The 8-channel myoelectric ring (Dting-One) produced by Beech Innovation Company was employed to obtain sEMG, as shown in Figure 1. The signals received from every channel were amplified 700 times and then transmitted by Bluetooth to the computer. In order to improve the acquisition phase, the Bluetooth channel was bypassed by directly drawing five signals through wired connections so as to increase the sampling frequency from 100 to 1,000 Hz; the five signals were directly associated with five of the main forearm muscles, as hereinafter reported. The signals’ processing and analysis were performed offline.

The collected data needed preprocessing so as to extract features. The procedures included amplification, de-biasing, the bandpass filter, and the Kalman filter. Since the output signals contained 2.5 V bias voltages, it was necessary to subtract 2.5 V from the obtained signals to eliminate the effect. The filter method adopted was the finite impulse response digital bandpass filter. According to the studies (Baocheng Wang et al., 2014; Long et al., 2016), the scope was 20–200 Hz, and a notch filter was performed. The notch is set between 48 and 52 Hz to avoid the interference of the 50 Hz power frequency. The lower arm muscles are mainly composed of brachioradialis, flexor carpi ulnar, flexor carpi radialis, teres pronator, extensor carpi radialis longus, extensor carpi ulnar, polpolissimus brevis, pronator, extensor index finger, extensor digitus, and extensor digitus little. The brachioradialis muscle mainly flexes the elbow, rotates the forearm in and out, and maintains the median position during proximal fixation; the flexor carpi radialis is mainly used for flexion of the radial wrist joint, participating in wrist abduction, assisting elbow flexion and forearm internal rotation; the pronator teres muscle is mainly used to rotate the forearm inward to assist elbow flexion. Musculus extensor carpi radialis longus is mainly used to extend the wrist joint near fixation and participate in radiocarpal abduction and elbow extension and rotation; the pronator teres muscle is mainly involved in arm backrotation. According to the relationship between muscles and lateral movement, the electrode placement was pronator teres muscles, flexor carpi radialis, musculus extensor carpi radialis longus, musculus supinator, and brachioradialis, as shown in Figure 2.

People could recognize the delay when the time is longer than 250 ms, so the data threshold of 250 ms was used as a set to get features. Besides, it was also critical to choose appropriate features to ensure classification accuracy. (Phinyomark et al., 2012) discussed the significance of selecting appropriate extraction feature methods. This study used mean absolute value (MAV), discrete Fourier transform (DFT), and wavelet transform (WT) as features (Yang et al., 2014).

(1) MAV

The Fourier transform converts signals to the frequency domain. SEMG collected are discrete, so DFT is needed for x(n). The transformation formulas are defined as { X ( k ) = ∑ n = 0 N − 1 x ( n ) W N n k x ( n ) = 1 N ∑ k = 0 N − 1 X ( k ) W N − n k (2) where W N = e − j 2 π N and N is the number of samples.

(3) WT

For the signals x(t), the wavelet transformation is obtained as W f ( a , b ) = 1 a ∫ − ∞ ∞ x ( t ) ψ a , b ( t − b a ) d t (3) where 1 a ψ a , b ( t − b a ) is the selected wavelet sequence, a is the scaling factor, b is the translation factor, and a, b ∈ R and a≠0.

There was a close relationship between the sEMG and the joint angles during the execution of specific movements (Ding et al., 2017; Bergil et al., 2021; Makaram et al., 2021). Choosing the appropriate feature extraction method and machine learning algorithm was imperative for the human body motion angle estimation. Compared with KNN, LDA, and other processes (Liao et al., 2020), the BP neural network was appropriate to the case where the amount of classification data was small, and the classification results were extensive. Due to the limited training data in this study, a BP neural network model of sEMG features and motion angles was established to realize the human motion angles estimation. The model’s input signals were the features of sEMG, and the output signals were the movement angle of the upper limb.

The input layers of the BP estimation model contain fifteen neurons, the hidden layers six neurons, and output layers one neuron. The transfer functions of the hidden and output layers were tansig and purelin, respectively; the training number, training speed, and target error were 10,000, 0.01, and 0.001 (Chen et al., 2018). The training result of an individual is shown in Figure 3, from which we can see that the performance of the BP model is satisfying by using the corresponding parameters.

SEMG was utilized to predict the joint movement angle, but with its strong nonlinearity and the angle estimation of the pronation–supination movement controlled by many different muscles, the estimation results had a significant error. The nonlinear Kalman filter was employed to modify the estimation result.

The essence of the Kalman filter is to estimate the system’s operating statement based on the data obtained in the past and realize the estimation and correction functions. The discrete nonlinear control model is obtained as x k = f k - 1 ( x k - 1 , u k - 1 , w k - 1 ) (4) z k = h h ( x k , v k ) (5) where k and k-1 are two consecutive moments, μ k − 1 ∈ R r is the input matrix of the system at time k-1, xk is the state of the system at time k, and w k ∈ R p and v k ∈ R q are Gaussian white noise, and there is no correlation between the two.

The statistical relationship between wk and vk is given as { E ( w k ) = q k , Cov ( w k , w j ) = Q k δ k j E ( v k ) = r k , Cov ( v k , v j ) = R k δ kj Cov ( w k , v j ) = 0 (6) where Rk is a symmetric positive definite matrix, and Q k is a symmetric non-negative definite matrix.

The initial state x0 is independent of wk and vk. The mean and the covariance matrix of x0 are given by { x ^ 0 = E ( x 0 ) P 0 = Cov ( x 0 , x 0 ) = E [ ( x 0 − x ^ 0 ) ( x 0 − x ^ 0 ) T ] (7)

The nonlinear control model f_k-1 (·) is expanded into a Taylor series based on the filtered value x ^ k − 1 , and the second and higher orders are omitted, and xk is obtained as x k ≈ f k − 1 ( x ^ k − 1 , u k − 1 , q k − 1 ) + ∂ f ∂ x ^ k − 1 ( x k − 1 − x ^ k − 1 ) + ∂ f ∂ w k − 1 ( w k − 1 − q k − 1 ) , (8) where fk-1 (·), xk-1, and wk-1 are given, respectively. f k − 1 ( ⋅ ) = [ f k - 1 1 ( ⋅ )   f k - 1 2 ( ⋅ )   ⋯   f k - 1 n ( ⋅ ) ] T ; x k - 1 = [ x k - 1 1 x k - 1 2 ⋯ x k - 1 n ] T ; w k − 1 = [ w k − 1 1 w k − 1 2 ⋯ w k − 1 p ] T ; ∂ f ∂ x ^ k - 1 = ∂ f k - 1 ( x k - 1 , u k - 1 , w k - 1 ) ∂ x k - 1 | x k - 1 = x ^ k - 1 w k - 1 = q k - 1 = [ ∂ f k − 1 1 ( ⋅ ) ∂ x k − 1 1 ∂ f k − 1 1 ( ⋅ ) ∂ x k − 1 2 ⋯ ∂ f k − 1 1 ( ⋅ ) ∂ x k − 1 n ∂ f k − 1 2 ( ⋅ ) ∂ x k − 1 1 ∂ f k − 1 2 ( ⋅ ) ∂ x k − 1 2 ⋯ ∂ f k − 1 2 ( ⋅ ) ∂ x k − 1 n ⋮ ⋮ ⋮ ∂ f k − 1 n ( ⋅ ) ∂ x k − 1 1 ∂ f k − 1 n ( ⋅ ) ∂ x k − 1 2 ⋯ ∂ f k − 1 n ( ⋅ ) ∂ x k − 1 n ] x k - 1 = x ^ k - 1 w k - 1 = q k - 1 ; ∂ f ∂ w k - 1 = ∂ f k - 1 ( x k - 1 , u k - 1 , w k - 1 ) ∂ w k - 1 | x k - 1 = x ^ k - 1 w k - 1 = q k - 1 = [ ∂ f k − 1 1 ( ⋅ ) ∂ w k − 1 1 ∂ f k − 1 1 ( ⋅ ) ∂ w k − 1 2 ⋯ ∂ f k − 1 1 ( ⋅ ) ∂ w k − 1 p ∂ f k − 1 2 ( ⋅ ) ∂ w k − 1 1 ∂ f k − 1 2 ( ⋅ ) ∂ w k − 1 2 ⋯ ∂ f k − 1 2 ( ⋅ ) ∂ w k − 1 p ⋮ ⋮ ⋮ ∂ f k − 1 n ( ⋅ ) ∂ w k − 1 1 ∂ f k − 1 n ( ⋅ ) ∂ w k − 1 2 ⋯ ∂ f k − 1 n ( ⋅ ) ∂ w k − 1 p ] x k - 1 = x ^ k - 1 w k - 1 = q k - 1 . Suppose ∂ f ∂ x ^ k - 1 = Φ k ,   k - 1 , ∂ f ∂ w k - 1 = Γ k , k - 1 , and f k − 1 ( x ^ k - 1 , u k - 1 , q k - 1 ) − ∂ f ∂ x ^ k - 1 x ^ k - 1 = U k - 1 , then the first order linearization of the state function of the nonlinear model can be transformed into x k ≈ Φ k , k - 1 x k - 1 + U k - 1 + Γ k , k - 1 ( w k - 1 − q k - 1 ) . (9)

After expanding the nonlinear measurement function h _k (·) around the filter value x ^ k | k - 1 and omitting the Taylor series of the second and higher orders, the function z _k is explained as z k ≈ h k ( x ^ k | k - 1 , r k ) + ∂ h ∂ x ^ k | k - 1 ( x k − x ^ k | k - 1 ) + ∂ h ∂ v k ( v k − γ k ) , (10) where h _k (·) and v _k are obtained by h k ( ⋅ ) = [ h k 1 ( ⋅ )   h k 2 ( ⋅ )   ⋯   h k m ( ⋅ ) ] T ; v k = [ v k 1 v k 2 ⋯ v k q ] T ; ∂ h ∂ x ^ k | k - 1 = ∂ h k ( x k , v k ) ∂ x k | x k = x ^ k | k - 1 v k = r k             = [ ∂ h k 1 ( ⋅ ) ∂ x k 1 ∂ h k 1 ( ⋅ ) ∂ x k 2 ⋯ ∂ h k 1 ( ⋅ ) ∂ x k n ∂ h k 2 ( ⋅ ) ∂ x k 1 ∂ h k 2 ( ⋅ ) ∂ x k 2 ⋯ ∂ h k 2 ( ⋅ ) ∂ x k n ⋮ ⋮ ⋮ ∂ h k m ( ⋅ ) ∂ x k 1 ∂ h k m ( ⋅ ) ∂ x k 2 ⋯ ∂ h k m ( ⋅ ) ∂ x k n ] x k = x ^ k | k - 1 v k = r k             ∂ h ∂ v k = ∂ h k ( x k , v k ) ∂ v k | x k = x ^ k | k - 1 v k = r k             = [ ∂ h k 1 ( ⋅ ) ∂ v k 1 ∂ h k 1 ( ⋅ ) ∂ v k 2 ⋯ ∂ h k 1 ( ⋅ ) ∂ v k q ∂ h k 2 ( ⋅ ) ∂ v k 1 ∂ h k 2 ( ⋅ ) ∂ v k 2 ⋯ ∂ h k 2 ( ⋅ ) ∂ v k q ⋮ ⋮ ⋮ ∂ h k m ( ⋅ ) ∂ v k 1 ∂ h k m ( ⋅ ) ∂ v k 2 ⋯ ∂ h k m ( ⋅ ) ∂ v k q ] x k = x ^ k | k - 1 v k = r k             . Suppose ∂ h ∂ x ^ k | k − 1 = H k , h k ( x ^ k | k - 1 , r k ) − ∂ h ∂ x ^ k | k - 1 x ^ k | k - 1 = y k , and   ∂ h ∂ v k = Λ k , then the first order linearization of the measurement function of the nonlinear system model is z k ≈ H k x k + y k + Λ k ( v k − r k ) . (11)

The methods used to process the obtained angles are as follows: use eqs 9, 11 to convert the state model from nonlinear to linear, and then, use the basic linear equations of the discrete system for the Kalman filter.

The exoskeleton robot of upper limbs has many DOFs, but it was not easy to foresee movements of all DOFs. The DOF of the pronation–supination movement was controlled by multiple muscles, so obtaining the most effective muscle combination was difficult. Moreover, the sEMG obtained was relatively weak and susceptible to external interference; thus, the angle estimation was complex. Existing studies, such as those by (Huang et al., 2020; Xi et al., 2021), are less involved in the DOF of the pronation–supination movement. This study took the DOF of the pronation–supination movement as the research object to expand the application range of the continuous movement estimation.

An exoskeleton robot of the upper limb was used to verify the angle estimation accuracy and observe the error between the estimation and the human motion angle. Before the structure of the exoskeleton robot was defined, the human physiological structure was studied to determine the appropriate range of the DOF. The movement range could be gained according to ergonomic characteristics to ensure the safety of the exoskeleton robot during operation. The limit for the pronation–supination movement was -90–90.0°. At the same time, we defined that the center of the palm back to the ground was called 0° (see in Figure 4 supination), and the opposite was 180.0°. The movement begin the posion supination and ended the posiont pronation The angle definition of the DOF is illustrated in Figure 4.

The absolute error Δ and relative error δ of the joint rotation angle are respectively Δ = | x 2 − x 1 | (12) δ = | x 2 − x 1 | x 1 × 100 % (13) where x ₁ is the human body joint angle, and x ₂ is the exoskeleton robot angle. Two 9-axis attitude sensors (WT901C) are used to measure the x ₁ and x ₂.

To verify the effect of the continuous movement estimation on the exoskeleton robot control, we designed an exoskeleton robot with one DOF after a comprehensive consideration of the physiological structure of different upper limbs. In the designing process, we mainly considered the following key measures.

One DOF was designed for the upper limb exoskeleton robot, which was then utilized to perform a tracking test. Then, a relationship model between sEMG features and the upper limb movement angle was set up. The participants in different trials vary from 5 to 20 according to the studies in (Pang et al., 2013; Geng et al., 2016; Wu and Chen 2021). The number of subjects in this trial was eight (including seven males, one female), aging between 23 and 32 years old, and six right-hands and two left-hands were included. Before attaching the EMG sensor, the electrode sticking site is kept clean and moist; an informed consent is signed; at least 2-min rest is needed between each group of movements in the trial to avoid the influence of muscle fatigue on the quality of sEMG. It was approved by the Medical and Experimental Animal Ethics Committee of Northwestern Polytechnical University.

The exoskeleton robot was fixed on the upper limb of a participant. The angle of the pronation–supination movement and the rotation angle of the exoskeleton robot’s wrist ring are measured by two attitude sensors. The attitude sensor lay flat on an individual’s palm, and the x-axis was collinear with the forearm (the individual was the subject). By analyzing the change, the pronation–supination movement angle could be obtained. Another attitude sensor was put on the wrist of the robot. The x-axis was collinear with the exoskeleton robot’s forearm, and the x-axis angle change was analyzed to obtain the rotation angle of the robot’s wrist ring. We could get lateral DOF’s tracking effect by comparing the differences between angles.

During the test, the subject sat in a chair, keeping the body upright and looking straight ahead, and the angle between the upper arm and the forearm was 90.0°. Initially, the subject’s palm was parallel to the horizontal plane, and the palm was upward, and then rotated 180.0° until the palm was downward. The whole process lasted 5.0 s and tried to ensure a constant speed rotation, and other joints were kept as immobile as possible. During the participant’s forearm rotation with the exoskeleton robot, the DOF of the other joints should be kept as immobile as possible except for the lateral freedom of the movement. The subject’s forearm was rotated 180.0° laterally. The subject’s sEMG was employed as training data, and participants' signals were used as test data. Extracted features from the data and imported them into the BP neural network to generate an angle estimation model and used it to predict the lateral rotation angle of humans. Every subject received tests five times, and the results from five tests were averaged. The experimental flow is shown in Figure 7. First, the sEMG was obtained from the subjects and preprocessed. Then, the signals' feature was extracted, and finally, features were imported into BP for prediction. The predicted results are imported into the computer to drive the exoskeleton, and the tracking error is obtained according to the angle obtained from the exoskeleton and the actual rotation angle of the human body.

This study employed the neural network model as an alternative strategy to the Hill muscle model, which requires optimizing many different parameters. The designed BP estimation model could realize the forearm’s angle estimation: different subjects were selected to test the developed estimation model’s performance; then the average absolute and relative errors of results were obtained. The average relative error and the average absolute error was about 23.3% and 17.6°, respectively. The Kalman filter model is a good method to correct the predicted value. The results show that the proposed method also achieves good experimental results.

Scholars had conducted extensive research on the estimation of continuous movement of the human body. For example, (Han et al., 2015) selected the Hill muscle model to predict the continuous movement angle, which greatly improved the estimation accuracy of the upper limb motion. Jimson et al. (Vogel et al., 2013) proposed an activation model that parameterizes the electromechanical delay artificial neural network by extracting sEMG, estimating finger joints’ angle, and using the estimation results to drive the right-hand index finger exoskeleton robot to evaluate the effect. The Kalman filter estimates the current state based on the state of the last moment and estimates the optimal state through the correction of the estimated state and the observed state at the current moment, to obtain the optimal solution and realize the correction of the whole prediction process. Ang et al. (Pang et al., 2013) used the Kalman filter to process surface EMG signals and conducted experiments on five subjects. The results showed that the designed Hill muscle model could predict the angle of fingers when they naturally bent. In this study, the Kalman filter was used to modify the predicted value to improve the prediction accuracy of the pronation–supination movement DOF, and the BP neural network model was used to estimate the rotation angle of the human forearm, which expanded the freedom range of the upper limb continuous movement estimation, and improved the accuracy of the human–machine collaborative control process of the upper limb exoskeleton robot.

The rotation angle of the pronation–supination movement DOF was 0–180.0°. In future work, our estimation method needs to be improved to enhance accuracy, and the signals’ processing and analysis will be performed online. Figure 8 shows that despite the errors, the DOF is in line with the increasing trend of the actual angle, indicating that the errors do not affect the exoskeleton robot’s standard control.