IAES International Journal of Artificial Intelligence (IJ-AI)

Received Aug 12, 2021 Revised Jun 30, 2022 Accepted Jul 29, 2022 This paper presents a new approach to control the position of the microrobotics system with a proportional-integral-derivative (PID) controller. By using sparrow search algorithm (SSA), the optimal PID controller indicators were obtained by applying a new objective function namely, integral square time multiplied square error (ISTES). The effeciency of the proposed SSAbased controller was verified by comparisons made with grey wolf optimization (GWO) algorithm-based controllers in terms of time. Each control technique will be applied to the identified model using MATLAB Simulink and the experimental test facility was conducted using LabVIEW software. The simulation and experimental results show that the performance of SSA-PID controller based on ISTES cost function achieves the best performance among various techniques. Moreover, the SSA technique had the highest performance compared to GWO technique based on rising and setting time and many other performance measurements. Thus, it is recommended to apply SSA for tuning the parameters of PID as it can enhance its performance in micro-robotic systems. It was found that the amount of error is reduced by 50% using SSA than other former experiments.


INTRODUCTION
Minimally invasive surgery (MIS) emphasizes declining the trauma of surgical patients [1]. Also, it makes the clinicians deep-seated every site in the body of the human. Besides, the patient may devote a smalltime amount in hospitals, and such may protect a worthy amount of money. One of the likely current surgeries' kinds utilized or implemented today is surgery as laparoscopic. They inserted instruments into the body of humans are through some incisions being small, and the operation is done according to images that are reserved through a camera that is closely attached to the instrument. Figure 1 shows the variance for the two methods of surgery.
The robots usages of MIS are of an advantage to medicine through invasiveness minimizing of MIS. Also, it facilitates the previous treatment of inoperable patients. Such systems as robotic may be implemented to accurately guide the needles to the site as specified in the body of the human. It is associated with the organs as natural in the body of humans according to veins, arteries, and the gastrointestinal tract. They utilize them to aim target as specific needed for treatment, diagnosis, and drug delivery. If the robot came to of smaller size, 1396 the depth of penetration may be elevated inside the body of the human. Such will cause efficient medicine travel pathways to be smaller to achieve their goal. Keuning et al. [2] constructed a controlling system for the spherical site of the paramagnetic microparticles with 100 diameters as average. The system arrived at the control position with a settling error of a maximum of 8.4 on a step response experiment with the hollow coil. Extra over, Farag et al. [3] implemented the same experiment with a solid coil and attained a maximum settling time equal to 8 according to an auto-tuned control system. In our suggested study, the same experiment was done in [3] It may be noticed that the maximum settling error attained is 4 . It may be noticed that the amount of error is reduced by 50% than other previous experiments through the Sparrow search algorithm.
For meeting such control goals, the suitable design of a controller is of a vital role. Despite developments in control methods, the controller as proportional-integral-derivative (PID) is still utilized widely in the industry because of its recognized benefits i.e., as not hard to understand because of its just 3 parameters being tunable, the structure being simple, and implementation ease [4]- [8]. Nevertheless, the proper PID tuning as controller gains to achieve optimum performance is quite not easy. Over time, numerous heuristics approaches of design have been suggested. Ziegler and Nichols are among them, some of the most popular customary PID control methods. Generally, it is not easy to get the greatest-tuned gain for achieving the greatest performance through Ziegler and Nichols approach. Likewise, the method of tuning according to the customary method needed extra calculations mathematically that render the system extra complex [9], [10]. To avoid the mentioned problem, recent artificial intelligence-based optimization and tuning methods are favored for controller parameters optimization.
To support meta-heuristic algorithms, optimization techniques are now being used in different engineering fields. The reason of which is that these techniques are very flexible, easy to implement, and do not require gradient information. There are two main categories of meta-heuristics techniques which include population-based algorithms and single-based algorithms. On every run, a single-based optimization algorithm generates a single optimal solution which is also known as trajectory algorithms. Another category is the population-based optimization algorithm which involves the generation of a series of multiple solutions with redundancy. These solutions are further divided into five main categories including physics-based, chemicalbased, evolutionary-based, human-based, and swarm intelligence-based algorithms of optimization [11]- [17], [18]- [24].
The current study involves an optimization algorithm called the Sparrow search algorithm (SSA) which has been developed quite recently. SSA has been used by micro-robotic systems to tune the PID controller which is essential to reduce the robustness of integral square time multiplied error square (ISTES). Among the optimization algorithms, SSA is preferred because it is efficient in the frequency and time domain. In this paper, section 2 is about the description of the system and different PID controller types, section 3 is about the details of optimization techniques, section 4 involves the results of simulation and experiment, while sections 5 and 6 include the discussion, conclusion, and future work regarding SSA. These data are collected based on the experimental setup, in which some of experimental results were reported and published in Ref. [3], and this work study is an extension of this work with advanced optimization techniques.

RESEARCH METHOD 2.1. Mathematical model
The particle is constructed of a paramagnetic material, and it needs Fe2O3 in lactic acid. Such particle is of 100 diameters. The velocity of particles is associated with 2 chief factors. Such factor(s) is the viscous drag force and the force as magnetic applied for micro-particles based on the need field as magnetic through coils. If acceleration arrives at 0, velocity as a maximum is attained, thus, the force as magnetic will be equivalent to the drag viscous force. The magnetic force may be designated, Since is designated as particles volumes, whereas B is recognized as the magnetic density of flux. B associated with the time and distance, , and are constants. The previous volume of the formula may be substituted to get the force formula as shown in (2), Since is recognized as the micro radius of particles, whereas the force of drag is signified through as shown in (3), Since is viscosity, in which is designated as micro-particles velocity, and according to 2 nd law of Newton motion, Using (4), the maximum velocity takes place if the acceleration of the particle is equal to zero. The velocity as a maximum is designated utilizing (5), Lastly, the particles are regarded as spheres being perfect. It is stimulated utilizing force as magnetic designated through . A force as drag which associated with the particles' speed in respect to the liquid. If the liquid is stable the drag is then associated with the speed of the particle in respect to the world is fixed. The system of continuous-time model is designated through, Since the drag is designated continuously through drag Stokes of Reynolds being low, is the particle mass and ̇ is the velocity, and ïs the acceleration. The micro-particle transfer role may be signified utilizing (7),

PID controller
One of the chief controller kinds which are needed in the practice of industry is the proportionalintegral-derivative as idyllic (ideal-PID) [4]. Such controller develops the error of state as steady and transient. The PID as ideal loses the higher enactment in the case of the disturbances. Such controllers are recognized as customary ones.
Since the proportional, integral, derivative is designated in the previous formulation is signified utilizing the , , and correspondingly. The general intelligent controller PID structure is illustrated in Figure 2(b). The chief PID controller components are the role of fitness, methods of optimization, sensor, and process.

Fitness function
To design any type of controller there must exist many optimum control parameters. These parameters are estimated by reducing the objective function. These objective functions are selected for reducing the time response features because of the error on time dependency ISTES. The role of fitness designated at the existing work is according to the ISTES for the simulation performance evaluation [25]- [27]. The ISTES fitness function is estimates from (9).
The optimization problem can be formulated using the following rules, Minimize (Objective function) Subjected to, < < < < < <

Optimization techniques
Meta-heuristic techniques are mainly divided into two main algorithm categories: single-based and population-based algorithm. Single-based algorithm is capable of generating a single optimal solution on every run. It is also called trajectory algorithm, and it is enhanced when a neighboring methodology is used. The population-based algorithm generates multiple solutions on every run and is further classified into five types: Swarm intelligence, human, physical, chemical, and evolutionary-based algorithms. In this evolutionary-based algorithm, the techniques use three main operations:Mutation, recombination, and selection. These techniques are inspired by nature's evolutionary phenomenon. For a swarm intelligent algorithm, the information is gathered on the basis of a collective behavior adopted by nature. Physical-based algorithm gathers information according to different theories obtained from the multiverse concept. Chemical-based algorithm uses chemical compounds and chemical rules for optimization while humans and their actions are associated with humanbased algorithm. Population-based algorithms have a standard feature in common as per their nature, and the search processes in such algorithms are categorized into two phases:Exploitation and exploration [28]- [32]. The methodologies of optimization used in this study include grey wolf optimization (GWO) and SSA.  [18]. There are four major types of simulations present in the grey wolves hierarchy. These types include Alpha (α) which present the best solution and is the leader, Beta which is the second-best solution and has a role in assisting alpha in any decision process, Delta which is the third-best solution, and Omega is the rest of the population and also considered the worst-ranked [18]. The mathematical equations of GWO are given, In this equation, t depicts the current iteration, whereas and denote the vector of coefficients.
=2 . − In this equation, represents the variable that decreases linearly from 2 to 0 during a series of iteration. This equation represents the vector at random present in the interval from [0 1]. The algorithm then saves the top three best solutions are saved and searched on different search agents with the inclusion of omegas. The position in the best search agents is used to update their position. The beta, alpha, omega, and delta terms are defined by (14)- (16). The pseudocode and flowchart are described in Figure 3(a) and Figure 3

Sparrow search algorithm
As described, SSA is a technique of swarm intelligence optimization technique. The main idea behind this algorithm was inspired by closely observing the sparrow population's behavior and with the concept of foraging [33]. Depending on the behavioral characteristics, sparrows are classified into two groups; producers and scroungers. Producers are the ones who have a larger space to locate the sources of food and the other  (17)- (21).
Step 1: The matrix given is used to determine the position of sparrows.
In the equation presented, d represents the total dimension numbers, and n is the total sparrow number. In case of high energy levels in sparrows, they are called producers, and they are designated to find certain areas which have rich food supplies and to scavenge such zones to scroungers. Sparrow's value of cost is evaluated by (18), Once sparrows locate the producers, alarming signals are produced for other sparrows depending upon the threshold criteria. Producers lead scroungers to a safe destination if the alarm's value exceeds the safety threshold's value. Producers which have the best cost value are most likely to find food as compared to the scroungers. In (19) is used to continuously update the position of producers. In (21) is used to determine the positions of producers. In this equation, is the value of the current global optimal location, K is a random value, α is another random value which is normally distributed with a variance of 1 and mean value 0, and fw is the worst fitness value, and are the current individuals and current global best costs respectively. The pseudocode of SSA and the flowchart are present in Figure 4(a) and Figure 4(b), respectively.

System architecture
The system architecture consists of seven components includes reservoir, coils, microparticles, pantograph robots, real-time controllers, microscope cameras, control algorithms, and power supply units. The microparticle's major components in 2D space would be presented by us as displayed in Figure 5. We utilized the controller of My Rio to arrive to a controller of real-time and for operation in real-time. We utilize four coils for controlling the 2D micro-particle position in the water. A COMSOL software was used for simulating the density of magnetic flux based on X and Y positions for particles coordination. The coil is made of isolated copper wire with a 0.7mm dimension diam., the turns number is 1200. A robot of pantograph contains four links with two encoders for computing the 2 chief angles. The pantograph chief role is to permit the operator to controlling the trajectory of the micro-particle.

SIMULATION AND EXPERIMENTAL RESULTS
This section involves comprehensive details about the investigation of micro-robotics systems' performance by using multiple advanced control methods. Multiple tests are used to examine the execution of different control techniques and their performance. These techniques are examined at a constant position i.e. 1000 µm used as a reference command. A Simulink diagram displaying the different advanced control techniques in a micro-robotic system as shown in Figure 6. Regarding the maintenance and controlling of the micro-robotics system's position at 1000 µm, the parameters of GWO and SSA are presented in Table 1, and the proposed system parameters are listed in Table 2. Besides, Table 3 summarizes GWO and SSA output results based on different fitness functions in the time domain. Figure 7(a) and Figure 7(b) describe the behavior of a micro-robotics system by observing the reference of the position with the best fitness function (ISTES). The minor variance observed between the practical curves and the simulation is due to the card time acquisition delay, system uncertainty, and noise.

DISCUSSION
This section includes a thorough comparison between two methodologies of optimization which have been performed on different measurements in the time domain. The measurements include setting time (ts), rising time(tr ), and settling error. The results of the previously recorded measurements on GWO and SSA are presented in Table 4.

CONCLUSION
This paper includes the main optimization techniques which are used to tune the PID control in a micro-robotic system. It can be concluded that based on a set of different fitness functions to discover the best, the ISTES had the highest performance. A comparison between two main optimization techniques based on GWO and SSA was developed. It has been observed that SSA displays a very good performance when compared with GWO according to their rising and setting time and along with it several other measurements of performances were considered, due to which SSA is recommended to tune the PID parameters. SSA should be preferred over GWO because it enhances the efficiency of the parameter in the systems. It can be seen that the amount of error is decreased by 50% using SSA than other former experiments. For future practices, various optimization approaches such as whale optimization algorithm (WOA), hybrid PSO, Sine Cosine Algorithm (SCA), and flower pollination algorithm (FPA) will need further investigations.