Positioning control of robots using a novel nature inspired optimization based neural network

Positioning control of robots using a novel nature inspired optimization based neural network | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Positioning control of robots using a novel nature inspired optimization based neural network Guo Kai, Bo Zhi, Wang Sai, Ge Jingjing This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3908374/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Positioning control methods for robot arms are offered within a broad framework for the purposes of unification and categorization. In robot control, the issue of Inverse Kinematics (IK) is crucial. Several conventional IK solutions, including geometry, iterations, and algebraic approaches, are insufficient for high-speed solutions and precise positioning. In recent years, the subject of robot IK using neural networks has attracted a great deal of attention, although its precise control is convenient and need improvement. To tackle the IK issue of a UR3 robot, we offer the Global Iterative Sunflower Optimized Binary Multi Layer Perceptron (GISOB-MLP) neural network technique. The GISOB-MLP improves upon previous methods in terms of generalizability, convergence speed, and convergence accuracy. In order to perform medical puncture surgery, which necessitates precise robot positioning to within 1 mm, the study method solves the position error for the UR3 robot IK only with joint angle or less 0.1 degree courses and the output end tool less than 0.1 mm. The study was conducted, and initial results were obtained, with the goal of pinpointing the robot's puncturing application; this laid the groundwork for the robot's eventual widespread use in medical settings. Positioning control Inverse Kinematics (IK) Global Iterative Sunflower Optimized Binary Multi Layer Perceptron (GISOB-MLP) UR3 robot Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Background Robots are being utilized in industrialized and medicinal settings where high levels of precision, repeatability, and stability are essential. Robotics has been extensively applied in new domains, such as medicine, thanks to the advancement of contemporary control technology [ 1 ]. A surgical robot operating system is a combination of several cutting-edge, sophisticated technologies that allows a surgeon to operate on patients without ever having to touch them. For performing puncture surgery on a patient, a minimally invasive surgical robot combines using a robot arm and processing of medical images to meet the minimum intrusiveness, precision, efficiency, and stability [ 2 ]. In the past, the IK problem of the robot has been addressed using the geometrical approach, the algebraic approach, and the optimization algorithm. In order to solve the IK, every solution has its own limitations. The geometrical method, for example, requires that shuttered options exist again for robot's initial three joints, however closed-form solutions for the algebraic methods are not guaranteed. Similar to this, the approach of iterative IK solution converges to a single solution that depends on the initial position [ 3 ]. The computation accuracy cannot be guaranteed for these approaches because they frequently call for powerful computer gear. Academics have been focusing on the application of neural networks that are artificial in the kinematic of the robot as a result of these aspects [ 4 ]. In recent decades, a wide variety of control structures have been included into developed societies to address the limitations of the traditional controllers. Using the idea of differentiators and integrators of fractional power, the proportional integral derivative (PID) controller that have been subject by industrial organizations has been modified [ 5 ]. It was demonstrated that combining more degree of independence with differentiators and fractional power integrators allowed for a higher level of flexibility and performance that would otherwise be challenging or perhaps impossible to achieve with traditional PID controllers [ 6 ]. The fractional-order PID (FOPID) controllers are the generalization of broadly valid PID controllers, and both academia and business have recently given them a lot of attention [ 7 ]. The aim of [ 8 ] was to investigate the shortcomings and demonstrate that they are a result of the conventional direction/angle of bend parameter of the state rather than a result of the piecewise constant curvature assumption itself. The study [ 9 ] was to describe a new route planning approach for aerial robots that enables them to quickly and easily traverse their environments. Planner uses motion primitives to discover acceptable pathways that explore the configuration space, making use of the dynamic flying capabilities of tiny aerial robots, to meet the combined demand for large-scale exploration of tough and constrained situations. The research [ 10 ] introduces a revolutionary, hierarchical local motion planning framework for autonomous vehicles to track a path and deftly sidestep obstacles. This study explores the use of ML approaches, and notably RL in DP applications for deepwater drilling rigs. It is suggested to use a deep Q-learning network in an RL-based DP control technique [ 11 ]. Research [ 12 ] was to provide a new approach for designing unmanned aerial vehicle (UAV) trajectories within the bounds of system positioning accuracy. To minimise the total flight time of the UAV and the number of times it has to make course adjustments, the modified genetic algorithm (GA) and A* algorithm are utilised in the trajectory planning process. Study [ 13 ] details efforts to create a synchronous and endogenous Electroencephalography-based Brain-Computer Interface that may be used to control a mobile robot's mobility in response to the blinking of a person driver's eyelids. Research [ 14 ] offers an approach for managing the movement of soft robots with manipulative and mobile capabilities. Whether the soft robot, its actuators, or its environment is deformable, we employ the Finite Element Method (FEM) to model the resulting changes. The study [ 15 ] introduces a low-cost, ultra-compact, 3D-printed, autonomous field robot for agricultural activities, complete with high-precision control and deep learning-based algorithms for counting corn stands. The study [ 16 ] put out a unique fuzzy-based step-optimal path planning approach. Initially, the spherical mobile robot's motion model was analyzed to finalize the ultrasonic sensors' (HC-SR04) setup and debugging. An alignment and drilling assignment that is part of a piecewise collaborative drilling task is the subject of the present investigation [ 17 ]. Surgeons may be able to execute the procedure faster and with more precision with its help. Intention recognition, which is trained through demonstrations of human-guided force during collaborative drilling, can be used to solve the problem of a virtual fixture (VF) being switched between drilling and aligning. The research [ 18 ] examines the cutting edge of Ultra-wideband (UWB) networking and localization for robotic and autonomous systems. They go discuss cutting-edge methods that use machine learning to increase precision and focus on creating more cutting - edge solutions, collaboration localization strategies, ad hoc networking, and more. The author of [ 19 ], a hybrid adaptive control framework is suggested, which combines offline qualified robot IK with a neural network and online adaptive adaptation of the parameters of the PID controller with some other neural network, giving the cyborg system more driving amount to compensate for tracking error brought on by interference. The study [ 20 ] describes a technique for robotic endoscope holder-assisted endoscopic positioning in minimally invasive surgery. This technique allows the endoscope holder to recognize the surgeon's view projection and move the camera autonomously, which greatly enhances human-robot collaboration in robot-assisted surgery. The goal of the study [21 examine the effects of robot behavior on the social dynamics of a group by observing how a robot interacted with a human and a kid as they solved a task. Children who engaged with the trustworthy robot performed better on the test, while those who interacted with the less trustworthy robot showed more task-related social interactions. The required circular path is put on an inclined plane, the tests in the current study [ 22 ] confirm the notion of the motion of all the robot joints. By positioning analysis on a simulated version of the robot, the established hypothesis is validated in the first portion of the studies. The major goal of this work is to boost the accuracy of the SOA + MLP algorithm's IK solution, particularly for processing data quickly and the duration of the robot's motion. In order to overcome the inherent flaws in the MLP neural network and identify the best solution, the SOA technique is used. This enhances the generalization capability, convergence speed, and meeting precision of the MLP neural network. Contributions to the paper In the simulated study, 950 data sets were used for training the UR3 manipulator and 50 data sets were used for testing in a total data set size of 1000. To tackle the IK issue of a UR3 robot, we offer the Global Iterative Sunflower Optimized Binary Multi Layer Perceptron (GISOB-MLP) neural network technique. Aiming for the exact use of the puncturing robot, the basic test was carried out and preliminary findings were achieved, laying the groundwork for the robot's popularization in the medical field. The paper is laid out as follows. A review of current methodologies is covered in Section II, and proposed methodology is covered in Section III. Section IV presents the results and the discussion; section V presents the research's future potential directions and conclusions. Problem statement Getting the manipulator's kinematics sorted out is the serial robot's biggest challenge, but it's also one that can be overcome. The robot's kinematics may be broken down into two categories: forward kinematics and internal kinematics. Forward kinematics describes the transformations required to move from joint angles to Cartesian coordinates. IK is well-known for its ability to solve joint variables in accordance with the end effectors' positions and postures. Several scientists are devoting their efforts to developing genetic algorithms to determine the robot's IK. The robot's positional inaccuracy and the sum of all joint displacements must be calculated independently due to the way the fitness function is designed. This study seeks to enhance the accuracy of the IK solution generated by a SOA + MLP algorithm in order to address the IK challenge posed by a four-degrees-of-freedom (DOF) serial robot manipulator while the robot is in motion. 2. Proposed methodology 3.1 Precision Positioning of a Puncture Robot-assisted minimally-invasive surgery (MIS) is a less expensive alternative to traditional open surgery that accomplishes the similar ends by inserting surgical tools through a series of small incisions. Figure 1 depicts the basic puncture robot design. An initial CT scan is necessary, and the computer will then create the medical image needed for the 3D reconstruction. The doctor may then use the 3D model to provide an accurate diagnosis based on what they see. The doctor next analyses the patient's skin to locate the puncture target point coordinates and decides where to place the device. The path of puncture is between the intended location and the connection's insertion site. The success of the puncturing procedure is directly proportional to the precision of the chosen puncture path. In this study, the serial robot piercing route was built by research on the manipulator's precision positioning technology. The robot's puncture guide tube-equipped end-effectors keep the robot in the proper position and posture while precisely putting the needle into the patient's skin using measurements that are obtained from the data processing computer and identify the desired location and insertion point. 3.2 Analysis of the UR3 Manipulator The Universal Robots Corporation has developed the new, compact UR3 manipulator, a six-DOF collaborative robot. The UR3 manipulator is a table-top robot that combines flexibility, lightness, safety, and collaboration. The end effectors of the UR3 may morph and rotate because to the six joints in the device. Compared to previous manipulators, the UR3's kinematics analysis is more intricate. There aren't any exact Matlab models available for this robot right now. The exact placement method for surgical medical puncture utilizing the UR3. Figure 2 represents the schematic and frame assignment of UR. The homogeneous robot transformation \(matri{x}_{j}^{j-1}S\) equations ( 1 ) and ( 2 ), which employ four connection parameters, represent a single joint. The D-H notation is the name given to this conversion. $$S={S}_{tran}({v}_{j-1},{c}_{j}){S}_{tran}({y}_{j-1},{b}_{i}){S}_{rot}({y}_{j-1},{b}_{i})$$ 1 $${x}_{j}^{j-1}S=\left[\begin{array}{cccc}d{\theta }_{j}& -{d\alpha }_{j}{t\theta }_{j}& {t}_{\alpha }{t\theta }_{j}& {b}_{j}{d\theta }_{j}\\ t{\theta }_{j}& {d\alpha }_{j}{d\theta }_{j}& {-T\alpha }_{j}{d\theta }_{j}& {b}_{j}{t\theta }_{j}\\ 0& t{\theta }_{j}& d{\alpha }_{j}& {c}_{j}\\ 0& 0& 0& 1\end{array}\right]$$ 2 The matrix of transformations among pairs of neighboring connections \({}_{j}{}^{j-1}S\left(j=\text{1,2},\dots ,6\right).\) Among them, \({b}_{j},{c}_{j},{\alpha }_{j}\) depending just on robot's standard structure parameter ; \({\theta }_{j}\left(j=\text{1,2},\dots 6\right)\) resprent the joint variables, \(d{\theta }_{j}=cos {\theta }_{j},t{\theta }_{j}=sin{\theta }_{j},t{\alpha }_{j}=sin{\alpha }_{j},and d{\alpha }_{j}=cos {\alpha }_{j}\) Thus, When we use the homogeneous linear interpolation, we may use equation to get the linear transformation from the base to a end effectors depicted in Eq. ( 3 ). $${}_{6}{}^{0}S=\prod _{j=1}^{6}{}_{j}{}^{j-1}S=\left[\begin{array}{cc}{}_{6}{}^{0}{Q}_{3\times 3}& {}_{6}{}^{0}{O}_{3\times 1}\\ 0& 1\end{array}\right]=\left[\begin{array}{cccc}{q}_{11}& {q}_{12}& {q}_{13}& {o}_{y}\\ {q}_{21}& {q}_{22}& {q}_{23}& {o}_{y}\\ {q}_{31}& {q}_{32}& {q}_{33}& {o}_{v}\\ 0& 0& 0& 1\end{array}\right]$$ 3 One of them is \({}_{6}{}^{0}{Q}_{3\times 3}\) robotic end effectors rotational grid \({}_{ 6}{}^{0}{O}_{3\times 1}\) , and its coordinates the orientation matrix of a robot end controller, where the components of the position vector and \({q}_{ji}\) denotes the rotational components of the transition \(matrix\left(j \text{a}\text{n}\text{d} \text{i}=\text{1,2},3\right)\text{a}\text{n}\text{d} {o}_{y},{o}_{x},{o}_{v}\) . In this research, we employed six degrees of freedom (DOF) UR3 robot. The six DOF Cartesian location of the end effectors is retrieved directly from the matrix, and the RPY (roll, pitch, yaw) rotation describes the end effectors’ orientation. As can be seen in the Eq. ( 4 ), the angular displacements result from these revolutions from around axis. In this investigation, a six DOF UR3 robot was employed. The end effectors of the manipulator is positioned in a six DOF Cartesian space at positions \((y,x,v)\) , that are directly derived from the \({}_{6}{}^{0}S\) matrix. The end effector's orientation is represented by the RPY rotation. Eq. ( 4 ) illustrates these rotations as angles around the \(V-X-V\) axis. $${Q}_{{V}^{{\prime }}{X}^{{\prime }}{V}^{{\prime }}}\left(\alpha ,\beta ,\gamma \right)=\left[\begin{array}{ccc}d\alpha dd\gamma -t\alpha t\gamma & -d\alpha d\beta t\gamma -t\alpha d\gamma & d\alpha t\beta \\ t\alpha d\beta d\gamma +d\alpha t\gamma & -t\alpha d\beta t\gamma +d\alpha d\gamma & t\alpha t\beta \\ -t\beta d\gamma & t\beta t\gamma & d\beta \end{array}\right]$$ 4 Equations ( 5 )–( 7 ) may be used to compute the angles, which can then be obtained by solving the \({}_{6}{}^{0}S\) matrix: $$\alpha =Btan2({q}_{23},{q}_{13})$$ 5 $$\beta =Btan2({q}_{13}\text{cos}\alpha +{q}_{23}\text{sin}\alpha , {q}_{33})$$ 6 $$\gamma =Btan2({q}_{13}\text{cos}\alpha +{q}_{22} sin\alpha -{q}_{12}sin\alpha )$$ 7 The robot's position, as it relates to the universe's coordinate system, may be determined using this equation. The location and orientation of the robot are described by the coordinates of each joint. Eq. (8) describes the robot's forward kinematics equation; \({E}_{forward kinematics}\left({\theta }_{1},{\theta }_{2},{\theta }_{3},{\theta }_{4},{\theta }_{5},{\theta }_{6}\right)=({o}_{y},{o}_{x},{o}_{v},\alpha ,\beta ,\gamma\) ) (8) Equation (8) demonstrates how to determine the robot's Cartesian coordinate system using forward kinematics after the six joint angles are known. However an industrial application necessitates computing the six joint angles of the robot shown in Eq. (9). \({E}_{forward kinematics}({o}_{y},{o}_{x},{o}_{v},\alpha ,\beta ,\gamma\) ) \(\left({\theta }_{1},{\theta }_{2},{\theta }_{3},{\theta }_{4},{\theta }_{5},{\theta }_{6}\right)\) (9) The joint angles \({\theta }_{j}(j=\text{1,2},\dots ,6)\) will be utilized as the output variables of the MLP neural network in the subsequent section. The input variables for the MLPNN model will be \(\alpha ,\beta ,\gamma ,{o}_{y},{o}_{x},{o}_{v}\) and the joint angles. 3.3 Global iterative sunflower optimized binary MLP (GISOB-MLP) 3.3.1 Sunflower optimization algorithm (SOA) One of the most recent developments in soft computing techniques that draw inspiration from nature is SOA. The basic idea behind the SOA is a repetitive process that simulates sunflowers moving in search of the finest photo opportunities as they follow the light each morning at daybreak. Sunflowers follow the same cycle every day, waking up and moving with the sun like the hands of a clock. They go in the other way at night to wait once more for their departure. The cycle of a sunflower is controlled by the law of radiation as; $${R}_{y}=\frac{{O}_{y}}{4\pi {q}^{2}}$$ 10 Where \({ R}_{y}\) is the amount of heat that each sunflower individual \(\left(y\right)\) receives, \({O}_{y}\) is the amount of solar energy, and \({q}_{y}\) is the separation between each individual and the best member of the present population. The emitted heat and distance have an inverse square relationship, as shown by Eq. ( 10 ). Each sunflower modifies its direction in relation to the sun, as seen in Eq. ( 11 ); $${\overrightarrow{T}}_{Y}=\frac{{Y}^{*}-{Y}_{Y}}{‖{Y}^{*}-{Y}_{Y}‖}, y=\text{1,2},\dots .MO$$ 11 Where \({Y}_{*}\) denotes the top member of the present population, Xx denotes each solution, and NP denotes the population's predetermined amount. The following diagram illustrates how sunflowers migrate across the sun. $${e}_{y}={\lambda }..{O}_{y}\left(‖{Y}_{y}+{Y}_{y-1}‖\right).‖{Y}_{y}+{Y}_{y-1}‖$$ 12 Where \({O}_{y}\left(‖{Y}_{y}+{Y}_{y-1}‖\right)\) the chance that a sunflower will be is pollinate λ, and is a specified constant relating to the inertial movement of each sunflower. The least spacing among each flower and the flower in back is used in SFOA to randomly carry out pollinating. As a result, the sunflower moves into a new position to pollinate, while the sunflowers farther from the sun move normally. The closer sunflowers to the sun make smaller movements to promote the local search improvement. Based on the foregoing, the sunflowers' movement \(\left({e}_{y}\right)\) and orientation \(\left({T}_{y}\right)\) in relation to the sun are used to update each location of a sunflower as follows: $${Y}_{y+1}={Y}_{y}+{c}_{y}+{T}_{y}$$ 13 The fundamental SOA stages summed up in algorithm 1 : Algorithm 1 SOA Step 1 Initialize,, the iterations number (t = 0), and the limitations that are provided (2). Step 2 : Randomly generate the starting population of sunflowers \({(Y}_{Y}\left(U\right))\) . Every sunflower is shown as follows: (2). As a result, each sunflower is made up of concurrent capacitor deployments with certain controls turned on. Step 3 Evaluation of the relevant fitness function (1). Step 4 The finest sunflower with the least OF should be chosen. Step 5 Check to see whether is reached. Extract X∗ and terminate the program if it is satisfied. Step 6 Orient the sunflowers so that they face the sun (11). Step 7 The poorest m% of sunflowers should be eliminated after calculating the orientation vector for every sunflower (10). Step 8 Update the sunflowers in accordance with (13) and the m% sunflowers by generating them at random inside their bounds. Step 9 The counter increments should be raised then go to step 3. 3.3.2 Multilayer Perceptron neural network (MLPNN) A MLPNN was used as the classifier in this study. This choice was decided due to the popularity of MLPNN as a machine learning approach and the large number of MLPNN successful applications. As there are eight amplitude summation inside the feature vector (four for each channel), the classifier's input image consists of a total of eight neurons. There are 4 neurons in the output layer as well since there are 4 classes accessible. There are another two buried levels with a total of 100 neurons each. After a process of trial and error, the number of buried layers and neurons was established. Particularly, 1–3 buried layers were taken into account. Moreover, 20–200 neurons in steps of 20 were evaluated for each layer. 175 distinct network configurations were taken into account altogether. In terms of classification accuracy, it was determined that a two hidden layer network with 100 neurons in each layer performed as anticipated. Figure 3 shows a visual representation of the classifier developed. Rectified Linear Unit (ReLU) is the function that activates the buried layers. ReLU has the benefits of faster training and less suffer from the vanishing grade problem. $$ReLU\left(y\right)=\text{max}\left(0,y\right)$$ 14 The output layers were employed with the sigmoid purpose, which is represented by Eq. ( 15 ): $$\sigma \left(y\right)=\frac{1}{1+{f}^{-y{\prime }}}$$ 15 This restricts the [0, 1] range of each layer's output. This indicates that every neuron in the output layer generates odds that the input will be one of the 4 instructions. A control is chosen based on which has the best chance of succeeding. Binary cross-entropy, a frequently used loss function in binary classification issues, is the method used to calculate the prediction error of the network during training. It's characterized as $$K=\frac{1}{M}[{x}_{m}.log{\widehat{x}}_{m}+\left(1-{x}_{m}\right).\text{log}\left(1-{\widehat{x}}_{m}\right)]$$ 16 Where N is the sample size, yn denotes the desired output, and yn denotes the projected result. Last but not least, Adam, with the default hyperparameter settings, is an optimization technique that modifies the weight of each neuron to lower the forecast error. Using the Keras API and TensorFlow, all models were trained. 3. Results and Discussion The method is trained using the test data in conjunction with the MLPNN optimized using the SOA [ 21 ]. Using the UR3 manipulator in a workspace containing one thousand data sets, 950 sets were selected as training samples for a simulated experiment and 50 sets were used as test samples. In order to maximize convergence, the SOA was applied to the weights and thresholds of the MLP neural network, which was then used to train the six robot joint angles in a loop, yielding 50 training sets from which to draw a single output prediction sample. The MLPNN was trained using samples of the UR3 robot's end-position coordinates and Euler angles, and the UR3 robot's six joint angles were utilized as the prediction sample. During training, the MLPNN uses the UR3 robot's position vector and rotation angle as input points, and the values of the 6 joint angles as output points. As the fitness function is optimized, the SOA method is applied. The MLPNN weights and thresholds are determined through SOA, and the output value of each joint variable is determined by simulation. Table 1 displays the test set error range and Mean Square Error (MSE) that we get for the trained network. The MLP neural network had an error range of [-0.3061, 0.4132], and the MSE was in the range of [6.73 × 10 − 3 , 8.13 × 10 − 2 ] for a set of 50 joint angles, whereas the GISOB-MLP had an error range of [-0.1861, 0.1081] and the MSE was in the range of [2.40 × 10 − 4 , 6.44 × 10 − 3 ]. The output robot joint angle error 4 is compared between the MLP neural network and the GISOB-MLP neural network in Fig. 4 and Fig. 5 . MSE for the two techniques is shown in Fig. 6 . The experimental findings demonstrate that a significant improvement in MSE occurs after comparing the machine arm acquired by IK of the robot to the MLP neural network joint angle error at a greater extent. The manipulator's efficacy is validated by solving its inverse kinematics using GISOB-MLP. Table 1 Error ratio test set and MSE Joint Angles and MSE (Mean Square Error) MLP GISOB-MLP ∆θ 1 ∆θ 2 ∆θ 3 ∆θ 4 ∆θ 5 ∆θ 6 MSE −0.2005–0.4132 −0.2100–0.1954 −0.2178–0.2046 −0.3061–0.2178 −0.2376–0.1661 −0.2376–0.3168 6.73 × 10 − 3 –8.13 × 10 − 2 −0.0534–0.065 −0.1199–0.0605 −0.0672–0.0704 −0.0486–0.0508 −0.1861–0.0526 −0.0658–0.1081 2.40 × 10 − 4 –6.44 × 10 − 3 Proportional Integral Derivatives and Particle Swarm Optimization Algorithm (PID-PSOA), Fruit Fly and Particle Swarm Optimization (FF-PSO) and Inequality and Equality Constrained Optimization Recurrent Neural Network (IECORNN) are the Existing approaches are utilized to assess the effectiveness of our suggested methods and performance measures like as accuracy and MSE. Table 2 represents numerical results for proposed and existing methods. Table 2 Numerical results for proposed and existing methods Methods Accuracy (%) MSE (%) PID-PSOA [ 24 ] 89 52 FF-PSO [ 25 ] 91.42 47.36 IECORNN [ 26 ] 85 42.1 Proposed 98 34.2 Accuracy is essentially how well a positioning system's displacements adhere to predetermined length criteria. It is reasonable to categories positioning model accuracy into two groups: (a) the accuracy of the route itself, and (b) the linear positioning accuracy along the route. The former discusses how well a single axis translation is provided by a way, while the latter is concerned with the accuracy of incremental motion along the axis. While our proposed method has a higher in accuracy when compared to the existing methods. Figure 7 represents the accuracy. The mean squared error (MSE) measures how well a regression line matches a set of data points. The expected value of the squared error loss is a risk function that represents this quantity. MSE is calculated by taking the average (or more accurately, the mean) of all the squared mistakes in the data set for a given function. Current approaches have larger MSE, but the suggested method has lower ones. The MSE is depicted in Fig. 8 . Discussion PID-PSOA was still issues with certain control systems that must be resolved, and further investigation into robustness and universality is required. The controller also has to be more accurate and quicker to respond. The optimal parameters are found by adjusting the fuzzy controller in such a way that the actual size of the quantized component factor is changed [ 24 ]. When a FF-PSO is tasked with following a predetermined course, it encounters tracking error for a variety of reasons, including but not limited to: sound, trouble, slippage, and the errors detected by sensors due to both internal and external sources. Due to these issues, the mobile robot has difficulty following instructions to shift routes or using other sensors to find its way [ 25 ]. IECORNN are combat the issue of excessively high joint velocities and accelerations for redundant robot manipulators using the DQP formulation and neural network solver, IECORNN introduced and researched a novel positioning control strategy with mutually joint velocity and joint acceleration reduction. In spite of this, it has been shown that the aforementioned solutions obtained by the optimization strategy based on the DQP only have the asymptotic convergence feature [ 26 ]. The suggested approach outperforms the existing methods in addressing the aforementioned problems. 4. Conclusion In this study, we describe a hybrid method for solving the IK issue for a six-degree manipulator that uses end-effector error reduction and the GISOB-MLP. The suggested method uses SOA features to address the shortcomings of the MLP neural network, resulting in enhanced convergence accuracy, convergence speed, and generalization ability. The six DOF robot arm is complicated, making it hard to acquire high-precision IK solutions for a variety of reasons. These include, but are not limited to, high computational complexity, lack of assurance of accuracy, lengthy calculation time, and so on. It would be very helpful in this situation to employ the recommended strategy to increase the accuracy of the GISOB-output. MLP's Compared to a purely MLPNN, the GISOB-MLP is an order of magnitude more efficient in reducing both joint error and MSE. This technique is being used in a novel way in the field of precise positioning in medical puncture surgery to address a number of problems associated with traditional puncture procedures, such as a lack of reliability, high patient pain, a heavy reliance on the physician's expertise, and a need to perform a lot of manual labor. It has been shown to meet the requirements of precise placement in medical needle surgery, and it has both theoretical and practical significance in the study of the basic technologies behind accurate puncturing robots. Declarations Ethics Approval and Consent to Participate: No participation of humans takes place in this implementation process Human and Animal Rights: No violation of Human and Animal Rights is involved. Data availability statement: Data sharing not applicable to this article as no datasets were generated or analyzed during the current study Conflict of Interest: Conflict of Interest is not applicable in this work. Authorship contributions: All authors are contributed equally to this work Acknowledgement: There is no acknowledgement involved in this work. Funding information The Research Platform of Anhui Provincial Engineering Laboratory on Information Fusion and Control of Intelligent Robot under grants.(IFCIR2020005) Fund number: （IFCIR2020005） Fund level: Provincial level ② The Research Platform of Suzhou University under grants (2022ykf29，2022ykf27，2022ykf30) Fund number: (2022ykf29，2022ykf27，2022ykf30) Fund level: School level ③ Suzhou university key project（2022yzd07） Fund number: （2022yzd07） Fund level: School level References Lindner, T., Milecki, A. and Wyrwał, D., 2021. Positioning of the robotic arm using different reinforcement learning algorithms. International Journal of Control, Automation and Systems, 19(4), pp.1661-1676. Xiwei, W.U., Bing, X.I.A.O., Cihang, W.U., Yiming, G.U.O. and Lingwei, L.I., 2022. 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A novel local motion planning framework for autonomous vehicles based on resistance network and model predictive control. IEEE Transactions on Vehicular Technology, 69(1), pp.55-66. Wang, F., Bai, Y., Bai, J. and Zhao, L., 2022. Deep reinforcement learning in dynamic positioning control: by rewarding small response of riser angles. Ships and Offshore Structures, pp.1-8. Korovesis, N., Kandris, D., Koulouras, G. and Alexandridis, A., 2019. Robot motion control via an EEG-based brain–computer interface by using neural networks and alpha brainwaves. Electronics, 8(12), p.1387. Zhang, L., Chen, Z., Cui, W., Li, B., Chen, C., Cao, Z. and Gao, K., 2020. Wifi-based indoor robot positioning using deep fuzzy forests. IEEE Internet of Things Journal, 7(11), pp.10773-10781. Coevoet, E., Escande, A. and Duriez, C., 2019, April. Soft robots locomotion and manipulation control using FEM simulation and quadratic programming. In 2019 2nd IEEE International Conference on Soft Robotics (RoboSoft) (pp. 739-745). IEEE. Zhang, Z., Kayacan, E., Thompson, B. and Chowdhary, G., 2020. High precision control and deep learning-based corn stand counting algorithms for agricultural robot. Autonomous Robots, 44(7), pp.1289-1302. Guo, J., Li, C. and Guo, S., 2019. A novel step optimal path planning algorithm for the spherical mobile robot based on fuzzy control. IEEE Access, 8, pp.1394-1405. Duan, X., Tian, H., Li, C., Han, Z., Cui, T., Shi, Q., Wen, H. and Wang, J., 2021. Virtual-fixture based drilling control for robot-assisted craniotomy: Learning from demonstration. IEEE Robotics and Automation Letters, 6(2), pp.2327-2334. Xianjia, Y., Qingqing, L., Queralta, J.P., Heikkonen, J. and Westerlund, T., 2021, June. Applications of uwb networks and positioning to autonomous robots and industrial systems. In 2021 10th Mediterranean Conference on Embedded Computing (MECO) (pp. 1-6). IEEE. Wang, Z., Wang, T., Zhao, B., He, Y., Hu, Y., Li, B., Zhang, P. and Meng, M.Q.H., 2021. Hybrid adaptive control strategy for continuum surgical robot under external load. IEEE Robotics and Automation Letters, 6(2), pp.1407-1414. Zinchenko, K. and Song, K.T., 2021. Autonomous Endoscope Robot Positioning Using Instrument Segmentation With Virtual Reality Visualization. IEEE Access, 9, pp.72614-72623. Charisi, V., Merino, L., Escobar, M., Caballero, F., Gomez, R. and Gómez, E., 2021, May. The effects of robot cognitive reliability and social positioning on child-robot team dynamics. In 2021 IEEE international conference on robotics and automation (ICRA) (pp. 9439-9445). IEEE. Kuric, I., Tlach, V., Sága, M., Císar, M. and Zajačko, I., 2021. Industrial robot positioning performance measured on inclined and parallel planes by double ballbar. Applied Sciences, 11(4), p.1777. Kuo, P.H., Liu, G.H., Ho, Y.F. and Li, T.H.S., 2016, October. PSO and neural network based intelligent posture calibration method for robot arm. In 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC) (pp. 003095-003100). IEEE. Liu, Y., Jiang, D., Yun, J., Sun, Y., Li, C., Jiang, G., Kong, J., Tao, B. and Fang, Z., 2022. Self-tuning control of manipulator positioning based on fuzzy PID and PSO algorithm. Frontiers in Bioengineering and Biotechnology, 9, p.1443. Ibraheem, G.A.R., Azar, A.T., Ibraheem, I.K. and Humaidi, A.J., 2020. A novel design of a neural network-based fractional PID controller for mobile robots using hybridized fruit fly and particle swarm optimization. Complexity, 2020, pp.1-18. Chen, D., Li, S. and Liao, L., 2019. A recurrent neural network applied to optimal motion control of mobile robots with physical constraints. Applied Soft Computing, 85, p.105880. Chen, D., Li, S. and Liao, L., 2019. A recurrent neural network applied to optimal motion control of mobile robots with physical constraints. Applied Soft Computing, 85, p.105880. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3908374","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":269862856,"identity":"afa46539-1bbf-47ad-9213-07180b3f634d","order_by":0,"name":"Guo Kai","email":"","orcid":"","institution":"Anhui University of Science and Technology, Suzhou University","correspondingAuthor":false,"prefix":"","firstName":"Guo","middleName":"","lastName":"Kai","suffix":""},{"id":269862857,"identity":"6d754012-45dd-478c-9072-376c94cf497f","order_by":1,"name":"Bo Zhi","email":"","orcid":"","institution":"Anhui University of Science and Technology, Suzhou University","correspondingAuthor":false,"prefix":"","firstName":"Bo","middleName":"","lastName":"Zhi","suffix":""},{"id":269862858,"identity":"e80b49e9-3d06-47e4-af5a-ffd41f700ac4","order_by":2,"name":"Wang Sai","email":"","orcid":"","institution":"Anhui University of Science and Technology, Suzhou University","correspondingAuthor":false,"prefix":"","firstName":"Wang","middleName":"","lastName":"Sai","suffix":""},{"id":269862859,"identity":"b191b1bd-ae09-4b4c-af8e-d16226a45479","order_by":3,"name":"Ge Jingjing","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBElEQVRIiWNgGAWjYHCChAMMDGw8DAzsBx98AHLZ2InXwpNsOAOkhZkE68ykeUAUIS3y7g0PDxf84pMx51+QJm3za5s8HzMD44ePObi1GJ45kHB4Zh8bj+WMh4etc/tuG7YxMzBLztyGR8uMhITDvD1sPAY3DiTezu25zQjUwsbMi0/L/AdwLQbSlj237QlqkZdgSDjM8wOo5XyDkTTDj9uJBLUY8IAc1gCyBRjIvQ23k9uYGZvx+kW+/UzyZ54/x+wNzh8/+ODHn9u289ubD374iM+WAzwJDIxtxxgYJBIYgAyQGGMDbvUgWxrYDzAw/KlhYOAH0gx/8CoeBaNgFIyCEQoAINtW7gJ+C7cAAAAASUVORK5CYII=","orcid":"","institution":"University of Shanghai for Science and Technology, Suzhou University","correspondingAuthor":true,"prefix":"","firstName":"Ge","middleName":"","lastName":"Jingjing","suffix":""}],"badges":[],"createdAt":"2024-01-29 07:46:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3908374/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3908374/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50454517,"identity":"7d7b8fc2-f543-496f-8c34-f98d0f10fa39","added_by":"auto","created_at":"2024-01-31 18:29:10","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":228017,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePrinciple of robot position for puncturing\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/432115054945141005bf0e5a.png"},{"id":50454515,"identity":"0d160e18-7f66-4923-b341-d20bc9611473","added_by":"auto","created_at":"2024-01-31 18:29:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":78106,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic and frame assignment of UR\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/77e27b99cd5c9d8e3c2d40b6.png"},{"id":50454516,"identity":"482a5397-ade9-41f7-ae33-542cab1d3b44","added_by":"auto","created_at":"2024-01-31 18:29:10","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":635041,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eArchitecture of MLPNN\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/851f76ed40bd8bf6efc879f8.png"},{"id":50454937,"identity":"f4cff9c6-f3b6-4ab3-8a7e-5816ab7517d2","added_by":"auto","created_at":"2024-01-31 18:37:10","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":289676,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eError ratio of test set (a)\u003c/strong\u003eθ\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e (b)\u003c/strong\u003eθ\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e (c)\u003c/strong\u003eθ\u003csub\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/588e8413aba38d07f0410830.png"},{"id":50454522,"identity":"d2436336-eea8-4eca-8702-ce805fda91ae","added_by":"auto","created_at":"2024-01-31 18:29:10","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":397922,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eError ratio of test set (a)\u003c/strong\u003eθ\u003csub\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e (b)\u003c/strong\u003eθ\u003csub\u003e\u003cstrong\u003e5\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e (c)\u003c/strong\u003eθ\u003csub\u003e\u003cstrong\u003e6\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/231eff60f011587c6e0fb643.png"},{"id":50455767,"identity":"729e2a98-2c58-4442-b836-5924786b5922","added_by":"auto","created_at":"2024-01-31 18:45:10","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":128720,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of MSE\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/2c26d181a4b66f8eabdb4921.png"},{"id":50454518,"identity":"d82cd4fa-c877-4ade-a4cc-08e2879a2acc","added_by":"auto","created_at":"2024-01-31 18:29:10","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":72746,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAccuracy\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/cf3ddd95f74c5735aa46d22b.png"},{"id":50454520,"identity":"757bfb24-512a-40d4-a769-d1a613df9240","added_by":"auto","created_at":"2024-01-31 18:29:10","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":131388,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMSE\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/c43978832eab107fb7be0993.png"},{"id":55941641,"identity":"2853fdcb-eae5-4823-a1f9-1dbb734837af","added_by":"auto","created_at":"2024-05-06 15:23:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2393102,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3908374/v1/6b902590-2b89-440c-8762-059d083d0a4a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Positioning control of robots using a novel nature inspired optimization based neural network","fulltext":[{"header":"1. Background","content":"\u003cp\u003eRobots are being utilized in industrialized and medicinal settings where high levels of precision, repeatability, and stability are essential. Robotics has been extensively applied in new domains, such as medicine, thanks to the advancement of contemporary control technology [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. A surgical robot operating system is a combination of several cutting-edge, sophisticated technologies that allows a surgeon to operate on patients without ever having to touch them. For performing puncture surgery on a patient, a minimally invasive surgical robot combines using a robot arm and processing of medical images to meet the minimum intrusiveness, precision, efficiency, and stability [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. In the past, the IK problem of the robot has been addressed using the geometrical approach, the algebraic approach, and the optimization algorithm. In order to solve the IK, every solution has its own limitations. The geometrical method, for example, requires that shuttered options exist again for robot's initial three joints, however closed-form solutions for the algebraic methods are not guaranteed. Similar to this, the approach of iterative IK solution converges to a single solution that depends on the initial position [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The computation accuracy cannot be guaranteed for these approaches because they frequently call for powerful computer gear. Academics have been focusing on the application of neural networks that are artificial in the kinematic of the robot as a result of these aspects [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn recent decades, a wide variety of control structures have been included into developed societies to address the limitations of the traditional controllers. Using the idea of differentiators and integrators of fractional power, the proportional integral derivative (PID) controller that have been subject by industrial organizations has been modified [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. It was demonstrated that combining more degree of independence with differentiators and fractional power integrators allowed for a higher level of flexibility and performance that would otherwise be challenging or perhaps impossible to achieve with traditional PID controllers [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The fractional-order PID (FOPID) controllers are the generalization of broadly valid PID controllers, and both academia and business have recently given them a lot of attention [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe aim of [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] was to investigate the shortcomings and demonstrate that they are a result of the conventional direction/angle of bend parameter of the state rather than a result of the piecewise constant curvature assumption itself. The study [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] was to describe a new route planning approach for aerial robots that enables them to quickly and easily traverse their environments. Planner uses motion primitives to discover acceptable pathways that explore the configuration space, making use of the dynamic flying capabilities of tiny aerial robots, to meet the combined demand for large-scale exploration of tough and constrained situations. The research [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] introduces a revolutionary, hierarchical local motion planning framework for autonomous vehicles to track a path and deftly sidestep obstacles. This study explores the use of ML approaches, and notably RL in DP applications for deepwater drilling rigs. It is suggested to use a deep Q-learning network in an RL-based DP control technique [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Research [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] was to provide a new approach for designing unmanned aerial vehicle (UAV) trajectories within the bounds of system positioning accuracy. To minimise the total flight time of the UAV and the number of times it has to make course adjustments, the modified genetic algorithm (GA) and A* algorithm are utilised in the trajectory planning process. Study [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] details efforts to create a synchronous and endogenous Electroencephalography-based Brain-Computer Interface that may be used to control a mobile robot's mobility in response to the blinking of a person driver's eyelids. Research [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] offers an approach for managing the movement of soft robots with manipulative and mobile capabilities. Whether the soft robot, its actuators, or its environment is deformable, we employ the Finite Element Method (FEM) to model the resulting changes. The study [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] introduces a low-cost, ultra-compact, 3D-printed, autonomous field robot for agricultural activities, complete with high-precision control and deep learning-based algorithms for counting corn stands. The study [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] put out a unique fuzzy-based step-optimal path planning approach. Initially, the spherical mobile robot's motion model was analyzed to finalize the ultrasonic sensors' (HC-SR04) setup and debugging.\u003c/p\u003e \u003cp\u003eAn alignment and drilling assignment that is part of a piecewise collaborative drilling task is the subject of the present investigation [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Surgeons may be able to execute the procedure faster and with more precision with its help. Intention recognition, which is trained through demonstrations of human-guided force during collaborative drilling, can be used to solve the problem of a virtual fixture (VF) being switched between drilling and aligning. The research [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] examines the cutting edge of Ultra-wideband (UWB) networking and localization for robotic and autonomous systems. They go discuss cutting-edge methods that use machine learning to increase precision and focus on creating more cutting - edge solutions, collaboration localization strategies, ad hoc networking, and more. The author of [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], a hybrid adaptive control framework is suggested, which combines offline qualified robot IK with a neural network and online adaptive adaptation of the parameters of the PID controller with some other neural network, giving the cyborg system more driving amount to compensate for tracking error brought on by interference. The study [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] describes a technique for robotic endoscope holder-assisted endoscopic positioning in minimally invasive surgery. This technique allows the endoscope holder to recognize the surgeon's view projection and move the camera autonomously, which greatly enhances human-robot collaboration in robot-assisted surgery. The goal of the study [21 examine the effects of robot behavior on the social dynamics of a group by observing how a robot interacted with a human and a kid as they solved a task. Children who engaged with the trustworthy robot performed better on the test, while those who interacted with the less trustworthy robot showed more task-related social interactions. The required circular path is put on an inclined plane, the tests in the current study [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] confirm the notion of the motion of all the robot joints. By positioning analysis on a simulated version of the robot, the established hypothesis is validated in the first portion of the studies.\u003c/p\u003e \u003cp\u003eThe major goal of this work is to boost the accuracy of the SOA\u0026thinsp;+\u0026thinsp;MLP algorithm's IK solution, particularly for processing data quickly and the duration of the robot's motion. In order to overcome the inherent flaws in the MLP neural network and identify the best solution, the SOA technique is used. This enhances the generalization capability, convergence speed, and meeting precision of the MLP neural network.\u003c/p\u003e \u003cp\u003e \u003cb\u003eContributions to the paper\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eIn the simulated study, 950 data sets were used for training the UR3 manipulator and 50 data sets were used for testing in a total data set size of 1000.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eTo tackle the IK issue of a UR3 robot, we offer the Global Iterative Sunflower Optimized Binary Multi Layer Perceptron (GISOB-MLP) neural network technique.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAiming for the exact use of the puncturing robot, the basic test was carried out and preliminary findings were achieved, laying the groundwork for the robot's popularization in the medical field.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe paper is laid out as follows. A review of current methodologies is covered in Section II, and proposed methodology is covered in Section III. Section IV presents the results and the discussion; section V presents the research's future potential directions and conclusions.\u003c/p\u003e \u003cp\u003e \u003cb\u003eProblem statement\u003c/b\u003e \u003c/p\u003e \u003cp\u003eGetting the manipulator's kinematics sorted out is the serial robot's biggest challenge, but it's also one that can be overcome. The robot's kinematics may be broken down into two categories: forward kinematics and internal kinematics. Forward kinematics describes the transformations required to move from joint angles to Cartesian coordinates. IK is well-known for its ability to solve joint variables in accordance with the end effectors' positions and postures. Several scientists are devoting their efforts to developing genetic algorithms to determine the robot's IK. The robot's positional inaccuracy and the sum of all joint displacements must be calculated independently due to the way the fitness function is designed. This study seeks to enhance the accuracy of the IK solution generated by a SOA\u0026thinsp;+\u0026thinsp;MLP algorithm in order to address the IK challenge posed by a four-degrees-of-freedom (DOF) serial robot manipulator while the robot is in motion.\u003c/p\u003e"},{"header":"2. Proposed methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Precision Positioning of a Puncture\u003c/h2\u003e \u003cp\u003eRobot-assisted minimally-invasive surgery (MIS) is a less expensive alternative to traditional open surgery that accomplishes the similar ends by inserting surgical tools through a series of small incisions. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e depicts the basic puncture robot design.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAn initial CT scan is necessary, and the computer will then create the medical image needed for the 3D reconstruction. The doctor may then use the 3D model to provide an accurate diagnosis based on what they see. The doctor next analyses the patient's skin to locate the puncture target point coordinates and decides where to place the device. The path of puncture is between the intended location and the connection's insertion site. The success of the puncturing procedure is directly proportional to the precision of the chosen puncture path. In this study, the serial robot piercing route was built by research on the manipulator's precision positioning technology. The robot's puncture guide tube-equipped end-effectors keep the robot in the proper position and posture while precisely putting the needle into the patient's skin using measurements that are obtained from the data processing computer and identify the desired location and insertion point.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Analysis of the UR3 Manipulator\u003c/h2\u003e \u003cp\u003eThe Universal Robots Corporation has developed the new, compact UR3 manipulator, a six-DOF collaborative robot. The UR3 manipulator is a table-top robot that combines flexibility, lightness, safety, and collaboration. The end effectors of the UR3 may morph and rotate because to the six joints in the device. Compared to previous manipulators, the UR3's kinematics analysis is more intricate. There aren't any exact Matlab models available for this robot right now. The exact placement method for surgical medical puncture utilizing the UR3.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e represents the schematic and frame assignment of UR. The homogeneous robot transformation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(matri{x}_{j}^{j-1}S\\)\u003c/span\u003e\u003c/span\u003e equations (\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), which employ four connection parameters, represent a single joint. The D-H notation is the name given to this conversion.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$S={S}_{tran}({v}_{j-1},{c}_{j}){S}_{tran}({y}_{j-1},{b}_{i}){S}_{rot}({y}_{j-1},{b}_{i})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${x}_{j}^{j-1}S=\\left[\\begin{array}{cccc}d{\\theta }_{j}\u0026amp; -{d\\alpha }_{j}{t\\theta }_{j}\u0026amp; {t}_{\\alpha }{t\\theta }_{j}\u0026amp; {b}_{j}{d\\theta }_{j}\\\\ t{\\theta }_{j}\u0026amp; {d\\alpha }_{j}{d\\theta }_{j}\u0026amp; {-T\\alpha }_{j}{d\\theta }_{j}\u0026amp; {b}_{j}{t\\theta }_{j}\\\\ 0\u0026amp; t{\\theta }_{j}\u0026amp; d{\\alpha }_{j}\u0026amp; {c}_{j}\\\\ 0\u0026amp; 0\u0026amp; 0\u0026amp; 1\\end{array}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe matrix of transformations among pairs of neighboring connections \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({}_{j}{}^{j-1}S\\left(j=\\text{1,2},\\dots ,6\\right).\\)\u003c/span\u003e\u003c/span\u003e Among them, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{j},{c}_{j},{\\alpha }_{j}\\)\u003c/span\u003e\u003c/span\u003e depending just on robot's standard structure parameter ;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\theta }_{j}\\left(j=\\text{1,2},\\dots 6\\right)\\)\u003c/span\u003e\u003c/span\u003eresprent the joint variables, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(d{\\theta }_{j}=cos {\\theta }_{j},t{\\theta }_{j}=sin{\\theta }_{j},t{\\alpha }_{j}=sin{\\alpha }_{j},and d{\\alpha }_{j}=cos {\\alpha }_{j}\\)\u003c/span\u003e\u003c/span\u003e Thus, When we use the homogeneous linear interpolation, we may use equation to get the linear transformation from the base to a end effectors depicted in Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${}_{6}{}^{0}S=\\prod _{j=1}^{6}{}_{j}{}^{j-1}S=\\left[\\begin{array}{cc}{}_{6}{}^{0}{Q}_{3\\times 3}\u0026amp; {}_{6}{}^{0}{O}_{3\\times 1}\\\\ 0\u0026amp; 1\\end{array}\\right]=\\left[\\begin{array}{cccc}{q}_{11}\u0026amp; {q}_{12}\u0026amp; {q}_{13}\u0026amp; {o}_{y}\\\\ {q}_{21}\u0026amp; {q}_{22}\u0026amp; {q}_{23}\u0026amp; {o}_{y}\\\\ {q}_{31}\u0026amp; {q}_{32}\u0026amp; {q}_{33}\u0026amp; {o}_{v}\\\\ 0\u0026amp; 0\u0026amp; 0\u0026amp; 1\\end{array}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eOne of them is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({}_{6}{}^{0}{Q}_{3\\times 3}\\)\u003c/span\u003e\u003c/span\u003e robotic end effectors rotational grid \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({}_{ 6}{}^{0}{O}_{3\\times 1}\\)\u003c/span\u003e\u003c/span\u003e, and its coordinates the orientation matrix of a robot end controller, where the components of the position vector and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({q}_{ji}\\)\u003c/span\u003e\u003c/span\u003edenotes the rotational components of the transition \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(matrix\\left(j \\text{a}\\text{n}\\text{d} \\text{i}=\\text{1,2},3\\right)\\text{a}\\text{n}\\text{d} {o}_{y},{o}_{x},{o}_{v}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eIn this research, we employed six degrees of freedom (DOF) UR3 robot. The six DOF Cartesian location of the end effectors is retrieved directly from the matrix, and the RPY (roll, pitch, yaw) rotation describes the end effectors\u0026rsquo; orientation. As can be seen in the Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), the angular displacements result from these revolutions from around axis.\u003c/p\u003e \u003cp\u003eIn this investigation, a six DOF UR3 robot was employed. The end effectors of the manipulator is positioned in a six DOF Cartesian space at positions \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((y,x,v)\\)\u003c/span\u003e\u003c/span\u003e, that are directly derived from the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({}_{6}{}^{0}S\\)\u003c/span\u003e\u003c/span\u003e matrix. The end effector's orientation is represented by the RPY rotation. Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) illustrates these rotations as angles around the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(V-X-V\\)\u003c/span\u003e\u003c/span\u003e axis.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$${Q}_{{V}^{{\\prime }}{X}^{{\\prime }}{V}^{{\\prime }}}\\left(\\alpha ,\\beta ,\\gamma \\right)=\\left[\\begin{array}{ccc}d\\alpha dd\\gamma -t\\alpha t\\gamma \u0026amp; -d\\alpha d\\beta t\\gamma -t\\alpha d\\gamma \u0026amp; d\\alpha t\\beta \\\\ t\\alpha d\\beta d\\gamma +d\\alpha t\\gamma \u0026amp; -t\\alpha d\\beta t\\gamma +d\\alpha d\\gamma \u0026amp; t\\alpha t\\beta \\\\ -t\\beta d\\gamma \u0026amp; t\\beta t\\gamma \u0026amp; d\\beta \\end{array}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEquations\u0026nbsp;(\u003cspan refid=\"Equ5\" class=\"InternalRef\"\u003e5\u003c/span\u003e)\u0026ndash;(\u003cspan refid=\"Equ7\" class=\"InternalRef\"\u003e7\u003c/span\u003e) may be used to compute the angles, which can then be obtained by solving the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({}_{6}{}^{0}S\\)\u003c/span\u003e\u003c/span\u003e matrix:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\alpha =Btan2({q}_{23},{q}_{13})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\beta =Btan2({q}_{13}\\text{cos}\\alpha +{q}_{23}\\text{sin}\\alpha , {q}_{33})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\gamma =Btan2({q}_{13}\\text{cos}\\alpha +{q}_{22} sin\\alpha -{q}_{12}sin\\alpha )$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe robot's position, as it relates to the universe's coordinate system, may be determined using this equation. The location and orientation of the robot are described by the coordinates of each joint. Eq.\u0026nbsp;(8) describes the robot's forward kinematics equation;\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({E}_{forward kinematics}\\left({\\theta }_{1},{\\theta }_{2},{\\theta }_{3},{\\theta }_{4},{\\theta }_{5},{\\theta }_{6}\\right)=({o}_{y},{o}_{x},{o}_{v},\\alpha ,\\beta ,\\gamma\\)\u003c/span\u003e \u003c/span\u003e) (8)\u003c/p\u003e \u003cp\u003eEquation (8) demonstrates how to determine the robot's Cartesian coordinate system using forward kinematics after the six joint angles are known. However an industrial application necessitates computing the six joint angles of the robot shown in Eq.\u0026nbsp;(9).\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({E}_{forward kinematics}({o}_{y},{o}_{x},{o}_{v},\\alpha ,\\beta ,\\gamma\\)\u003c/span\u003e \u003c/span\u003e)\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({\\theta }_{1},{\\theta }_{2},{\\theta }_{3},{\\theta }_{4},{\\theta }_{5},{\\theta }_{6}\\right)\\)\u003c/span\u003e\u003c/span\u003e (9)\u003c/p\u003e \u003cp\u003eThe joint angles \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\theta }_{j}(j=\\text{1,2},\\dots ,6)\\)\u003c/span\u003e\u003c/span\u003e will be utilized as the output variables of the MLP neural network in the subsequent section. The input variables for the MLPNN model will be \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha ,\\beta ,\\gamma ,{o}_{y},{o}_{x},{o}_{v}\\)\u003c/span\u003e\u003c/span\u003eand the joint angles.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Global iterative sunflower optimized binary MLP (GISOB-MLP)\u003c/h2\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Sunflower optimization algorithm (SOA)\u003c/h2\u003e \u003cp\u003eOne of the most recent developments in soft computing techniques that draw inspiration from nature is SOA. The basic idea behind the SOA is a repetitive process that simulates sunflowers moving in search of the finest photo opportunities as they follow the light each morning at daybreak. Sunflowers follow the same cycle every day, waking up and moving with the sun like the hands of a clock. They go in the other way at night to wait once more for their departure. The cycle of a sunflower is controlled by the law of radiation as;\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${R}_{y}=\\frac{{O}_{y}}{4\\pi {q}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ R}_{y}\\)\u003c/span\u003e\u003c/span\u003eis the amount of heat that each sunflower individual \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(y\\right)\\)\u003c/span\u003e\u003c/span\u003e receives, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({O}_{y}\\)\u003c/span\u003e\u003c/span\u003e is the amount of solar energy, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({q}_{y}\\)\u003c/span\u003e\u003c/span\u003e is the separation between each individual and the best member of the present population. The emitted heat and distance have an inverse square relationship, as shown by Eq.\u0026nbsp;(\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e10\u003c/span\u003e). Each sunflower modifies its direction in relation to the sun, as seen in Eq.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e11\u003c/span\u003e);\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$${\\overrightarrow{T}}_{Y}=\\frac{{Y}^{*}-{Y}_{Y}}{‖{Y}^{*}-{Y}_{Y}‖}, y=\\text{1,2},\\dots .MO$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Y}_{*}\\)\u003c/span\u003e\u003c/span\u003edenotes the top member of the present population, Xx denotes each solution, and NP denotes the population's predetermined amount. The following diagram illustrates how sunflowers migrate across the sun.\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$${e}_{y}={\\lambda }..{O}_{y}\\left(‖{Y}_{y}+{Y}_{y-1}‖\\right).‖{Y}_{y}+{Y}_{y-1}‖$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({O}_{y}\\left(‖{Y}_{y}+{Y}_{y-1}‖\\right)\\)\u003c/span\u003e\u003c/span\u003ethe chance that a sunflower will be is pollinate λ, and is a specified constant relating to the inertial movement of each sunflower. The least spacing among each flower and the flower in back is used in SFOA to randomly carry out pollinating. As a result, the sunflower moves into a new position to pollinate, while the sunflowers farther from the sun move normally. The closer sunflowers to the sun make smaller movements to promote the local search improvement. Based on the foregoing, the sunflowers' movement \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({e}_{y}\\right)\\)\u003c/span\u003e\u003c/span\u003e and orientation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({T}_{y}\\right)\\)\u003c/span\u003e\u003c/span\u003ein relation to the sun are used to update each location of a sunflower as follows:\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$${Y}_{y+1}={Y}_{y}+{c}_{y}+{T}_{y}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe fundamental SOA stages summed up in algorithm \u003cspan refid=\"FPar1\" class=\"InternalRef\"\u003e1\u003c/span\u003e:\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eAlgorithm 1\u003c/strong\u003e \u003cp\u003e \u003cb\u003eSOA\u003c/b\u003e \u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eStep 1\u003c/strong\u003e \u003cp\u003eInitialize,, the iterations number (t\u0026thinsp;=\u0026thinsp;0), and the limitations that are provided (2).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eStep 2\u003c/b\u003e: Randomly generate the starting population of sunflowers\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({(Y}_{Y}\\left(U\\right))\\)\u003c/span\u003e\u003c/span\u003e. Every sunflower is shown as follows: (2). As a result, each sunflower is made up of concurrent capacitor deployments with certain controls turned on.\u003c/p\u003e \u003cp\u003e \u003cstrong\u003e\u003cem\u003eStep 3\u003c/em\u003e\u003c/strong\u003e \u003cp\u003eEvaluation of the relevant fitness function (1).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eStep 4\u003c/strong\u003e \u003cp\u003eThe finest sunflower with the least OF should be chosen.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eStep 5\u003c/strong\u003e \u003cp\u003eCheck to see whether is reached. Extract X\u0026lowast; and terminate the program if it is satisfied.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eStep 6\u003c/strong\u003e \u003cp\u003eOrient the sunflowers so that they face the sun (11).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eStep 7\u003c/strong\u003e \u003cp\u003eThe poorest m% of sunflowers should be eliminated after calculating the orientation vector for every sunflower (10).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eStep 8\u003c/strong\u003e \u003cp\u003eUpdate the sunflowers in accordance with (13) and the m% sunflowers by generating them at random inside their bounds.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eStep 9\u003c/strong\u003e \u003cp\u003eThe counter increments should be raised then go to step 3.\u003c/p\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Multilayer Perceptron neural network (MLPNN)\u003c/h2\u003e \u003cp\u003eA MLPNN was used as the classifier in this study. This choice was decided due to the popularity of MLPNN as a machine learning approach and the large number of MLPNN successful applications. As there are eight amplitude summation inside the feature vector (four for each channel), the classifier's input image consists of a total of eight neurons. There are 4 neurons in the output layer as well since there are 4 classes accessible. There are another two buried levels with a total of 100 neurons each.\u003c/p\u003e \u003cp\u003eAfter a process of trial and error, the number of buried layers and neurons was established. Particularly, 1\u0026ndash;3 buried layers were taken into account. Moreover, 20\u0026ndash;200 neurons in steps of 20 were evaluated for each layer. 175 distinct network configurations were taken into account altogether. In terms of classification accuracy, it was determined that a two hidden layer network with 100 neurons in each layer performed as anticipated. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows a visual representation of the classifier developed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eRectified Linear Unit (ReLU) is the function that activates the buried layers. ReLU has the benefits of faster training and less suffer from the vanishing grade problem.\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$ReLU\\left(y\\right)=\\text{max}\\left(0,y\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe output layers were employed with the sigmoid purpose, which is represented by Eq.\u0026nbsp;(\u003cspan refid=\"Equ13\" class=\"InternalRef\"\u003e15\u003c/span\u003e):\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\sigma \\left(y\\right)=\\frac{1}{1+{f}^{-y{\\prime }}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThis restricts the [0, 1] range of each layer's output. This indicates that every neuron in the output layer generates odds that the input will be one of the 4 instructions. A control is chosen based on which has the best chance of succeeding.\u003c/p\u003e \u003cp\u003eBinary cross-entropy, a frequently used loss function in binary classification issues, is the method used to calculate the prediction error of the network during training. It's characterized as\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$K=\\frac{1}{M}[{x}_{m}.log{\\widehat{x}}_{m}+\\left(1-{x}_{m}\\right).\\text{log}\\left(1-{\\widehat{x}}_{m}\\right)]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere N is the sample size, yn denotes the desired output, and yn denotes the projected result. Last but not least, Adam, with the default hyperparameter settings, is an optimization technique that modifies the weight of each neuron to lower the forecast error. Using the Keras API and TensorFlow, all models were trained.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eThe method is trained using the test data in conjunction with the MLPNN optimized using the SOA [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Using the UR3 manipulator in a workspace containing one thousand data sets, 950 sets were selected as training samples for a simulated experiment and 50 sets were used as test samples. In order to maximize convergence, the SOA was applied to the weights and thresholds of the MLP neural network, which was then used to train the six robot joint angles in a loop, yielding 50 training sets from which to draw a single output prediction sample. The MLPNN was trained using samples of the UR3 robot's end-position coordinates and Euler angles, and the UR3 robot's six joint angles were utilized as the prediction sample. During training, the MLPNN uses the UR3 robot's position vector and rotation angle as input points, and the values of the 6 joint angles as output points. As the fitness function is optimized, the SOA method is applied. The MLPNN weights and thresholds are determined through SOA, and the output value of each joint variable is determined by simulation.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e displays the test set error range and Mean Square Error (MSE) that we get for the trained network. The MLP neural network had an error range of [-0.3061, 0.4132], and the MSE was in the range of [6.73 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e, 8.13 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e] for a set of 50 joint angles, whereas the GISOB-MLP had an error range of [-0.1861, 0.1081] and the MSE was in the range of [2.40 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e, 6.44 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e ]. The output robot joint angle error 4 is compared between the MLP neural network and the GISOB-MLP neural network in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. MSE for the two techniques is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe experimental findings demonstrate that a significant improvement in MSE occurs after comparing the machine arm acquired by IK of the robot to the MLP neural network joint angle error at a greater extent. The manipulator's efficacy is validated by solving its inverse kinematics using GISOB-MLP.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eError ratio test set and MSE\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eJoint Angles and MSE (Mean Square Error)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMLP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGISOB-MLP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e∆θ\u003csup\u003e1\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e∆θ\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e∆θ\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e∆θ\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e∆θ\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e∆θ\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026minus;0.2005\u0026ndash;0.4132\u003c/p\u003e \u003cp\u003e\u0026minus;0.2100\u0026ndash;0.1954\u003c/p\u003e \u003cp\u003e\u0026minus;0.2178\u0026ndash;0.2046\u003c/p\u003e \u003cp\u003e\u0026minus;0.3061\u0026ndash;0.2178\u003c/p\u003e \u003cp\u003e\u0026minus;0.2376\u0026ndash;0.1661\u003c/p\u003e \u003cp\u003e\u0026minus;0.2376\u0026ndash;0.3168\u003c/p\u003e \u003cp\u003e6.73 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u0026ndash;8.13 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;0.0534\u0026ndash;0.065\u003c/p\u003e \u003cp\u003e\u0026minus;0.1199\u0026ndash;0.0605\u003c/p\u003e \u003cp\u003e\u0026minus;0.0672\u0026ndash;0.0704\u003c/p\u003e \u003cp\u003e\u0026minus;0.0486\u0026ndash;0.0508\u003c/p\u003e \u003cp\u003e\u0026minus;0.1861\u0026ndash;0.0526\u003c/p\u003e \u003cp\u003e\u0026minus;0.0658\u0026ndash;0.1081\u003c/p\u003e \u003cp\u003e2.40 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u0026ndash;6.44 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eProportional Integral Derivatives and Particle Swarm Optimization Algorithm (PID-PSOA), Fruit Fly and Particle Swarm Optimization (FF-PSO) and Inequality and Equality Constrained Optimization Recurrent Neural Network (IECORNN) are the Existing approaches are utilized to assess the effectiveness of our suggested methods and performance measures like as accuracy and MSE. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e represents numerical results for proposed and existing methods.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eNumerical results for proposed and existing methods\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMethods\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAccuracy (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMSE (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePID-PSOA [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFF-PSO [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e91.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e47.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIECORNN [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e42.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProposed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e98\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e34.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAccuracy is essentially how well a positioning system's displacements adhere to predetermined length criteria. It is reasonable to categories positioning model accuracy into two groups: (a) the accuracy of the route itself, and (b) the linear positioning accuracy along the route. The former discusses how well a single axis translation is provided by a way, while the latter is concerned with the accuracy of incremental motion along the axis. While our proposed method has a higher in accuracy when compared to the existing methods. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e represents the accuracy.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe mean squared error (MSE) measures how well a regression line matches a set of data points. The expected value of the squared error loss is a risk function that represents this quantity. MSE is calculated by taking the average (or more accurately, the mean) of all the squared mistakes in the data set for a given function. Current approaches have larger MSE, but the suggested method has lower ones. The MSE is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eDiscussion\u003c/b\u003e \u003c/p\u003e \u003cp\u003ePID-PSOA was still issues with certain control systems that must be resolved, and further investigation into robustness and universality is required. The controller also has to be more accurate and quicker to respond. The optimal parameters are found by adjusting the fuzzy controller in such a way that the actual size of the quantized component factor is changed [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. When a FF-PSO is tasked with following a predetermined course, it encounters tracking error for a variety of reasons, including but not limited to: sound, trouble, slippage, and the errors detected by sensors due to both internal and external sources. Due to these issues, the mobile robot has difficulty following instructions to shift routes or using other sensors to find its way [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. IECORNN are combat the issue of excessively high joint velocities and accelerations for redundant robot manipulators using the DQP formulation and neural network solver, IECORNN introduced and researched a novel positioning control strategy with mutually joint velocity and joint acceleration reduction. In spite of this, it has been shown that the aforementioned solutions obtained by the optimization strategy based on the DQP only have the asymptotic convergence feature [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The suggested approach outperforms the existing methods in addressing the aforementioned problems.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eIn this study, we describe a hybrid method for solving the IK issue for a six-degree manipulator that uses end-effector error reduction and the GISOB-MLP. The suggested method uses SOA features to address the shortcomings of the MLP neural network, resulting in enhanced convergence accuracy, convergence speed, and generalization ability. The six DOF robot arm is complicated, making it hard to acquire high-precision IK solutions for a variety of reasons. These include, but are not limited to, high computational complexity, lack of assurance of accuracy, lengthy calculation time, and so on. It would be very helpful in this situation to employ the recommended strategy to increase the accuracy of the GISOB-output. MLP's Compared to a purely MLPNN, the GISOB-MLP is an order of magnitude more efficient in reducing both joint error and MSE. This technique is being used in a novel way in the field of precise positioning in medical puncture surgery to address a number of problems associated with traditional puncture procedures, such as a lack of reliability, high patient pain, a heavy reliance on the physician's expertise, and a need to perform a lot of manual labor. It has been shown to meet the requirements of precise placement in medical needle surgery, and it has both theoretical and practical significance in the study of the basic technologies behind accurate puncturing robots.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eEthics Approval and Consent to Participate:\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;No participation of humans takes place in this implementation process\u003c/p\u003e\n\u003cp\u003eHuman and Animal Rights:\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; No violation of Human and Animal Rights is involved.\u003c/p\u003e\n\u003cp\u003eData availability statement:\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;Data sharing not applicable to this article as no datasets were generated or analyzed during the current study\u003c/p\u003e\n\u003cp\u003eConflict of Interest:\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Conflict of Interest is not applicable in this work.\u003c/p\u003e\n\u003cp\u003eAuthorship contributions: \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;All authors are\u0026nbsp;contributed equally to this work\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;Acknowledgement: \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; There is no acknowledgement involved in this work.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eFunding information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Research Platform of Anhui Provincial Engineering Laboratory on Information Fusion and Control of Intelligent Robot under grants.(IFCIR2020005)\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;Fund number:\u0026nbsp;（IFCIR2020005）\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Fund level: Provincial level\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;② The Research Platform of Suzhou University under grants (2022ykf29，2022ykf27，2022ykf30)\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Fund number: (2022ykf29，2022ykf27，2022ykf30)\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Fund level: School level\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; ③ Suzhou university key project（2022yzd07）\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; Fund number: （2022yzd07）\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; Fund level: School level\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eLindner, T., Milecki, A. and Wyrwał, D., 2021. 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Applied Soft Computing, 85, p.105880.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Positioning control, Inverse Kinematics (IK), Global Iterative Sunflower Optimized Binary Multi Layer Perceptron (GISOB-MLP), UR3 robot","lastPublishedDoi":"10.21203/rs.3.rs-3908374/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3908374/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePositioning control methods for robot arms are offered within a broad framework for the purposes of unification and categorization. In robot control, the issue of Inverse Kinematics (IK) is crucial. Several conventional IK solutions, including geometry, iterations, and algebraic approaches, are insufficient for high-speed solutions and precise positioning. In recent years, the subject of robot IK using neural networks has attracted a great deal of attention, although its precise control is convenient and need improvement. To tackle the IK issue of a UR3 robot, we offer the Global Iterative Sunflower Optimized Binary Multi Layer Perceptron (GISOB-MLP) neural network technique. The GISOB-MLP improves upon previous methods in terms of generalizability, convergence speed, and convergence accuracy. In order to perform medical puncture surgery, which necessitates precise robot positioning to within 1 mm, the study method solves the position error for the UR3 robot IK only with joint angle or less 0.1 degree courses and the output end tool less than 0.1 mm. The study was conducted, and initial results were obtained, with the goal of pinpointing the robot's puncturing application; this laid the groundwork for the robot's eventual widespread use in medical settings.\u003c/p\u003e","manuscriptTitle":"Positioning control of robots using a novel nature inspired optimization based neural network","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-31 18:29:05","doi":"10.21203/rs.3.rs-3908374/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bf1fc726-e420-404c-b97a-2f068ae7ec5c","owner":[],"postedDate":"January 31st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-05-06T15:22:35+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-31 18:29:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3908374","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3908374","identity":"rs-3908374","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}