Improving robotic hand control via adaptive Fuzzy-PI controller using classification of EMG signals

Abstract

Robotic or prosthetic organs are designed to have the maximum similarity to human organs. This paper aims to improve robotic hand control via an adaptive Fuzzy-PI controller using EMG signals. The data is collected from the FDS and FPL muscles of the forearm of five individuals who performed eight movements. Then, appropriate filters are used to eliminate the noise of the signals, and MAV, VAR, and SE features are extracted. Based on MAV and VAR, classification is carried out using DA, KNN, and SVM. With an average accuracy, specificity, and sensitivity of 90.69%, 94.64%, and 62.10%, SVM is a better choice for movement detection. Following the movement detection by SVM, an appropriate reference signal is sent to the controller. The reference signal is the angle change of the fingers during the movement. All the eight gestures are modeled in a new way through these angles. The adaptive fuzzy-PI controller is used to control a robotic hand model with fifteen degrees of freedom. It has the advantages of learning from human experiences and adapting to environmental changes. The performance of the controller is evaluated in two ways. One is the comparison of the fuzzy-PI with the PI by RMSE. The average RMSE for eight movements using the fuzzy-PI is 1.6067, and for the PI, 5.0082. These results show that the fuzzy-PI controller performs better than the PI. Another new evaluation way presented in this paper is comparing the EMG signal features with the robotic hand movement signal features in terms of RMSE. The small RMSE values indicate that the EMG signal and robotic hand movement data features are significantly similar. Therefore, it can be concluded that the robotic hand controlled by the proposed controller is notably identical to the human hand.

Electromyography; Robotic hand; Fuzzy control; Fifteen degrees of freedom robot; k-nearest neighbors; Support vector machine

1. Introduction

1.1. Background

The main goal of designing artificial or robotic organs is to create maximum behavioral similarity with human organs. It is possible to achieve such similarities by recording signals from body movements and using them as representations of muscle contractions. These signals are used to train intelligent models to perform gestures like humans. An experimental method used to record signals of the body muscles is electromyography [1]. Electromyography is the study of electrical signals generated by muscles. The signals known as electromyogram (EMG) are obtained by some electrodes placed directly on the skin. They are biomechanical waves that measure the electric currents of the muscles during a contraction [2], [3], [4], [5]. EMG signal analysis is one of the most recent applications for modeling biomechanical movements of the body and controlling artificial and prosthetic organs [6], [7], [8], [9]. The following section reviews some of the most critical studies on controlling artificial, robotic, or prosthetic organs. The main scheme of the reviewed studies is to use the EMG signal for controlling a prosthetic hand or any other artificial organ.

1.2. Similar works

Deng et al. [10] used the Fuzzy control based on wavelet transform to prevent the artificial arm from sliding and creating stable gestures. The advantage of this method is using a fuzzy logic controller, but there is a significant disadvantage. The model described in [10] can be used only for robots with one degree of freedom. Dosen et al. [11] presented a conceptual model based on various factors, including uncertainty, reliability, and movement characteristics. Although it can model closed-loop behavior, the developed model requires gradual adaptation to the actual signal, which makes the use of this method difficult. Hu et al. [12] provided a motor-based system for controlling the force of grasping objects by an artificial hand with the help of hierarchical control methods. While this method offers online implementation, it requires heavy initial processing, such as image processing and motion recognition, making it too costly for commercialization. Jain et al. [13] utilized an EMG-based PID controller to control a set of artificial fingers. This controller is simple and efficient, but it can be saturated in some movements, which causes problems for anyone using it. Clancy et al. [14] used the backward control method based on the EMG to control a prosthetic hand. As a result of using this control method, the error was reduced. However, it was used only to control one or two degrees of freedom robots, therefore considered a limitation. Yang et al. [15] created the force needed to grasp objects using a robotic hand controlled by EMG signals. This force is calculated based on statistical learning algorithms such as support vector machine (SVM). Saikia et al. [16] detected the index finger movements based on the EMG signals using neural networks with error backpropagation. Artemiadis et al. [17] extracted a mathematical model of EMG signals to control the robotic arm using EMG signals. This method requires a mathematical model and real-time data to develop, which leads to a computational load. Shyamala [18] presented a control scheme for a prosthetic hand focusing on finger muscles based on the ARM Cortex M3 microcontroller. Wang et al. [19] controlled a prosthetic hand with five fingers and only four degrees of freedom based on the EMG by a myoelectric system using two electrodes and eight movements.

1.3. Research gap

Based on an examination of the control methods proposed in the literature, it can be concluded that a control approach for robotic hand systems should have the following characteristics:

• a)the ability to adapt to environmental and parametric changes;
• b)the ability to recognize the force required to grasp objects;
• c)slip prevention capability;
• d)force and path tracking;
• e)the ability to use human experiences and human movement data.

These characteristics are necessary for parametric improvement and the update of the controller.

The reviewed works have some drawbacks that make them difficult to apply in practice. A number of the methods introduced lack the ability to adapt to environmental changes. Some of them are unable to recognize the needed force to grasp objects. The main drawback is the weakness in learning from human experiences. Furthermore, previous controllers in the literature have been designed for systems with a maximum of two degrees of freedom, whereas in reality, each finger can be easily modeled by a robot with 3 degrees of freedom. As a result, this study employs a new combination of fuzzy and PI controllers to address the shortcomings of previous works while also opening up a new horizon for experimental tests and real-world applications. In addition, the fuzzy-PI controller employed in this study is an outstanding choice for robotic hand control, as it has all the qualities mentioned from a) to e) in the previous paragraph. The adaptive network-based fuzzy inference system (ANFIS) described in [20], [21] is the type of fuzzy inference system (FIS). Due to their combination of neural and fuzzy networks, they have the advantages of both networks.

1.4. Contribution

This research aims to make robotic hand movements similar to human hand movements by analyzing the EMG signals and providing a suitable controller and model. So, the fuzzy-PI controller is designed for a robotic hand with five fingers and 15 degrees of freedom.

For this purpose, EMG data collected from the flexor digitorum superficialis (FDS) and flexor pollicis longus (FPL) muscles of the forearm of five people who performed eight hand movements were processed to calculate the mean absolute value (MAV), variance (VAR), and sample entropy (SE) features. Due to the SE's zero amount, classification based on MAV and VAR was carried out using discriminant analysis (DA), including linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA), and k-nearest neighbors (KNN) and SVM methods. The SVM with the radial basis function (RBF) kernel is the best option for movement detection, with an average accuracy, specificity, and sensitivity of 90.69%, 94.64%, and 62.10% for five subjects, respectively. Following the movement detected by the SVM, the controller receives the reference signal for that movement, which is the angle change of the fingers. A unique way of modeling hand movements is also presented in this paper, which is to model them according to how the fingers' angles change.

Two approaches are used to assess the performance of the control method. The first new approach proposed in this paper is comparing EMG signal features with robotic-hand movement signal features by the root mean square error (RMSE) criterion. The comparison results show that the robotic hand controlled by the fuzzy-PI controller is remarkably similar to the human hand. The second approach is comparing the performance of the fuzzy-PI to PI. The results obtained from the controllers' comparison demonstrate that the proposed controller has several notable benefits, such as tracking the reference signal with proper response speed, less overshoot and steady-state error, and adapting to various operating conditions and movements due to using the fuzzy system.

2. Materials and methods

2.1. EMG data

EMG signals are collected from the hands of 5 girls aged 20 to 23 years who are admitted to the biomechanics laboratory, Department of Sport Sciences, Bu Ali Sina University-Hamedan, Iran. The study was approved by the Research Ethics Committee of Bu Ali Sina University. Subjects have given informed consent that authorizes the registration and use of their EMG data for scientific purposes. The research complies with all regulations. The signals are recorded using two electrodes of the electromyography device embedded on the FDS and FPL muscles and the WinDaq Recording and Playback software in WDQ format [22]. The muscles end in the fingers of a human hand and play an essential role in moving the fingers. They are shown in Fig. 1. The 16-channel MA-300 electromyography device and its surface electrodes are shown in Fig. 2. The first electrode is located on the FDS muscle, and the second is located on the FPL muscle. The position of the electrodes on the forearm is shown in Fig. 3. The individuals should perform each of the following eight hand movements ten times, each for seven seconds. There is a five-minute interval for relaxation between the movements.

Figure 1.

The FDS and FPL muscles of a human hand [23].

Figure 2.

The 16-channel MA-300 electromyography device and the surface electrodes [24].

Figure 3.

The position of the electrodes on the forearm.

The Default MA-300 configuration is listed in Table 1. In this research, the sampling frequency of the EMG signal was set at 2000 Hz.

Table 1.

Default MA-300 configuration [17].

Parameter	Value
EMG signal bandwidth	20 Hz to 2,000 Hz (−3 dB)
EMG input level	2.5 mV pk-pk at pre-amp inputs.
EMG signal level	±5 Volts (maximum)
Analog foot switches	0 to 4.688 Volts in 16 discrete steps.

The eight hand movements include cylindrical, hook, lateral, point, rest, spherical, tripod, and tip, as shown in Fig. 4. These gestures are based on Taylor et al. [25] and are designed to test the myoelectric control system and hand design. They are the main gestures that include most of the hand tasks in the daily activities of life [14].

Figure 4.

The eight hand movements.

The movements are as follows [19]:

• 1)Cylindrical: To grasp cylindrical objects like a bottle or a glass.
• 2)Hook: To carry or pull objects using four fingers, like a bag.
• 3)Lateral: To keep objects between the thumb and the lateral part of the fourth finger, like a key.
• 4)Point: To show direction or push the buttons.
• 5)Rest: Like a bench to keep a plate or a book.
• 6)Spherical: To grasp objects with the whole hand, like a tennis ball.
• 7)Tripod: To sense the small objects between the thumb, forefinger, and middle finger, like a bottle cap.
• 8)Tip: To press smaller objects like pins.

2.2. EMG signal preprocessing

The recorded EMG signal is noisy for various reasons, including tissue characteristics, physiological waves interference of adjacent muscles, changes in electrode locations, sweating and skin oil, and external noise [1]. Before recording the EMG signal, the skin surface was thoroughly cleaned with alcohol, the electrodes were taped to the person's skin to prevent displacement of the electrodes, and their cell phones were turned off to remove external noise in the laboratory to record the low-noise signal in this study. In addition, some filters are used to reduce the noise impact.

This section aims to apply the appropriate filters to remove the data noise. EMG Analysis software, Automation Section, has been used for noise elimination. In this research, Time Shift Data, Auto Zero, Notch Filter, Low Pass Filter, High Pass Filter, and Noise Suppression options of the Automation Section have been used. Consequently, signals with less noise are obtained and stored in C3D format. The following options are described below [26]:

• a)Time Shift Data: This option allows the user to eliminate delays in receiving EMG data or delays caused by applying different filters. For example, if there is a 15 ms delay in the original or filtered data, it will become zero;
• b)Auto Zero: By enabling this option, an offset to zero, produced by the analog-to-digital converter, can be removed from the EMG signal;
• c)Notch Filter: Many factors can add noise at a particular frequency to an EMG signal, such as noise from AC lines (frequency 50 or 60 Hz). The notch filter was used in this study to eliminate 50 Hz noise and its harmonics;
• d)Low Pass Filter: The option deletes the part of the signal that contains a frequency higher than a particular value. A low-pass filter with a degree of 20 and a cut-off frequency of 500 Hz was used in this study;
• e)High Pass Filter: The option deletes the part of the signal that contains a frequency lower than a particular value. A high-pass filter with a degree of 20 and a cut-off frequency of 10 Hz was used in this study;
• f)Noise Suppression: This option activates the device's amplitude and background noise removal algorithm [26].

2.3. EMG features extraction

The raw EMG signal is not appropriate for classification due to its large size, leading to a heavy computational load and a reduced recognition rate [19]. Therefore, different features must be extracted from the EMG data. Various features are extracted from the EMG signals, including time-domain, frequency-domain, and time-frequency-domain. Based on previous research, optimal features for hand movement detection systems include MAV, VAR, and SE [19]. Also, SE added to MAV, VAR, and autoregressive time series (AR) features improved the classification accuracy for off-line and virtual hand applications [27], [28], [29]. So, the time-domain features MAV, VAR, and SE are calculated. The features in this study are used for the following purposes: classification of EMG data to detect movement and comparison of human hand movement signals (EMG) and robotic hand movement signals.

Suitable windows for analyzing the EMG data should first be considered because of the nonstationarity of these signals. So, the EMG data is analyzed in a 250 ms time window [30]. Eq. (1) calculates the number of windows [19].

$$\text{No. of windows}=\frac{\text{data length}-\text{window size}}{\text{window increment}}+1$$ (1)

where data length is the length of the vector in which the recorded data is located, the window size is the size of the window used to calculate the mathematical features, and window increment is the allowed increment size of the window. In this study, the window increment is considered to be 70 ms.

If the recorded EMG signal at the i-th point of the window represented with $s(i)$, its MAV is calculated using Eq. (2) [19]. N is the window size (250 ms).

$$\mathit{MAV}=\frac{1}{N}\sum _{i=1}^N|s(i)|$$ (2)

VAR is calculated using Eq. (3) [19]:

$$\mathit{VAR}=\frac{1}{N-1}\sum _{i=1}^{N}s{(i)}^2$$ (3)

SE is calculated according to Eq. (4) [19]:

$$\mathit{SE}(n,r,N)=-\ln \frac{B^{n+1}(r)}{B^n(r)}$$ (4)

N is the length of the window, n is the data vector dimension which is 2 in this paper, and $r=0.25\sigma$, where σ is the standard deviation of the EMG signal.

Fig. 5 (a) shows an example of an EMG signal and its characteristics for one of the individual's movements. Fig. 5 (b) magnifies the features in Fig. 5 (a) to compare the features with one another. The figures show the effect of extracting mathematical features on noise reduction and achieving the two-channel signal's general form. In Fig. 5 (a) and (b), the top figure is the signal from electrode # 1, located on the FDS muscle, and the bottom is the electrode # 2 signal, placed on the FPL muscle. The figures show these electrodes as EMG Electrode 1 and EMG Electrode 2, respectively. The EMG signal is blue, and MAV, VAR, and SE are black, red, and green. The primary signal is extremely noisy and cannot be used in data analysis. The MAV shows the mean absolute value of the EMG, and its amplitude is near the primary signal. The VAR shows the variance but has low amplitude in comparison to MAV. The SE's amplitude is near zero for this signal.

Figure 5.

(a) An example of a recorded EMG signal with MAV, VAR, and SE features; (b) the prominent form of the MAV, VAR, and SE.

2.4. Analysis of the features and classification

The purpose of classification is to separate the eight hand movements based on the features extracted from the data and detect the movement type by the classifier. When the classifier identifies a movement, the appropriate angle signals for the robotic fingers' movement are determined and sent as a reference signal to the fuzzy-PI controller.

In Fig. 5 in the previous section, the SE feature tends to zero over time, except in the first moments. Therefore, it is better not to use the SE feature to classify the data. Thus, data classification will be based on MAV, and VAR features by LDA, QDA, KNN, and SVM methods. These are four machine learning methods that are well known and widely used in EMG signal classification [31], [32]. The classification of movements for each subject is done. It is subject-specific because EMG signal varies in several people, even in one person, in repetitions of a movement.

In this research, K-fold cross-validation (CV) with $\mathrm{k}=5$ was utilized to evaluate the performance of each classifier. First, the data is randomly divided into K subsets, each with the same number of samples. Then, K-1 subsets are used for data training, and one subset is used for testing data each time [33]. The K-fold CV method repeats the entire process k times by changing the test and training data samples. Additionally, the best model is determined by finding the minimum error based on different error approximation statistics [34].

The classification results are evaluated in terms of accuracy, sensitivity, and specificity for each subject [35], [36]. These metrics are widely used for detection and classification [37]. They are defined using Eq. (5), (6), and (7). The number of true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN) are used for the calculation [38].

$$\text{Accuracy}=\frac{\mathit{TP}+\mathit{TN}}{\mathit{TP}+\mathit{TN}+\mathit{FP}+\mathit{FN}}\times 100$$ (5)

$$\text{Sensitivity}=\frac{\mathit{TP}}{\mathit{TP}+\mathit{FN}}\times 100$$ (6)

$$\text{Specificity}=\frac{\mathit{TN}}{\mathit{TN}+\mathit{FP}}\times 100$$ (7)

2.4.1. Discriminant analysis (DA)

The DA is a popular classification method to estimate the parameters of discriminant functions of the predictor variables. The DA Classification method has two subsets known as LDA and QDA [39], [40], [41].

The linear discriminant function fits a multivariate density for each class [39]. In the LDA method [42], [43], which is known as blind classification, the boundary between the classes is specified using the first order line equation [15]. The benefit of the LDA classifier is that iterative training is not needed, and it avoids under-training or over-training [44].

In the QDA method, the boundary between the classes is defined by curves [45]. The QDA models the probability of each class as a Gaussian distribution and then uses the following distributions to predict the class for a given test point [46]. The Gaussian parameters for each class can be estimated from training points using maximum likelihood estimation [47].

For LDA and QDA classifications in MATLAB, linear and quadratic discrimination metrics are used.

2.4.2. K-nearest neighbors (KNN)

Nearest Neighbor Classification is the most straightforward supervised learning technique that depends on the closest class label training patterns in a feature space. In KNN [48], more than one neighbor is taken [49]. The test sample's class is predicted according to k training samples. This research selects the optimal number of neighbors (K) and distance metric using automatic hyperparameter optimization in MATLAB. The OptimizeHyperparameters argument with HyperparameterOptimizationOptions is used for this purpose. In this structure, the expected-improvement-plus acquisition function is used for reproducibility, and the noncategorical predictor data is standardized by setting a standardization metric of one.

2.4.3. Support vector machine (SVM)

SVM [50], [51], [52], [53] is a classifier with a solid mathematical base and good performance with a small training data set [54]. The kernel function in an SVM classifier is usually a polynomial, Gaussian or sigmoid function [55]. In this work, an RBF is used as the kernel function, and optimal values of SVM parameters like the penalty parameter (C), which controls model overfitting, and the parameter gamma (γ), which controls the model's degree of nonlinearity, are chosen by optimization function in MATLAB [56]. This function finds hyperparameters that minimize five-fold cross-validation loss [56]. Also, the expected improvement-plus acquisition function is used for reproducibility in this structure.

2.5. Modeling and simulation of a robot with three degrees of freedom

The first step in designing a controller for each system is to model it. Fig. 6 shows a robot with three degrees of freedom in the spatial coordinate [57]. Each human finger has three knuckles and three joints [58]. The robot has three arms with lengths, $l_1$, $l_2$, and $l_3$, shown in blue in the figure, acting like three knuckles of a human finger. Also, the robot has three joints: bicep, forearm, and turntable, shown in the figure in orange colors. These three joints also play the role of the three joints of a human finger. ${\theta }_1$, ${\theta }_2$, and ${\theta }_3$ are the angles of the robot arms with the axes according to Fig. 6, and $P_x$, $P_y$, and $P_z$ are the positions of the robot's endpoint in the spatial coordinate. r is the direct distance from the zero point of coordinate system to the image of the point P on the XY plane, and D is the distance from the bicep joint to the point P. Finally, the human hand is modeled with five robots with three degrees of freedom, and the eight movements are performed by a robotic hand. This model can be implemented well in SIM-Mechanics of MATLAB.

Figure 6.

A robot with three degrees of freedom in the spatial coordinate.

The Simulink block diagram of the three degrees of freedom robot in MATLAB is shown in Fig. 7. The robot's bicep, forearm, and turntable joints are modeled with three revolute blocks: Revolute1, Revolute2, and Revolute3. A revolute block defines one rotational degree of freedom. The follower (F) Body rotates relative to the base (B) Body about a single rotational axis. Each of these blocks has two outputs. One of the outputs is connected to the joint sensor (joint sensor1, joint sensor2, joint sensor3) that measures the joint rotation angle. The measured angles are shown with theta0, theta1, and theta2. Another output is connected to a rigid body, which plays the role of a robot arm. The gray Env block defines the mechanical simulation environment like gravity and dimensionality. The RootGround block connects one side of the joint to a fixed location, the Weld block represents a zero degree of freedom mechanism to perform joint rotations relative to it, and the RigidSubsystem1 is a rigid subsystem. The model parameters are listed in Table 2 [59], [60].

Figure 7.

The Simulink block diagram of a robot with three degrees of freedom in MATLAB.

Table 2.

The model parameters used in the simulation.

Parameter title	Finger
	Thumb	Forefinger	Middle finger	Ring finger	Little finger
Mass of each joint and related robotic arm (g)	16.3	12.3	14.3	12.3	8.3
Length of each robotic arm (mm)	15	17	18	17	11
Moment of inertia of each joint and related robotic arm (Kg m2)	0.045	0.039	0.042	0.039	0.034
Bicep and forearm joint rotation range (dg)	250	250	250	250	250
Turntable joint rotation range (dg)	360	360	360	360	360

2.6. Designing and implementation of an adaptive fuzzy-PI controller

To design an adaptive fuzzy-PI controller, a set of PI controllers must first be designed for the various operating areas of the system using the Ziegler-Nichols Method. Initially, a PI controller is designed for each joint of the robotic finger based on the Ziegler-Nichols method, which can track the reference signal. According to the allowed maximum overshoot of 5% for adjusting and improving the primary controllers, the parameters of the final PI controllers are obtained and shown in Table 3.

Table 3.

The parameters of the final PI controllers for three joints of the robotic finger.

Joint	Proportional (P)	Integral (I)	Derivative (D)	Filter coefficient (N)	Setpoint weight (b)	Setpoint weight (c)
Turntable	4.5	12	0	25	1	1
Bicep	4.5	14	0	10	1	1
Forearm	8	60	0	15	1	1

In a three-degrees of freedom robot control system, the angles of each joint must be controlled to reach its target point. Therefore, a suitable PI controller for each joint and each angular position can be considered. The PI controller for each area is selected using a fuzzy system. It is needed to place the necessary data set in matrixes in Eq. (8) to set the rules of this fuzzy system. For this purpose, Gaussian white noise with proper mean and variance is applied to the input of each PI controller such that the input remains in its exclusive area. A frequency-rich input is necessary to detect all modes of the system. A mean of zero and a variance of 200 for the Gaussian white noise were selected through trial and error. The input is shown in Eq. (8) with x. Its corresponding output, which is normalized, is shown in Eq. (8) by y. Both the input and normalized output are saved in matrix $A_1$. The number m shows the number of samples taken from the Gaussian white noise, the input of the PI controller. The higher the value of m, the higher the accuracy of identifying the PI controller. However, it should not be too high to prevent overlearning. In this study, m is considered 501.

This process continues in the form of matrixes $A_2$ to $A_n$ for the number of considered PI controllers. This paper considers one PI controller for each robotic finger joint. Thus, three PI controllers are designed for the three robotic finger joints, and n is three.

$${\mathrm{A}}_1={\left[\begin{array}{c}\hfill \begin{array}{ccc}\hfill {\mathrm{x}}_1\hfill & \hfill \int {\mathrm{x}}_1\hfill & \hfill {\mathrm{y}}_1\hfill \\ \hfill {\mathrm{x}}_2\hfill & \hfill \int {\mathrm{x}}_2\hfill & \hfill {\mathrm{y}}_2\hfill \\ \hfill {\mathrm{x}}_3\hfill & \hfill \int {\mathrm{x}}_3\hfill & \hfill {\mathrm{y}}_3\hfill \end{array}\hfill \\ \hfill \begin{array}{ccc}\hfill {\mathrm{x}}_4\hfill & \hfill \int {\mathrm{x}}_4\hfill & \hfill {\mathrm{y}}_4\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill \\ \hfill {\mathrm{x}}_{\mathrm{m}}\hfill & \hfill \int {\mathrm{x}}_{\mathrm{m}}\hfill & \hfill {\mathrm{y}}_{\mathrm{m}}\hfill \end{array}\hfill \end{array}\right]}_{\mathrm{m}\times 3},{\mathrm{A}}_2={\left[\begin{array}{c}\hfill \begin{array}{ccc}\hfill {\mathrm{x}}_1\hfill & \hfill \int {\mathrm{x}}_1\hfill & \hfill {\mathrm{y}}_1\hfill \\ \hfill {\mathrm{x}}_2\hfill & \hfill \int {\mathrm{x}}_2\hfill & \hfill {\mathrm{y}}_2\hfill \\ \hfill {\mathrm{x}}_3\hfill & \hfill \int {\mathrm{x}}_3\hfill & \hfill {\mathrm{y}}_3\hfill \end{array}\hfill \\ \hfill \begin{array}{ccc}\hfill {\mathrm{x}}_4\hfill & \hfill \int {\mathrm{x}}_4\hfill & \hfill {\mathrm{y}}_4\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill \\ \hfill {\mathrm{x}}_{\mathrm{m}}\hfill & \hfill \int {\mathrm{x}}_{\mathrm{m}}\hfill & \hfill {\mathrm{y}}_{\mathrm{m}}\hfill \end{array}\hfill \end{array}\right]}_{\mathrm{m}\times 3},\dots ,{\mathrm{A}}_{\mathrm{n}}={\left[\begin{array}{c}\hfill \begin{array}{ccc}\hfill {\mathrm{x}}_1\hfill & \hfill \int {\mathrm{x}}_1\hfill & \hfill {\mathrm{y}}_1\hfill \\ \hfill {\mathrm{x}}_2\hfill & \hfill \int {\mathrm{x}}_2\hfill & \hfill {\mathrm{y}}_2\hfill \\ \hfill {\mathrm{x}}_3\hfill & \hfill \int {\mathrm{x}}_3\hfill & \hfill {\mathrm{y}}_3\hfill \end{array}\hfill \\ \hfill \begin{array}{ccc}\hfill {\mathrm{x}}_4\hfill & \hfill \int {\mathrm{x}}_4\hfill & \hfill {\mathrm{y}}_4\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill ⋮\hfill \\ \hfill {\mathrm{x}}_{\mathrm{m}}\hfill & \hfill \int {\mathrm{x}}_{\mathrm{m}}\hfill & \hfill {\mathrm{y}}_{\mathrm{m}}\hfill \end{array}\hfill \end{array}\right]}_{\mathrm{m}\times 3}$$ (8)

The matrixes obtained from each PI controller are sequentially placed in matrix A and entered into the fuzzy system training program as training data. The matrix A is shown in Eq. (9).

$$A=\left[\begin{array}{c}\hfill A_1\hfill \\ \hfill A_2\hfill \\ \hfill \begin{array}{c}\hfill ⋮\hfill \\ \hfill A_n\hfill \end{array}\hfill \end{array}\right]$$ (9)

The output of this program is a fuzzy logic controller, which can quite intelligently choose PI controller interests. Consequently, three fuzzy systems are considered to select and adaptively adjust the PI controller interests for the turntable, bicep, and forearm joints.

The output regulates (decreases or increases) the PI controller interests. Five fuzzy membership functions are defined for each input, so there will be 25 fuzzy rules in each fuzzy system. These fuzzy systems are of the Takagi-Sugeno type and have two inputs, including reference signal and feedback, and one output. The more precisely the membership functions and rules are set in fuzzy systems, the more desirable the system performance [61]. A minor error is obtained after testing different membership functions in this research using bell-shaped functions.

An example of implementing an adaptive fuzzy-PI controller is shown in Fig. 8. The FIS block inputs, Ref1 and feedback1, are entered into the FIS block. Ref1 (reference signal) is described below, and the feedback1 (feedback signal) is a signal resulting from the movement of a robotic hand controlled by a fuzzy-PI controller. The output of the FIS block regulates the PI gain. This regulator gain is multiplied by both the reference (Ref1) and the feedback (feedback1) value, in other words, the error signal, and enters the PI controller. If the regulator gain is multiplied by each PI gain or by the input error signal to the PID block, no difference will be obtained due to the commutative law of multiplication. Finally, the PI output signal, shown in the figure as a control signal, is sent to the DC motors.

Figure 8.

The implementation of an adaptive fuzzy-PI controller.

The fuzzy-PI controller reference signal (Ref1) is considered a predefined signal in the simulation. The reference signals are based on changes in the angles of the human fingers in a specific movement. In Fig. 9, Signal 1, Signal 2, and Signal 3 are the reference signals for the three fuzzy-PI controllers of the three joints of a robotic finger, bicep, forearm, and turntable for the cylindrical movement. The signals are angular and expressed as degrees. To determine the signals, the participant performs, for example, a cylindrical movement, then a photograph is taken of it, and the Radiant Dicom Viewer software is used to measure the angle of the fingers. Following that, the angle of each human hand finger in that movement is considered a reference signal for the three joints of each robotic finger to rotate and perform the same movement. In cylindrical movement, each of the human fingers has an angle of 60 degrees, so in simulation, the three joints of each of the five robotic fingers take an angle of 60 degrees. The process of performing the movement takes seven seconds for each iteration. Each movement has been done ten times. Therefore, the total time to do ten repetitions is 70 seconds. In Fig. 9, one iteration occurs in the form of one trapezius in seven seconds. As shown in the figure, the hand is initially at rest. Therefore, the angle of each of the joints is zero. Then, as the person begins to move the hand, the angle of each of the hand joints gradually reaches 60 degrees. When the hand returns to the rest state, the joint angle becomes zero again.

Figure 9.

The reference signal for the finger's joints controllers for cylindrical movement.

2.6.1. Modeling of the eight movements

In this section, all eight movements have been modeled using fingers' angle changes during each movement. The angle signals for each robotic finger that includes three joints are defined as three trapezoidal signals, as shown in Fig. 9 in the previous section. Table 4 shows the angles of the three joints of each finger in degrees when the person's hand is in a static state, as shown in the photos in Fig. 4. In other words, these angles are the small base of the trapezoidal shown in Fig. 9 in the previous section. They were calculated by taking movement images and then using the Radiant Dicom Viewer software [62] to measure the angles in the images. The software includes tools for image manipulation and measurements, such as the ability to rotate (90, 180 degrees, or horizontally and vertically), measure fragment length, mean, minimum, and maximum parameters in a circle or ellipse, and angle value (normal and cob angle), and the Pen tool for freehand drawing.

Table 4.

Modeling the eight movements.

Type of the movement	Finger 1	Finger 2	Finger 3	Finger 4	Finger 5
Cylindrical	60	60	60	60	60
Hook	90	90	90	90	0
Lateral	90	90	90	90	90
Point	90	90	90	0	90
Rest	20	20	20	20	0
Spherical	40	40	40	40	40
Tripod	90	90	60	60	60
Tip	0	0	0	60	60

2.7. The general simulation of a three-degrees of freedom robot with DC motors and the controller

Fig. 10 shows the block diagram of the general simulation of a robot with three degrees of freedom, DC motors, and the controller. The Robot Mechanics block models the robot with three degrees of freedom, moments of inertia, and torques. The DC Motors block represents the DC motors and amplifiers. A DC motor with an amplifier is required to move each joint. Due to the higher torque needed to move the bicep joint shown in Fig. 6, two DC motors are considered. The adaptive fuzzy-PI controller is implemented in the Controller block. The Controller block has two inputs: command and feedback. Based on the command signal, which is the reference signal explained in section 2.6 and feedback from the Robot Mechanics block, the controller generates the necessary commands for the DC motors. The controller's output contains three signals: tCMD, bCMD, and fCMD. The signals command the DC motors of the robot's turntable, bicep, and forearm joints to adjust the PWM, reverse the rotation, and break. Then, the DC motors produce the torque required to rotate the three joints of the robot. Motor torque is entered into the Robot Mechanics to rotate the three joints. Three rotation angles of the robot's turntable, bicep, and forearm joints are measured by three sensors. They are the robot mechanics block outputs named Teta0, Teta1, and Teta2.

Figure 10.

Block diagram of the general simulation of a three-degrees of freedom robot using DC motors and the controller.

3. Flowchart of the proposed idea

Fig. 11 depicts the idea proposed for controlling the robotic hand based on the EMG signals. The EMG data is first processed, after which the features including MAV, VAR, and SE are extracted. EMG data classification is performed based on MAV and VAR features by LDA, QDA, KNN, and SVM methods to detect the movement. Then, the robotic hand model is developed, and the adaptive fuzzy-PI controller (ANFIS) is designed. In the next step, the hand model and the controller are simulated. MAV, VAR, and SE are extracted from the robotic hand movement signal (simulated data). The performance of the model and controller is assessed by comparing the features of simulated and EMG data by RMSE. As a result of this comparison, the controller is modified if necessary.

Figure 11.

The flowchart of the proposed idea.

4. Results

4.1. Classification results

This section reports the classification results obtained with the machine learning methods. Table 5, Table 6, Table 7, Table 8 show the classification results based on LDA, QDA, KNN, and SVM algorithms.

Table 5.

The classification results by LDA.

Sub. ID.	Accuracy (%)	Specificity (%)	Sensitivity (%)
1	83.47	90.53	34.23
2	81.09	88.89	22.53
3	82.51	89.98	29.83
4	81.43	89.25	24.31
5	82.13	89.71	27.63
Average	82.12	89.67	27.70

Table 6.

The classification results by QDA.

Sub. ID.	Accuracy (%)	Specificity (%)	Sensitivity (%)
1	82.91	90.28	31.01
2	83.46	90.49	33.22
3	83.39	90.52	33.30
4	83.81	90.69	35.26
5	82.69	90.09	31.17
Average	83.25	90.41	32.79

Table 7.

The classification results by KNN.

Sub. ID.	Accuracy (%)	Specificity (%)	Sensitivity (%)
1	86.11	92.03	46.77
2	86.84	92.47	46.94
3	88.21	93.26	50.23
4	90.61	94.60	63.78
5	86.25	92.08	45.18
Average	87.60	92.88	50.58

Table 8.

The classification results by SVM.

Sub. ID.	Accuracy (%)	Specificity (%)	Sensitivity (%)
1	87.83	92.99	51.32
2	91.37	95.07	64.53
3	90.24	94.31	59.58
4	91.99	95.39	67.74
5	92.04	95.44	67.35
Average	90.69	94.64	62.10

In this study, the number of classes is eight, equal to the number of the movements. To calculate the three criteria of accuracy, sensitivity, and specificity to evaluate the performance of classifiers, a confusion matrix for each individual in each of the classification methods is calculated. Eight values are calculated for each individual from the confusion matrix: eight values for accuracy, eight values for specificity, and eight values for sensitivity. Table 5, Table 6, Table 7, Table 8 illustrate the accuracy, specificity, and sensitivity of the classifiers for each individual, calculated by the average of the eight values. Fig. 12 (a-d) shows an example of the confusion matrixes for the LDA, QDA, KNN, and SVM classifiers used in this study for one individual, respectively.

Figure 12.

An example of the confusion matrixes for the classifiers for one individual. (a) LDA; (b) QDA; (c) KNN; (d) SVM.

A comparison of the classifiers in terms of accuracy, specificity, and sensitivity is shown in Fig. 13. According to the figure and tables, the SVM, KNN, QDA, and LDA classifiers performed better, respectively. LDA and QDA have more simple structures and faster performance, but their average sensitivity is remarkably low, especially for LDA. Despite more complex structures and slower performance, SVM and KNN perform better than the other two classifiers. Finally, the SVM classifier with an average accuracy, specificity, and sensitivity of 90.69%, 94.64%, and 62.10% can be appropriate for EMG data classification.

Figure 13.

The comparison of the classifiers in terms of accuracy, specificity, and sensitivity.

4.2. Simulation results and analysis of eight movements

In this section, the eight hand movements are simulated using the PI controller and the fuzzy-PI controller. All eight hand movements are simulated, but two of the eight movements, cylindrical and tip, are described to keep the paper brief.

4.2.1. Simulation of the movement #1 (cylindrical)

Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 show the results of applying the PI controller and the fuzzy-PI controller to the five fingers of the robotic hand for cylindrical movement. Figs. 14 (a-c) illustrate the angular signals of the three joints of a robotic finger or the movement signals. In these figures, the dashed blue line is the reference signal, the red curve shows the signal obtained from applying the PI controller, and the black curve is the signal obtained from applying the fuzzy PI controller. The horizontal axis is the time in seconds, and the vertical axis is the robotic finger joints' angle in degrees. The results for 0 s to 7 s are plotted to show the details. The error curves are shown in Fig. 14 (d-f). The error is defined as the difference between the signal obtained after applying the controller (PI or fuzzy PI) and the reference signal. The red curve is the error diagram for the PI controller, and the black curve is the error diagram for the fuzzy PI controller. The error is the difference between the reference signal and the angular signal from the movement of each robotic joint. The joints of the three degrees of freedom robot used for modeling a human finger, turntable, bicep, and forearm, are depicted in Fig. 6. Fig. 14 shows the results of Finger 1 (little finger). In this figure, the maximum error of the PI controller and the proposed controller are 18 degrees and 8 degrees, respectively.

Figure 14.

The results of applying the PI and fuzzy-PI controllers to finger 1 (little finger) of the robotic hand for cylindrical movement. (a-c) The angular signals of the three joints of a robotic finger; (d-f) the error curves.

Figure 15.

The results of applying the PI and fuzzy-PI controllers to finger 2 (ring finger) of the robotic hand for cylindrical movement. (a-c) The angular signals of the three joints of a robotic finger; (d-f) the error curves.

Figure 16.

The results of applying the PI and fuzzy-PI controllers to finger 3 (middle finger) of the robotic hand for cylindrical movement. (a-c) The angular signals of the three joints of a robotic finger; (d-f) the error curves.

Figure 17.

The results of applying the PI and fuzzy-PI controllers to finger 4 (forefinger) of the robotic hand for cylindrical movement. (a-c) The angular signals of the three joints of a robotic finger; (d-f) the error curves.

Figure 18.

The results of applying the PI and fuzzy-PI controllers to finger 5 (thumb) of the robotic hand for cylindrical movement. (a-c) The angular signals of the three joints of a robotic finger; (d-f) the error curves.

Fig. 15 shows Finger 2 (ring finger) results. Figs. 15 (a-c) illustrate the angular signals of the three joints of a robotic finger or the movement signals, and Figs. 15 (d-f) show the error curves. Fig. 16 shows finger 3 (middle finger). Figs. 16 (a-c) show the angular signals of the three joints of a robotic finger or the movement signals, and Figs. 16 (d-f) display the error curves. Similar to Fig. 14, the maximum error of the PI controller and the proposed controller are about 18 degrees and 8 degrees, respectively.

Fig. 17 shows the results of Finger 4 (forefinger). Figs. 17 (a-c) illustrate the angular signals of the three joints of a robotic finger or the movement signals, and Figs. 17 (d-f) display the error curves. Fig. 18 shows the results of Finger 5 (thumb). Figs. 18 (a-c) show the angular signals of the three joints of a robotic finger or the movement signals, and Figs. 18 (d-f) depict the error curves. Similar to Figure 14, Figure 15, Figure 16, the maximum error of the PI controller and the proposed controller are about 18 degrees and 8 degrees, respectively.

For both applied controllers, the output signal tracks the reference signal well. However, the steady-state error of the PI controller reaches 18%, while that of the fuzzy-PI controller is less than 6%.

4.2.2. Simulation of the movement #8 (tip)

Figure 19, Figure 20, Figure 21 show the results of applying the PI controller and the fuzzy-PI controller to the simulation model for Spherical movement. Fig. 19 shows the results of Finger 1 (little finger). Since the result curves for finger 2 (ring finger) and finger 3 (middle finger) are similar to finger 1 (little finger), they are not plotted to avoid increasing the content of the article. Figs. 19 (a-c) show the angular signals of the three joints of a robotic finger or the movement signals, and Figs. 19 (d-f) display the error curves.

Figure 19.

The results of applying the PI and fuzzy-PI controllers to finger 1 (little finger), finger 2 (ring finger), and finger 3 (middle finger) of the robotic hand for Tip movement. (a-c) The angular signals of the three joints of a robotic finger; (d-f) the error curves.

Figure 20.

The results of applying the PI and fuzzy-PI controllers to finger 4 (forefinger) of the robotic hand for Tip movement. (a-c) The angular signals of the three joints of a robotic finger; (d-f) the error curves.

Figure 21.

The results of applying the PI and fuzzy-PI controllers to finger 5 (thumb) of the robotic hand for Tip movement. (a-c) The angular signals of the three joints of a robotic finger; (d-f) the error curves.

Fig. 20 shows the results of Finger 4 (forefinger). Figs. 20 (a-c) show the angular signals of the three joints of a robotic finger or the movement signals, and Figs. 20 (d-f) display the error curves. The maximum error of the PI controller and the proposed controller are about 17 degrees and 7 degrees, respectively. Fig. 21 shows the results of Finger 5 (thumb). Figs. 21 (a-c) show the angular signals of the three joints of a robotic finger or the movement signals, and Figs. 21 (d-f) display the error curves.

The maximum error of the PI controller and the proposed controller are about 16 degrees and 7 degrees, respectively.

As can be seen in the figures, both PI and fuzzy-PI controllers can track the reference signal, but the fuzzy-PI controller performs better than the PI. In summary, the advantages of using the fuzzy-PI controller over the PI controller are:

• a)proper tracking of the reference signal;
• b)more appropriate response speed;
• c)smaller steady-state error;
• d)smaller overshoot;
• e)robustness due to using the PI controller;
• f)compatibility with the operating conditions and different movements because of the fuzzy system.

5. Discussion

This study proposes an adaptive fuzzy-PI controller using EMG signals to enhance robotic hand control. The purpose of this work is to achieve the highest degree of resemblance between prosthetic limbs and human limbs since better performance will eventually be achieved if the prostheses are more similar to human organs. People with disabilities and amputees can benefit from these organs to live a more fulfilling life and be more productive at work.

Compared to other research, one of the principal advantages of this research is using a hand model with five fingers and fifteen degrees of freedom. There are more pros mentioned in Table 9. This table compares several well-known and recent methods with this study.

Table 9.

The comparison of the proposed method with other control methods.

Work	Degrees of freedom	Simplicity	Uncertainty handling	Ability of grasping different objects	Online adaption	Commercialization ability
Fuzzy control based on wavelet transform [10]	1	×	✓	×	×	×
Conceptual model [11]	2	×	✓	×	×	×
Hierarchical control method [12]	2	×	✓	✓	✓	×
PID controller [13]	1	✓	×	×	×	×
Backward control [14]	1-2	✓	×	×	×	×
Statistical learning algorithms [15]	2	×	×	✓	×	×
Neural networks with error backpropagation [16]	2	×	✓	✓	×	×
Adaptive Sliding Mode [63]	2	×	✓	×	✓	×
Model-free predictive control [64]	2	×	✓	✓	✓	×
Adaptive fuzzy-PI controller (current study)	3	×	✓	✓	✓	✓

Previous research [10] has shown that fuzzy control based on wavelet transformation was used for models of one degree of freedom. The model cannot grasp different objects without training, cannot be applied online, and is complex. The advantage of this method is uncertainty handling because fuzzy systems are not based on models. The conceptual model [11] is similar to fuzzy control, but it can handle mathematical models with two degrees of freedom. The hierarchical control method [12] has the capability of uncertainty handling, holding different objects, and online adaption. Nevertheless, it is limited to two degrees of freedom, which is considered a drawback. It is also complex and challenging to be commercialized.

The PID controller [13] can handle only models with one degree of freedom, cannot overcome uncertainties and be adapted online, and is inappropriate for grasping different objects. Thus, it is an inappropriate method for commercial solutions. Simplicity is the only benefit of the PID controller. The backward control [14] is similar to PID, but it can be designed to handle two degrees of freedom models. Statistical learning algorithms [15] can handle two degrees of freedom models and grasp different things because of their statistical basis. They do not have any other pros.

Neural networks [16] can address uncertainties and grasp various objects because of their intelligence. However, they are not simple enough to realize and need to be adapted offline. Hence, they are not reasonable solutions for commercialization. Adaptive sliding mode [63] is a complex method to handle models with two degrees of freedom, with the ability to be adapted online. It is an appropriate method for managing uncertainties, but it is not a reliable solution to grasp different objects without training. Because of the complexity, it is not recommended for commercial solutions. Model-free predictive control [64] with the ability to handle models with two degrees of freedom is a proper choice to manage model uncertainties and grasp different objects since it can be adapted online. However, it is not a suitable solution for practical usage because of its complexity.

The control method proposed in this study does have the ability to handle model uncertainties, grasp different objects, adapt online, and be commercialized. Consequently, it can be considered a practical and experimental method. The controller is evaluated in two ways in the following:

One is the numerical comparison of the fuzzy-PI controller with the PI based on the RMSE criterion. As mentioned in section 4.2, the fuzzy-PI controller outperforms the PI. These controllers are compared numerically to prove the results of section 4.2. In Table 10, RMSE-PI is the root mean square error of the PI controller, and RMSE-Fuzzy-PI is the root mean square error of the fuzzy-PI. The average RMSE for the fuzzy-PI is 1.6067, and the PI is 5.0082. The RMSE values demonstrate that the robotic hand movement signal generated by the fuzzy-PI controller is more compatible with the reference signal.

Table 10.

The comparison of RMSE of the simulation data for PI and Fuzzy-PI Controllers.

Type of movement	RMSE-PI	RMSE-Fuzzy-PI
Cylindrical	6.6088	2.6080
Hook	5.5096	1.8301
Lateral	4.0465	1.0366
Point	4.0565	1.0871
Rest	4.763	1.0231
Spherical	4.5006	1.8949
Tripod	3.972	0.6058
Tip	6.6088	2.7682
Average	5.0082	1.6067

Another way is to compare EMG data and the simulated data from the fuzzy-PI controller. Since the EMG and simulated signals do not have the same dimensions and units, both signals are first normalized using Eq. (10) to obtain non-unit signals. The resulting signals are then compared.

$$X_{\mathrm{normalized}}=\frac{X-X_{\min }}{X_{\max }-X_{\min }}$$ (10)

Fig. 22 compares the EMG signal with the robotic hand movement signal from the fuzzy-PI controller and their features for lateral movement.

Figure 22.

(a) and (b) the EMG and the robotic hand movement signals for Lateral movement; (c) and (d) Comparing the EMG signal with the robotic hand movement signal from the fuzzy-PI controller and their features for Lateral movement.

Figs. 22 (a) and (b) plot the EMG signals (recorded voltages from two electrodes) and the robotic hand movement signal from the simulation in blue and red, respectively. As mentioned in section 2.1, the EMG signals in this study were recorded by electrodes 1 and 2 placed on the FDS and FPL muscles of the forearm of each individual who performed eight movements. It is evident from the figure that the blue EMG signal is noisy and cannot be compared to the red simulated signal, so it is better to compare its characteristics, such as MAV, VAR, or SE. Figs. 22 (c) and (d) compare the simulated signal and its features with the EMG signal features. The EMG's MAV general form is relatively close to the simulated data form. Its VAR also has notable adaption with the VAR EMG signal and its SE with the SE EMG signal. These results indicate that the hand model with the controller can simulate the actual behavior of the human hand well in terms of angle and tracking changes.

The comparison of EMG signal features and robotic hand movement signal (simulated data) features in terms of RMSE for five subjects and eight movements is shown in Table 11. The RMSE1, RMSE2, and RMSE3 criteria are the RMSE between the MAVs, VARs, and SEs of the EMG and simulated data, respectively. Based on Table 11, it can be concluded that the RMSEs amount between the human hand movement signal (EMG) features and the robotic hand movement signal (simulated signal) features are significantly small. These small amounts show that the features of these two signals are remarkably similar. So, the conclusion is that the robotic hand model with the proposed controller can behave well like a human hand.

Table 11.

The comparison of RMSE of the EMG data features and simulated data features.

Sub. ID.	RMSE	Cylindrical	Hook	Lateral	Point	Rest	Spherical	Tripod	Tip
	RMSE1	0.0647	0.0720	0.1474	0.1042	0.1660	0.0652	0.0675	0.1569
1	RMSE2	0.0089	0.0107	0.0465	0.0198	0.0531	0.0089	0.0099	0.0533
	RMSE3	0.0387	0.0564	0.0358	0.0313	0.0546	0.0757	0.0374	0.0398
	RMSE1	0.0659	0.0730	0.1501	0.1021	0.1520	0.0630	0.0663	0.1509
2	RMSE2	0.0074	0.0115	0.0405	0.0175	0.0520	0.0072	0.0088	0.0453
	RMSE3	0.0367	0.0577	0.0315	0.0333	0.0552	0.0768	0.0355	0.0411
	RMSE1	0.0669	0.0750	0.1491	0.1008	0.1310	0.0510	0.0653	0.1498
3	RMSE2	0.0069	0.0137	0.0444	0.0203	0.0497	0.0061	0.0071	0.0498
	RMSE3	0.0411	0.0514	0.0338	0.0298	0.0531	0.0762	0.0401	0.0421
	RMSE1	0.0598	0.0690	0.1450	0.1028	0.1410	0.0750	0.0644	0.1495
4	RMSE2	0.0072	0.0115	0.0458	0.0189	0.0521	0.0059	0.0089	0.0541
	RMSE3	0.0355	0.0577	0.0375	0.0295	0.0498	0.0721	0.0361	0.0391
	RMSE1	0.0599	0.0730	0.1421	0.1041	0.1450	0.0671	0.0688	0.1530
5	RMSE2	0.0069	0.0108	0.0398	0.0171	0.0420	0.0069	0.0059	0.0441
	RMSE3	0.0347	0.0541	0.0342	0.0323	0.0512	0.0721	0.0351	0.0388

If any of the parameters in Table 2 change, the proposed controller can adapt the gains to the new condition. It is because of the adaptive nature of PI gains with the application of fuzzy logic. If any parameters of the controller change, the result will affect the learning procedure and the system behavior. For instance, the system will be more complex if the number of fuzzy rules increases, but the performance will improve. Therefore, it is necessary to make a trade-off between system performance and complexity. Different fuzzy rule bases are tested in this work. The PI gains have various values during execution, so changing them by about 5% will not affect the results.

The major limitation of this study is that the EMG signals are noisy and cannot be compared to the simulated data or used to train the controller. It is recommended to find a solution to improve EMG data's signal-to-noise ratio (SNR) for future works. Another limitation is the limited number of people for data gathering. It is suggested to conduct this research with more people, including healthy and amputee individuals.

6. Conclusion

In designing and controlling robotic or prosthetic limbs, the goal is to create the maximum similarity to healthy human limbs. This study aimed to improve robotic hand control through an adaptive fuzzy-PI controller using EMG signals so that the robotic hand would behave similarly to a human hand. The EMG signals were collected from the FPL and FDS muscles of the forearms of five girls performing the eight movements. Following preprocessing and filtering of the data, the optimal time-domain feature set for hand motion detection systems comprising MAV, VAR, and SE was extracted. Due to the zero value of the SE, EMG signals were classified based on MAV and VAR using four of the most common machine learning methods, namely LDA, QDA, KNN, and SVM. As a comparison of classification methods, SVM, with an average accuracy, specificity, and sensitivity of 90.69%, 94.64%, and 62.10% for five subjects, is a better choice for movement detection than the other three. While previous research has modeled fingers with one or two degrees of freedom, a robotic hand with five fingers, each with three degrees of freedom, was modeled. An ANFIS-type adaptive fuzzy-PI controller was designed to control the robotic hand. For determining the controller's reference signal, the eight movements were first modeled in a new way through the angles of the fingers while performing the movements. The angular signals entered the controller as a reference signal based on the motion detected by the SVM classifier. The proposed control method and robotic hand model were evaluated in two ways. One was the comparison of the fuzzy-PI and the PI controllers. For eight robotic hand movements using the fuzzy-PI, the average RMSE was 1.6067, and the PI was 5.0082. Also, the steady-state error was 6 to 8% for fuzzy-PI and 16 to 18% for PI. The results show that the fuzzy-PI controller outperforms the PI and has advantages such as proper tracking of the reference signal, more appropriate response speed, less steady-state error and overshoot, robustness as a result of the PI controller's use, and compatibility with operating conditions and different movements as a result of the fuzzy system's use. Another was a new evaluation method that uses the RMSE criterion to compare the features of human hand signals (EMG) and robotic hand movement signals. The comparison has demonstrated that the robot hand motion signal was significantly similar to the MAV of the EMG. EMG's VAR and SE were like the simulated signal's VAR and SE. As a result, the model with the designed controller could act like a human hand in terms of angle and tracking changes. The targets of future research are the utilization of other control methods, including robust control, neural control, and biologically based methods; modeling of gray box systems using neural networks based on EMG data; optimization of grey box models using repetitive algorithms; and collecting more EMG data from both healthy and amputee subjects.

Declarations

Author contribution statement

Mahsa Barfi: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Hamidreza Karami: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Fatemeh Faridi: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data.

Zahra Sohrabi, Manouchehr Hosseini: Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

Data associated with this study has been deposited at https://github.com/Hamidreza-Karami/Improving-Robotic-Hand-Control-via-Adaptive-Fuzzy-PI-Controller-using-Classification-of-EMG-Signals.

Declaration of interests statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.