to control the robot manipulator and to create best solutions for
the dynamic model, to obtain stable response with minimum steady state error. Several controllers have been
developed with various SI algorithms. A concise summary of previous related works is shown in this section.
In [10] mentioned that to solve the trajectory monitoring problem for a nonlinear design of wheeled robot,
PSO has been used to get the best values for the parameters of sliding mode control. In [11], the robotic
device stability was demonstrated using Lyapunov impedance based technique, with PSO algorithm for
optimization the parameters of the control. Jalali [12] introduced an adaptive sliding-mode controller with
PSO algorithm for optimizing PUMA robot manipulator, this controller can respond and adapt itself to
change system parameters according to the external intervention. PSO algorithm was used to enhance the
parameters of the sliding function and minimize the chattering action. Boundjou [13] developed a stable
adaptive controller with Particle Swarm Optimizer for automatic and systematic tuning of PID gains for two
degrees of freedom robot arm, thus optimizing the cost function of the parameters. In [14], evaluating of
SMC efficiency with PID was done, taking into account the ziegler-nichols (ZN) and the PSO tuning
algorithm implemented in the sliding surface. The computational and simulation results showed that
compared to traditional ZN variables the SMC is able to do well with the PSO variables added to the sliding
board.
PID controller auto-tuning system was implemented for PUMA robot manipulators [15]. Two
methods of SI multi-objective optimization were tested, namely multi objective cuckoo scan (MOCS) and
multi objective particle swarm optimization (MOPSO). Comparison was made between the results of the two
algorithms in the case of achieving a predefined trajectory with a reasonable tracking accuracy. Sliding mode
controller with boundary layer was presented for dynamic design with control of 6-DOF robot arm
manipulator type IRB-120 [16]. The chattering that generates unreliable signal with high frequency
oscillation in the sliding mode control was eliminated by using the boundary layer which provides the
controller with stabilization and improve the total performance. New technique was presented for robot
manipulators with a robust high degree composite, super-twisting of sliding mode controller (HOS-TSMC)
[17]. The suggested approach extends the traditional and conventional controller of sliding mode (TSMC)
and the approximate state of sliding mode (ESMC) to ameliorate the chatter. To minimize the influence of
numerous external disturbances, the non-linear simulator of the saturation integral backstepping controller
was implemented and the particle swarm algorithm was used to evaluate the controller parameters [18].
Three types of external disturbances (constant, intermittent, and random disturbances) were used separately
during the quadrotor aircraft's flight control. The outcome of the simulation reveals that in anti-disturbance
power, the saturation integral backstepping controller was much stronger than the classical backstepping
controller and integral back stepping controller. A modern adaptive terminal sliding mode controller with a
non-single specialty was used to control the behavior of quad rotor flight [19]. Besides, the controller of
backstepping sliding mode, was introduced to control the path of the quadrotor, despite the influence of
external disturbances, this leads to quick and reliable observation. The design process was illustrated with
Lyapunov principle. Then, the proposed controllers of backstepping, integral sliding mode and the second
sliding mode, were investigate with several flights checks. Where the simulation result shows an
improvement in the convergence of time, with good robustness and chattering free for control efforts.
Akkar and Haddad [4] introduced a strategy for tuning three types of dynamic control techniques
that were developed for the PUMA 560 robot manipulator, which are proportional integral derived (PID),
sliding mode control (SMC), and the modified type of integral sliding mode control (ISMC). Intelligent
particle swarm optimization (PSO) has been suggested to achieve the best parameters in order to maximize
the parameters in the proposed strategies. The PSO optimization approach has improved the parameters of
each controller according to the initial values of the particles, such as their swarm size and initial velocity.
3. CONTRIBUTION
In this work, based on the theory of SMC, an integral optimal control law was designed for the 6-
DOF PUMA robot manipulator. The integral sliding mode controller (ISMC) was proposed to improve the
manipulator output to perform the desired tasks with high stability. Then, particle swarm algorithm for
optimization (PSO), and social spider optimization (SSO) algorithm, were suggested to adjust the nonlinear
coefficients and optimizing the parameters of the ISMC. Where, adjusting the integral sliding mode control
parameters is an important part to reduce the chattering disadvantage and developing a stable coefficient for
nonlinear controllers.

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4. DYNAMIC DESIGN OF PUMA ROBOT MANIPULATOR
The dynamic equation of multi DOF for PUMA robot manipulator is about the analysis of motion
concerning forces. Dynamic design modelling is required for mechanical part model, control and finally in
implementing the simulation. It is used to define the parameters of the dynamic and also to explain the
relationship between displacement, distance, acceleration and the force that acts on the manipulator of the
robot. Lagrange-Euler mathematical model of the robot is used for calculation the control laws and design the
dynamic system of the robot. In of a multi DOF for robot manipulator is calculate is being as [20], [21]:
𝐴(գ)գ̇ + 𝑁(գ գ ) = 𝜏 (1)
Dynamic equation as an outcome for the robot can be described is being as:
𝑁 (գ գ ) = 𝑉(գ գ) + 𝐺(գ) (2)
𝑉(գ գ) = 𝐵(գ) [գ գ] + 𝐶(գ) (գ)2
(3)
𝜏 = 𝐴(գ) գ̇ + 𝐵(գ)[գ գ̇] +𝐶(գ)(գ)2
+ 𝐺(գ) (4)
where: 𝐴(գ):Symmetric positive matrix considered for kinetic energy and inertia matrix,with 𝑛𝑥𝑛 dimension.
𝐵(գ): is for Coriolis torques matrix, with 𝑛𝑥𝑛 (𝑛 − 1)/2 dimension. 𝐶(գ) : is for centrifugal torques, with
nxn dimension. 𝐺(գ) : is for gravity torques, with nx1 dimension. գ: is the joint position (or joint angle), for
գ = [գ1, գ2, … գ𝑛 ], գ̇:is consider as n- vector for joint velocities, գ̈: is consider as n- vector of accelerations.
And τ: is consider as the joint force vector (torque). [գ̇2]: that can a vector given by [գ̇1
2
, գ̇2
2
, … … գ̇𝑛
2 ]𝑇
, [գ̇գ̇]:
that can a vector given :[գ̇1գ̇2, գ̇1գ̇3, . . գ̇1գ̇𝑛, գ̇2գ̇3 … . ]𝑇
. The input of the dynamic system is torque matrix in
the robotic manipulator arrangement while the outcomes are real variables displacement and joints, as a result
it can be written is being as:
գ̈= 𝐴−1(գ). [𝜏 − 𝑁 (գ գ̇)] (5)
All the parameters of the forward and inverse kinematics and matrix of PUMA robot have been
computed as mentioned in [2], [22], [23]. In this work only the first, second and third links of PUMA robot
manipulator will be taken into consideration. Figure 2 illustrates the block diagram for dynamic and
kinematics model for PUMA robot manipulator.
Figure 2. Block diagram for dynamic and kinematics model for PUMA robot
5. METHOD OF DESIGNING SLIDING MODE CONTROL SMC
SMC is applied to impose the system’s state path to pass through the sliding surface, then imposes
the state's system path to ''slide" along the switching surface till it stays on the origin [4]. In order to define
the equation that control the total design of SMC, the nonlinear input single for dynamic system define is
being as:
𝑍𝑛= 𝛿 (Ζ) +𝑏(Z)𝜐(𝑡) (6)

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where (υ) is consider as the vector of the control input , 𝑍𝑛 is the 𝑛𝑡ℎ derivative of the state vector 𝑍. δ is
consider as unknown nonlinear function or uncertainty of dynamic, 𝑏(Z) is switching [𝑆𝐼𝐺𝑁] function. The
key objective of designing SMC is to train the appropriate state desire position 𝑍𝑑 according to the actual
joint variables, the trucking error vector will be defined is being as [3], [5].
𝑒 =Z
̃ = Ζ – 𝑍𝑑 (7)
where: Ζ is for real and actual position, 𝑍𝑑 is the desired position, and 𝑍
̃ : is for estimated trucking error
vector. According to the theory of the sliding mode controller, sliding surface is the key important part to
design this controller, the calculation of time varying for sliding surface S (z, t) , and the integral part of
sliding surface is shown is being as:
𝑆(𝑧, 𝑡) =(
𝑑
𝑑𝑡
+ 𝜇)
𝑛−1
(Z
̃)=0 (8)
𝑆(𝑧, 𝑡) = (
𝑑
𝑑𝑡
+ 𝜇)
𝑛−1
(∫ Z
̃
𝑡
0
𝑑𝑡) =0 (9)
μ is the sliding surface slope coefficient and it is positive constant, in this method the main target is to keep
the sliding surface slope near to zero. Therefore, best strategies to achieve this is to find the input control υ
outside the sliding surface and remains on it. To keep the 𝑆( 𝑒 , 𝑒̇ ) close to zero, the law control is design to
achieve the sliding condition of Lyapunov function [4], [6], is being as:
𝑉 =
1
2
𝑆2
≥ 0 (10)
So, the time derivative becomes 𝑉̇ =(𝑆̇2
𝑆) and the control 𝑢 is chosen such that:
𝑆̇2
𝑆 ≤ 𝜂 |𝑆| (11)
where 𝜂 is consider appositive constant [3], [6], so the sliding surface will have computed is being as:
1
2
𝑑
𝑑𝑡
𝑆2
(𝑧, 𝑡) ≤ 𝜂|𝑆(𝑧, 𝑡)| (12)
when the surface (𝑆) ≈ Zero .So , error 𝑒=Z
̂=𝑍 – 𝑍𝑑 ≈ Zero . Let us consider that:
𝑆=𝑒̇ + 𝜇 𝑒 (13)
𝑒̇ =
𝑑𝑒
𝑑𝑡
=Ż - 𝑍̇𝑑 (14)
𝑆=(Ż -𝑍̇𝑑) + 𝜇 (𝑍 – 𝑍𝑑) (15)
Derivative of (15), will consider as the change in sliding surface, is being as:
𝑆̇=
𝑑𝑆
𝑑𝑡
=(Z̈- 𝑍̈𝑑) + 𝜇 (Ż-𝑍̇𝑑) (16)
Since : Z̈=𝛿 + 𝜐 So : 𝑆̇ = 𝛿 + 𝑈 - 𝑍̈𝑑 + 𝜇 ( Ż - 𝑍̇𝑑) (17)
By imposing 𝑆 → 0 also 𝑆̇ → 0 , If we put 𝑆̇ = 0, in (17), as shown in
0 = 𝛿 + 𝑈 - 𝑍̈𝑑 + 𝜇 (Ż- 𝑍̇𝑑) (18)
where 𝛿 is the uncertainty of dynamic, under this hypothesis we get the best approximation for control (𝑈
̂)
which can be define as:
𝑈
̂ = - 𝛿
̂ +𝑍̈𝑑 - 𝜇 (Ż- 𝑍̇𝑑) (19)
Using the uncertainty switching control low to control the dynamic parameters of sliding mode:

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𝑈𝑑𝑖𝑠=𝑈
̂ –𝐾(𝑧, 𝑡)𝑆𝑆𝑖𝑔𝑛 (20)
where 𝐾: is a positive constant function of ( 𝑧 ,𝑡), and 𝑆𝑆𝑖𝑔𝑛 is the switching function define is being as:
{
𝑆𝑆𝑖𝑔𝑛 = 1 𝑖𝑓 𝑆 > 0
𝑆𝑆𝑖𝑔𝑛 = 0 𝑖𝑓 𝑆 = 0
𝑆𝑆𝑖𝑔𝑛 = −1 𝑖𝑓 𝑆 < 0
(21)
Keep the 𝑆(𝑒, 𝑒̇) close to zero in order to satisfy the sliding condition of Lyapunov function. So (9)
and (61) can be arranged is being as:
1
2
𝑑
𝑑𝑡
𝑆2
(𝑧, 𝑡)=𝑆̇ 𝑆=[𝛿 − 𝛿
̂ − 𝐾 𝑆𝑆𝐼𝐺𝑁] 𝑆 = (𝛿 − 𝛿
̂) 𝑆 − Κ|𝑆| (22)
𝑆(𝑧, 𝑡) = (
𝑑
𝑑𝑡
+ 𝜇)
2
(∫ Z
̃
𝑡
0
𝑑𝑡) =(Ż − 𝑍̇𝑑)+2𝜇(Ż − 𝑍̇𝑑)+𝜇2
(𝑍– Z𝑑) (23)
So, the approximation of 𝑈
̂ is computed is being as:
𝑈
̂ = - 𝛿
̂ +𝑍̈𝑑 - 2 𝜇 (Ż- 𝑍̇𝑑 ) + 𝜇2
(𝑍 – 𝑍𝑑) (24)
The SMC for robot manipulator with multi DOF is being as. Figure 3 shows the total of the 𝜏𝑇𝑜𝑡𝑎𝑙:
𝜏𝑇𝑜𝑡𝑎𝑙 = 𝜏𝑒𝑞 + 𝜏𝑑𝑖𝑠 (25)
Figure 3. Block diagram for the total equation of the torque in SMC of PUMA robot manipulator
Finally, the dynamic model of PUMA robot manipulator can be computed is being as [4], [6]:
𝜏𝑒𝑞=[ 𝐴-1
(𝐵 + 𝐶+ 𝐺 ) + 𝑆̇ ] 𝐴 (26)
𝜏𝑑𝑖𝑠 = 𝐾 𝑆𝑆𝑖𝑔𝑛 (27)
𝜏𝑇𝑜𝑡𝑎𝑙 = 𝜏𝑒𝑞 + 𝐾 𝑆𝑆𝑖𝑔𝑛 (28)
𝜏𝑇𝑜𝑡𝑎𝑙=[𝐴−1
( 𝐵+ 𝐶+ 𝐺 ) + 𝑆̇] 𝐴 + 𝐾 .𝑆𝑆𝑖𝑔𝑛 (29)

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5.1. Modified integral approach for sliding mode controller (ISMC)
In order to enhance the performance designed of the proposed controller scheme which is based on
SMC, besides improve stability and minimize total error, integral sliding mode controller (ISMC) was
designed, our goal is to keep the sliding surface close to zero all the time [4], [6], [10]. The formula that
defines ISMC surface is being as:
𝑆𝐼𝑛𝑡𝑒𝑔𝑟𝑎𝑙 = 𝜇𝑒 + 𝑒̇ + (
1
2
)2 ∑ 𝑒 (30)
In the SMC model, two parameters (K, μ) must be adjusted. If these parameters are appropriately
changed, the controller will reject external disturbances disrupting the tracking path and increase the torque
of the robot joints. PSO and SSO are the two algorithms that used in this work to pick the best values to the
parameters of both SMC and ISMC. Figure 4 shows the total output torque for ISMC design.
Figure 4. Block diagram illustrates the design of ISMC of PUMA robot manipulator
6. INTELLIGENT SWARM OPTIMIZATION ALGORITHMS
6.1. Particle swarm optimization (PSO)
Particle swarm optimization (PSO) algorithm used initial random solutions called particles, which
fly over the search space size by following the obtained optimum particle and their own acquired
experiences. The principle of this optimization is to use its best known positions of particles to converge the
swarm population in the solution space to a single optimal. The PSO algorithm requires, at each point,
changing the location and velocity of the particle to its 𝑃𝑏𝑒𝑠𝑡 and 𝐺𝑏𝑒𝑠𝑡 for each particle, the velocity is
modified iteratively by its personal best position, which is found by the particle, and also by the best position
found by the particles in its vicinity [24], as shown in (31), (32):
𝜁𝑖,𝑔
(𝑘+1)
=Φ . 𝜁𝑖,𝑔
(𝑘)
+ 𝑐1 𝜑1 (𝑃𝑏𝑒𝑠𝑡𝑖,𝑔 – Χ𝑖,𝑔
(𝑘)
) + 𝑐2 𝜑2(𝐺𝑏𝑒𝑠𝑡𝑖,𝑔 – Χ𝑖,𝑔
(𝑘)
) (31)
Χ𝑖,𝑔
(𝑘+1)
=Χ𝑖,𝑔
(𝑘)
+ 𝜁𝑖,𝑔
(𝑘+1)
(32)
where:𝑖: is for particles number. 𝑔: for dimensions’ number. = which are two for SMC. Χ𝑖 : is for 𝑔-
dimensional position vector ( Χ𝑖1 , Χ𝑖2 , . . , Χ𝑖𝑔). 𝜁𝑖 : velocity of the particle (𝜁𝑖1 , 𝜁𝑖1 , ….., 𝜁𝑖𝑔). 𝑃𝑏𝑒𝑠𝑡 : best
visited position for the particles. 𝐺𝑏𝑒𝑠𝑡 : best position explored in the population. 𝜑1 𝜑2 : consider as random
integer between 0 and 1. Φ : inertia weight. 𝑐1 𝑐2: positive constants. 𝑘 : for iteration pointer. Coefficients
𝑐1𝑎𝑛𝑑 𝑐2 include the relative weight of the probabilities that accelerate each particle in 𝑃𝑏𝑒𝑠𝑡 and 𝐺𝑏𝑒𝑠𝑡
position. Sufficient choice of inertia weight (Φ) will allow for a balance between global and local
exploration, which enables reduced aggregate iteration in order to find a fairly optimum solution. Table 1
illustrates the global pseudo code for PSO [25].

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Table 1. Global pseudo code for PSO algorithm
Step No. Description
1 Generate random initial population and initial parameters (initialization of individuals).
2 While not (The population converges towards the desired and optimum solution or the ultimate iteration obtained).
3 For each dimension in the particle
4 Update particle velocities using ( 31)
5 Update particles positions using ( 32 )
6 Evaluate fitness function ( Χi,g
(𝑘)
)
7 If function( Χi,g
(k)
) < function(Pbesti,g) then (Pbesti,g) ← Χi,g
(k)
8 End If
9 If function( Χi,g
(k)
) < function(Gbesti,g)) then function(Gbesti,g) ← Χi,g
(k)
10 End If
11 End If and Loop (Next generation)
6.2. Social spider optimization (SSO)
The SSO algorithm recognizes two search agents, or two genders of male and female in spider’s
webs. Each entity is accomplished with a different set of evolutionary operators, based on the gender, which
simulate different cooperative activities normally seen in the colony. It is observed that, within a certain
range of distance, dominant males mate with their female neighbors and non-dominant males remain in a
position close to other network males and rely on nutrients for the latter. In addition to mating, spiders
communicate with each other by vibrations and the frequency of the vibrations depends on two important
factors: the heaviness of the spider and the distance between the spiders that communicate [26]. The male and
female spiders are the search agents whose population can be determined as:
𝑁𝑓=[(0.9 − 𝑟𝑎𝑛𝑑 ∗ 0.25) ∗ 𝑁𝑘] (33)
𝑁𝑚=𝑁𝑘 − 𝑁𝑓 (34)
where: 𝑁𝑘, 𝑁𝑓, 𝑎𝑛𝑑 𝑁𝑚 denote the total population of all spiders in the communal web, reflecting the number
of female spiders and male spiders respectively. The weight that represent the heaviness of each spider in the
population 𝑊𝑖 is found is being as:
𝑊𝑖 =
𝑓𝑖𝑡𝑛𝑒𝑠𝑠𝑖−𝑤𝑜𝑟𝑠𝑡
𝑏𝑒𝑠𝑡−𝑤𝑜𝑟𝑠𝑡
for 0 ≤ 𝑖 ≤ 𝑁𝑘 (35)
where: 𝑖 : represent the population of the web. 𝑁𝑘: The iteration in the total population. 𝑓𝑖𝑡𝑛𝑒𝑠𝑠𝑖, 𝑏𝑒𝑠𝑡 and
𝑤𝑜𝑟𝑠𝑡 are objective function values. In the common popular web, the spiders connect with each other’s by
using the vibrations that calculated is being as:
𝑉𝑖,𝑗 = 𝑊
𝑗 ∗ 𝑒−𝑑𝑖,𝑗
2
(36)
where: 𝑊
𝑗 : is related to the heaviness of the spider that transmits the vibration. 𝑑𝑖,𝑗 : is considered as the
Euclidean distance computed between the two interacting spiders. The vibrations between spiders in the web
may be classified depending on the transmitting spider as shown in:
 The situation where the transmitting spider, 𝑆𝑐 is more heavier than the perceiving spider, 𝑖, ( 𝑊
𝑐 >
𝑊𝑖) contributing to vibration 𝑉𝑐,𝑖.
 The situation where the transmitting spider, 𝑆𝑏 is the best heaviest one in the web which contributing in
vibration 𝑉𝑏,𝑖 , ( 𝑊𝑏= max 𝑏𝑒𝑠𝑡 (𝑓𝑖𝑡𝑛𝑒𝑠𝑠𝑖)).
 The situation where the transmitting spider, 𝑆𝑓 is a female neighbor contributing in vibration 𝑉𝑓,𝑖.
The location of the female and male spiders is modified at each iteration of the optimization
algorithm using the formula is being as [27]:
𝑓𝑖
𝑘+1
= {
𝑓𝑖
𝑘
+ 𝛼 𝑉𝑐,𝑖( 𝑆𝑐 − 𝑓𝑖
𝑘
) + 𝛽 𝑉𝑏,𝑖 (𝑆𝑏 − 𝑓𝑖
𝑘
) + 𝛾 (𝑟𝑎𝑛𝑑 −
1
2
) 𝑖𝑓 𝑟𝑚 < 𝑃𝐹
𝑓𝑖
𝑘
− 𝛼 𝑉𝑐,𝑖( 𝑆𝑐 − 𝑓𝑖
𝑘
) − 𝛽 𝑉𝑏,𝑖 (𝑆𝑏 − 𝑓𝑖
𝑘
) + 𝛾 (𝑟𝑎𝑛𝑑 −
1
2
) 𝑖𝑓 𝑟𝑚 ≥ 𝑃𝐹
(37)
where: 𝛼, 𝛽, 𝛾, 𝑎𝑛𝑑 𝑟𝑚 are consider as random numbers, that are between [0 or 1]. 𝑃𝐹 is regarded as the
threshold of probability factor that is matched with all the randomly produced numbers while the spiders will

3951
travelled in the space. So, the transition is randomly regulated by the 𝑃𝐹 factor of likelihood and the motion
is generated in relation with the other spiders depending on their vibration through the space of search. In the
optimization procedure the male spider 𝑚𝑖
𝑘+1
, will operated is being as [26]:
𝑚𝑖
𝑘+1
= {
𝑚𝑖
𝑘
+ 𝛼 𝑉𝑐,𝑖( 𝑆𝑓 − 𝑚𝑖
𝑘
) + 𝛾 (𝑟𝑎𝑛𝑑 −
1
2
) 𝑖𝑓 𝑊𝑁𝑓+𝑖
> 𝑊𝑁𝑓+𝑚
𝑚𝑖
𝑘
+ 𝛼 (
∑ 𝑚ℎ
𝑘
𝑊𝑁𝑓+ℎ𝑖
𝑁𝑚
ℎ𝑖=1
∑ 𝑊𝑁𝑓+ℎ𝑖
𝑁𝑚
ℎ𝑖=1
− 𝑚𝑖
𝑘
) 𝑖𝑓 𝑊𝑁𝑓+𝑖
≤ 𝑊𝑁𝑓+𝑚
(38)
where: (
∑ 𝑚ℎ
𝑘
𝑊𝑁𝑓+ℎ𝑖
𝑁𝑚
ℎ𝑖=1
∑ 𝑊𝑁𝑓+ℎ𝑖
𝑁𝑚
ℎ𝑖=1
− 𝑚𝑖
𝑘
) is considered as the weighted average of the male spider in the web
population. The dominant males, as described earlier, will mate with the females in the mating range, which
is given is being as:
𝑟 =
∑ (𝑝𝑗
ℎ𝑖𝑔ℎ
−𝑝𝑗
𝑙𝑜𝑤
)
𝑛
𝑗=1
2𝑛
(39)
where: 𝑝𝑗
ℎ𝑖𝑔ℎ
𝑎𝑛𝑑 𝑝𝑗
𝑙𝑜𝑤
are assumed to be as the higher and lower initial limits. Table 2 illustrates the pseudo
code for SSO algorithm:
Table 2. The pseudo code for SSO algorithm
Step No. Description
1 Assign the initial parameters value for the SSO algorithm
2 Create the population of spiders and assign memory for them
3 Initial the first position for both male spider and female spider
4 Counting the k iterations in the population ( 𝑁𝑘)
5 While 𝑖 ≤ 𝑁𝑘
6 Calculate the mating radius for both female and male spiders as in (39)
7 Calculating the spiders’ weight as in (35)
8 Calculate the passage of female and male spider’s dependent on mutual female and male
operators as shown in (37) and (38)
9 Conduct mating between dominant males and females
10 Update solutions if there are heavier spider progenies
11 End the loop
7. RESULTS AND DISCUSSION
In this work, the Matlab/ Simulink structure version R2019b and M-File were used to apply the
design strategy of the controller in order to evaluate the performance of the proposed controller design. The
sampling time fixed on ∆t = 0.001 s. PSO and SSO algorithms are used to inspect and refine the parameters
of the controller (K, μ). The algorithms will take the (Χ𝑑𝑒𝑠𝑖𝑟𝑒) as a reference and check each particle in
(Χ𝑎𝑐𝑡𝑢𝑎𝑙) by using the mean square error between them until it reaches the best fitness function with
smallest mean square error, is being as:
𝑀𝑠𝑒 =
1
𝑁
∑ (𝑋𝑑 − 𝑋𝑎)2
𝑁
𝑖=1 (40)
where: N: is number of random samples that were used 𝑋𝑑: is for desire position. 𝑋𝑎: is for actual position.
PSO algorithm is initialized with the following parameters: N=20 birds, Iteration=100, 𝑐1=𝑐2=2, Φ=0.5, and
the k (dimension vector) for SMC and ISMC=2 parameters.
For SSO algorithm the initialized is with the following parameters: Spider=20, Iteration=100, all the
random number [𝛼, 𝛽, 𝛾, 𝑟𝑚] = 1. The upper female percent=0.9, lower female percent=0.65. The total time
for implementation is 100 Sec. Only the first three links of PUMA robot were being considered in this work.
Figure 5 shows the step response for the first, second and third links for the robot, from which it can
be seen that ISMC/SSO has the best response with nearly zero maximum overshoot and stable steady state,
minimum settling time, and near zero mean square error comparing with the ISMC/PSO. Figure 6 shows the
final torque in the third links with ISMC/SSO, and ISMC/PSO techniques, it can be noticed that the torque
response becomes more stable besides eliminating the chattering phenomena. Table 3 shows the
configuration of the range for the initial values of the parameters (K, μ) for ISMC, the values after
optimization with PSO, and the values after optimization with SSO.

 ISSN: 2088-8708
3952
(a) (b)
(c)
Figure 5. The step response for the first, second and third links (a, b, c) for the robot
(a) (b)
(c)
Figure 6. The final torque in the first three links (a, b, c) with ISMC/SSO, and ISMC/PSO techniques

3953
Table 3. The configuration of the basic values for the parameters range of ISMC
The Parameters Initial Value Optimization with PSO Optimization with SSO
𝐾 30 489.2526 70.9456
𝜇 2 4.4726 9.3382
7.1. Robustness test
In order to test the robustness of the proposed techniques, a white Gaussian noise predefined of 40%
power from the input signal was introduced to the system between 5 s to 10 s. Figure 7 shows the effect of
the disturbance noise on the response signal for the three links, we can notice that a slight oscillations occur
in the trajectory response of the links. Figure 8 shows the iteration of SSO and PSO algorithms with mean
square error and objective function, from which it can be seen that SSO successively iterates until it reaches
the optimal value for parameters, with best fitness=4.4876 𝑒−6
. Besides PSO has best fitness=3.4948 𝑒−4
. In
order to evaluate the performance of the proposed techniques, a comparison were made with some existing
methods. Table 4 shows a comparison with existing approaches specifically used to operate with robot
manipulator in order to verify the validation of the proposed controller techniques in terms of robustness and
stability, these techniques are shown in [11], [12], [17].
(a) (b)
(c)
Figure 7. The effect of disturbance of a white Gaussian noise for the first three links (a, b, c)
Figure 8. Iteration and objective function for SSO and PSO algorithm

 ISSN: 2088-8708
3954
Table 4. Comparison between proposed techniques and existing methods
Category The Techniques Mean Square Error
1 Proposed method ISMC /SSO 4.4876 𝑒−6
2 Proposed method ISMC /PSO 3.4948 𝑒−4
3 Adaptive fuzzy SMC 0.0016
4 Fuzzy SMC 0.0001
5 Estimated SMC 0.00172
6 Super-twisting of sliding mode controller STSMC 0.00085
7 Impedance controller /PSO 0.00208
7.2. Discussion
The results demonstrate significant response with almost zero maximum overshoot and stable steady
state with the ISMC and SSO optimization algorithm compared with the ISMC/PSO, the oscillations are
dampened faster, besides reduce the chattering phenomenon. The torque reaction becomes more stable. The
comparison with the existing techniques shows that ISMC/SSO has the best fitness.
8. CONCLUSION
This work introduces an optimal technique and robust control strategy based on conventional SMC,
and integral sliding mode control (ISMC) with two novel swarm intelligent algorithms, SSO and PSO, to
control the first three links of PUMA robot manipulators. Therefore, the evolutionary algorithms SSO and
PSO are used to determine the optimal values for the parameters of the proposed controllers such that the
suggested techniques trajectory response is ensure the stability and robustness for variable conditions that
affect the end effector of the robot manipulator. Thus, the developed method effectiveness was observed by
simulations, where a comparison with the conventional SMC has been done. The simulation results
demonstrated that the proposed ISMC/SSO offering high performance in term of step response, stability, and
smoothness of control signal despite disturbance noise, with minimum mean square error and best fitness
compared to the other existing techniques.
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BIOGRAPHIES OF AUTHORS
Suhad Haddad received her BSc in Electronic and Communication Engineering from
Department of Electrical and Electronic Engineering at University of Technology.She received
her Higher Deploma in Computer Enginnering at University of Technology in2000 .She received
her Master’s degree from the Electrical and Electronics Engineering Department at the
University of Technology in2015.Ph. D student in Electronic and communication Department at
the University of Technology, Baghdad, Iraq.Her research activites in ANN, image processing,
electronic circuits, robotic system.Having 15 years of teaching experience.
Hanan A. R. Akkar received her Bachelor’s Degree from the Electrical and Electronics
Engineering Department at the University of Technology in 1988. She received her Master’s
degree and Ph.D. degree from the Electrical and Electronics Engineering Department at the
University of Technology in 1994 and 1998, respectively. She has been Professor in the
Department of Electrical Engineering at the University of Technology in the filled of ANN, FL,
GA and swarm intelligent based on FPGA and electronic circuits. Currently she is Head of
scientific Upgrade committee in the University of Technology.

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