Mirror motion recognition method about upper limb rehabilitation robot based on sEMG

Abstract

A novel method of mirror motion recognition by rehabilitation robot with multi-channels sEMG signals is proposed, aiming to help the stroked patients to complete rehabilitation training movement. Firstly the bilateral mirror training is used and the model of muscle synergy with basic sEMG signals is established. Secondly, the constrained L ${}_{1/2}$ -NMF is used to extracted the main sEMG signals information which can also reduce the limb movement characteristics. Finally the relationship between sEMG signal characteristics and upper limb movement is described by TSSVD-ELM and it is applied to improve the model stability. The validity and feasibility of the proposed strategy are verified by the experiments in this paper, and the rehabilitation robot can move with the mirror upper limb. By comparing the method proposed in this paper with PCA and full-action feature extraction, it is confirmed that convergence speed is faster; the feature extraction accuracy is higher which can be used in rehabilitation robot systems.

Keywords

sEMG constrained NMF ELM with truncated singular value decomposition muscle synergy model

1. Introduction

The number of patients with nerve damage caused by strokes has increased year by year in the world, which seriously affects their ability to take care of themselves and imposes a heavy burden on families and society. In the past 20 years, a number of rehabilitation robot systems have emerged to help doctors and patients with rehabilitation training [1, 2, 3]. They can monitor the rehabilitation process, and can adjust parameters and training programs according to the patient’s condition, by many intelligent assistance systems and sensors [4, 5].

The surface electromyography (sEMG) signal is an electrical signal. It is formed by the spatio-temporal superposition effect of the action potential on the skin surface when muscle system moves under the control of the nervous system. There is a significant linear mapping between sEMG amplitude and muscle strength [6]. Comparing with other signals, the sEMG is ahead of limb movement which can compensate for the hysteresis of motion signals effectively. At the same time the sEMG signals collected by different subjects under the same conditions have higher similarity. For example, Kiguchi [7] used a neurofuzzy matrix modifier with EMG to make the controller suitable for most users. Vahab Khoshdel [8] took sEMG as force sensors to estimate the exerted force, so the controller is not affected by dynamical models of robot and patients, and designed a adaptive fuzzy system to estimate the uncertainty. Guo [9] took Detrended Fluctuation Analysis, Root Mean Square, Muscular Model and Weight Peaks as feature extraction methods, took Support Vector Machine and Neural Networks as classifiers, and got the recognition accuracy rate 88.7% for Neural Networks and 85.9% for Support Vector Machine.

Clinical researches have shown that rehabilitation training with exercise intention is more effective for neurological reconstruction and function recovery in patients [10]. But for stroke patients (especially those in the early stage of rehabilitation), the contraction ability and strength of the muscle from affected limb are very small, and the corresponding sEMG signals are very weak. It is difficult to judge the patient’s motion intention with the sEMG signals of the affected limb, but the sEMG signals from healthy limb can respond the limb movement intention very well. Because the muscles of the upper limbs are coordinate, the symmetry movement is more stable than the asymmetric movement and the frequency and phase of the two-upper limbs’ movement will be synchronized. Therefore, the bilateral mirror rehabilitation training method can be used to control rehabilitation robot. In order to make the robot follow the movement of the limb movement, the first step is to recognize the posture accurately.

Muscle synergy is a theory that is used for dimension reduction in muscle coordination, it has been shown to form the basis of complex muscle coordination patterns involved in activities such as kicking, swimming, jumping of frogs postural standing and human arm movements [11]. NMF is a kind of decomposition method proposed by Lee et al. [12]. It can decomposed the given data into two non-negative matrices, and it is widely used for pattern recognition and hyperspectral unmixing [13]. Israely [14] used a single set of muscle synergies to express movements in different directions, which is implemented by NMF (non-negative matrix factorization). Ma [6] also used NMF to map muscle synergy model to realize the proportional control of hand and wrist. Compared with PCA (Principal Component Analysis) [15] and ICA (Independent Component Analysis), the reconstruction process is closer to a whole with clear physics significance [16]. Moreover, the NMF decomposition result not only has some sparsity for non-negative matrices, but also can suppress the adverse effects caused by external changes to feature extraction in a certain extent [17, 18, 19]. However, these studies have no constraints on NMF algorithm, which makes the coordination separation incomplete and affects the recognition effect.

Extreme Learning Machine (ELM) as a single hidden layer feed-forward neural network learning algorithm developed in recent years [20]. It is simple to implement, with extremely fast learning speed and less human intervention. It has been applied in the fields of time series prediction and pattern recognition, and so on [21, 22]. Unlike conventional ELM, SVD-ELM effectively avoids the failure of calculating matrix inversion due to matrix singular, during the process of computing output weight [22, 23, 24].

In this paper, the sEMG signals of the limbs moving are collected and the muscle coordination model is established. Combined with the characteristics of NMF, constrained L ${}_{1/2}$ -NMF is applied for multi-feature dimension reduction to achieve more accurate results. Finally, the improved SVD-ELM algorithm is used to identify the processed signals, and the rehabilitation robot is controlled to drive the limbs of the affected side by mirror image of healthy limb movement.

2. Muscle synergy model

Muscle synergy, that is, when a subject is moving his body, the central nervous system (CNS) will send a set of commands to muscles. Some researchers studied that CNS could build complex motor patters by coordinating musculature and a set of muscle is defined as muscle synergy. A single muscle which belongs to many synergy sets can determine global muscle activation patterns by weighted combinations. For a certain ongoing or upcoming limb movement, the CNS groups will produce a combined moment to perform the desired action [11]. Therefore, it could be assumed that $V(t)=[{v_{1}(t),v_{2}(t),\ldots,v_{m}(t)}]^{T}$ is the time-varying instruction issued by the CNS, $v_{i}(t)$ indicates the expected motion level of the $i$ -th coordination point at time $t$ , $m$ is the total number of related motion, and a simple action is only done by a group of muscles [6].

Therefore, the level of muscle activity $V(t)$ can be expressed by $H(t)$ and the coordination matrix $W$ is

$\displaystyle V(t)_{M\times O}=W_{M\times K}\times H(t)_{K\times O}$ (1) $\displaystyle V(t)_{M\times O}=\left[{{\begin{array}[]{*{20}c}{v_{1}(t)}\\ {v_{2}(t)}\\ \vdots\\ {v_{M}(t)}\\ \end{array}}}\right]^{T},W_{M\times K}=\left[{{\begin{array}[]{*{20}c}{w_{11}}% &{w_{21}}&\cdots&{w_{k1}}\\ {w_{12}}&\ddots&&{w_{k2}}\\ \vdots&&\ddots&\vdots\\ {w_{1M}}&\cdots&\cdots&{w_{KM}}\\ \end{array}}}\right],H(t)_{K\times O}=\left[{{\begin{array}[]{*{20}c}{h_{1}(t)% }\\ {h_{2}(t)}\\ \vdots\\ {h_{K}(t)}\\ \end{array}}}\right]^{T},$

where the number of muscles is $M$ , the number of observations is $O$ and the number of synergies is $N$ , $M>N$ . $W_{i}h_{i}(t)$ indicates the effect to all $M$ muscles for $i$ -th synergy.

From Eq. (1), $H$ contains every motion detail, but $V$ (non-measurable) is not equal or linearly related with $Z$ which is the sEMG signal. But $V$ is approximate related to $f(Z)$ (the eigenvalue of $Z$ ), so Eq. (1) can be written as

$\displaystyle f(Z)_{N\times O}\approx W_{N\times K}\times H_{K\times O},$ (2)

where $O$ is equal to the length of time series of the sEMG.

3. Arm gesture recognition based on sEMG signal

NMF Foundation. The essence of non-negative matrix factorization is a technique of matrix decomposition and projection. The basic principles are as follows:

For non-negative matrix $X$ , existing $S\geqslant 0$ and $A\geqslant 0$ , satisfies

$\displaystyle X_{n\times m}\approx S_{n\times r}\times A_{r\times m},$ (3)

where: $r$ is the characteristic dimension, usually $r<\min(m,n)$ . $S$ is a base matrix, and $A$ is a coefficient matrix.

They are smaller than the original matrix $X$ , so data compression can be achieved.

The NMF algorithm can be used to decompose the muscle synergy, which not only satisfies its formal requirements, but also has non-negative decomposition results. It is a more superior advantage which explains the mechanism of the human nervous system. That is, the nervous system emits a either excites or suppressed nerve signal and the value of it is non-negative. So we can used Eq. (3) to deal with Eq. (2), and get the $H(t)$ .

Constrained L ${}_{1/2}$ -NMF. In order to get enough detail of limb movement characteristics, $H$ should be as sparse as possible. Non-negative sparse matrix factorization is an algorithm that can get the sparse coefficient matrix $H$ , where the norm of each column of the base matrix $W$ is 1. And L ${}_{1}$ rule is often used to establish sparsity as a very important constraint for NMF. The L ${}_{1}$ rule cannot perform further sparsity when a large number of fully attached constraints are used and is sensitive to the noise. Therefore, the application of NMF in sEMG is limited. The constrained L ${}_{1/2}$ -NMF algorithm is used in this paper, which is much sparser and more accurate than L ${}_{1}$ [12].

Corresponding cost function of Eq. (2) is:

$\displaystyle D(f(Z)||WH)=\frac{1}{2}\|{f(Z)-WH}\|_{2}^{2}+\lambda\|H\|_{1% \mathord{/{\vphantom{12}}.\kern-1.2pt}2},$ (4)

where $\|H\|_{1\mathord{/{\vphantom{12}}.\kern-1.2pt}2}$ is the weight and it is defined as:

$\displaystyle\|H\|_{1\mathord{/{\vphantom{12}}.\kern-1.2pt}2}=\sum_{i,j}^{K,O}% {H_{ij}^{1\mathord{/{\vphantom{12}}.\kern-1.2pt}2}}.$ (5)

The corresponding iterative algorithm is:

$\displaystyle W\leftarrow W.\ast f(Z)H^{T}./\textit{WHH}^{T},$ (6) $\displaystyle H\leftarrow H.\ast W^{T}f(Z).\mathord{/{\vphantom{{H.\ast W^{T}f% (Z).}{({W^{T}WH+\lambda\mathord{/{\vphantom{\lambda 2}}.\kern-1.2pt}2H^{-1/2}}% )}}}.\kern-1.2pt}{({W^{T}WH+\lambda\mathord{/{\vphantom{\lambda 2}}.\kern-1.2% pt}2H^{-1/2}})},$ (7)

where “.*” and “./” represent the multiplication and division of the corresponding elements respectively; “ $+$ ” means all elements in $W^{T}WH$ add to $\lambda\mathord{/{\vphantom{\lambda 2}}\kern-1.2pt}2H^{-1/2}$ correspondingly, $H^{-1/2}$ represents the sum of the inverse of the square root of all elements in $H$ . If the element value in $H$ is zero, it is added with a smaller normal number.

Design of Improved ELM Based on TSVD. For different samples $({x_{i},t_{i}})$ , ( $x_{i}=[{x_{i1},x_{i2},\cdots,x_{in}}]^{T}\in R^{n}$ and $t_{i}=[{t_{i1},t_{i2},\cdots,t_{im}}]^{T}\in R^{m}$ ) whose number is $N$ , the activation function is $g(x)$ , and the number of hidden layer neurons is $\bar{N}$ .

Then the SLFNs model is:

$\displaystyle\sum_{i=1}^{\bar{N}}\beta_{i}g_{i}(x_{j})=\sum_{i=1}^{\bar{N}}% \beta_{i}g(a_{i}\cdot x_{j}+b_{i})=t_{j},j=1\cdots N,$ (8)

where $a_{i}=[{a_{i1},a_{i2},\cdots,a_{in}}]^{T}$ is the weight of the $i$ -th hidden layer to the input layer, $b_{i}$ is the threshold for the $i$ -th hidden layer neuron, and $\beta_{i}=[{\beta_{i1},\beta_{i2},\cdots,\beta_{im}}]^{T}$ is the weight of the $i$ -th hidden layer neuron to the output layer [18].

So Eq. (8) can be written as

$\displaystyle M\beta=T,$ (9)

where

$\displaystyle M({a_{1},\cdots a_{\bar{N}};b_{1},\cdots,b_{\bar{N}};x_{1},% \cdots x_{N}})=\left[{{\begin{array}[]{*{20}c}{g(a_{1}\cdot x_{1}+b_{1})}&% \cdots&{g(a_{\bar{N}}\cdot x_{1}+b_{\bar{N}})}\\ \vdots&\cdots&\vdots\\ {g(a_{1}\cdot x_{N}+b_{1})}&\cdots&{g(a_{\bar{N}}\cdot x_{N}+b_{\bar{N}})}\\ \end{array}}}\right]_{N\times\bar{N}},$ (10) $\displaystyle\beta=\left[{{\begin{array}[]{*{20}c}{\beta_{1}^{T}}\\ \vdots\\ {\beta_{\bar{N}}}\\ \end{array}}}\right]_{\bar{N}\times m},T=\left[{{\begin{array}[]{*{20}c}{t_{1}% ^{T}}\\ \vdots\\ {t_{N}^{T}}\\ \end{array}}}\right]_{N\times m}$

The input weight in ELM can be selected randomly, so the SLFNs can be obtained simply as the least squares solution of $\widehat{\beta}$ to Eq. (8).

That is

$\displaystyle\|{M({a_{1},\cdots a_{\bar{N}};b_{1},\cdots,b_{\bar{N}};x_{1},% \cdots x_{N}})\widehat{\beta}-T}\|=\mathop{\min}\limits_{\beta}\|{M({a_{1},% \cdots a_{\bar{N}};b_{1},\cdots,b_{\bar{N}};x_{1},\cdots x_{N}})\beta-T}\|.$ (11)

Then the least squares solution with minimum 2 norm of output weight is

$\displaystyle\widehat{\beta}=M^{-1}T,$ (12)

where $M^{-1}$ is the inverse of $M$ .

For unconstrained least squares problem

$\displaystyle\min\|{Ax-b}\|,A\in R^{m\times n},m\geqslant n,$ (13)

as the condition in matrix $A$ is ill, a small disturbance in $b$ will cause a result of seriously deviate from the actual value. At this time the problem in Eq. (13) is called ill-posed problem. Therefore, the solution process of ELM output weight will be affected by the ill-condition of matrix $M$ . Trying to solve the least squares problem in Eq. (11) will result in noise pollution directly.

So it could applying singular value decomposition on matrix $M$ , where

$\displaystyle M=U\sum V^{T}=\sum_{i=1}^{n}{u_{i}\sigma_{i}v_{i}^{T}},$ (14) $\displaystyle\lambda=({\sigma_{k}\sigma_{k+1}})^{1/2},$ (15)

and calculate optimal regularization parameters by GCV (Generalized Cross-Validation) by

$\displaystyle G(\lambda)=\frac{\frac{1}{n}\|{({I-M(\lambda)})T}\|^{2}}{\left[{% \frac{1}{n}\textit{Trace}({I-M(\lambda)})}\right]^{2}}.$ (16)

Then apply TSVD to calculate the generalized inverse of $M$ with Eq. (17)

$\displaystyle M_{k}^{+}=V\sum_{k}^{+}U^{T},\sum_{k}^{+}=\textit{diag}({\sigma_% {1},\ldots,\sigma_{k},0,\ldots,0}),$ (17)

and the output weight $\beta$ could be gotten by Eq. (12).

So the algorithm used in this paper is:

Step 1. Collect the sEMG signals $Z=x(t)$ , $x(t)$ is the time series of signals; Step 2. Take the root mean square $\textit{RMS}=\sqrt{\frac{1}{N}\sum_{N}^{t=1}{x^{2}(t)}}$ , eight order coefficients of the AR model by $X(t)=w(n)-\sum_{k=1}^{p}{a_{k}X(t-k)}$ and three order wavelet energy coefficients $P_{k}=\sqrt{\sum_{i=1}^{N_{j}}{[{DF({k,i})}]^{2}}}$ of sEMG signals as the eigenvalue of $Z$ ; Step 3. Use constrained L ${}_{1/2}$ -NMF to compressed data with the iterative algorithm of Eq. (6), Eq. (7); Step 4. Establish the model of TSSVD-ELM with the algorithm mentioned above; Step 5. Take the $H$ as the input of ELM when $W=1$ , and get the output.

4. Experimental analysis

Sampling Point Selection for sEMG. There are 5 degrees of freedom in our upper limb rehabilitation robot system, that is shoulder abduction, shoulder flexion and extension, elbow flexion and extension, wrist flexion and extension and wrist rotation. In actual rehabilitation training, it can provide rehabilitation training for 5 upper limb joints. In this paper, three common proximal joint movements are selected, that is elbow joint motion, shoulder forward flexing, shoulder abduction, and two common upper limb movements, lifting trousers and eating, are mentioned too. The actual movement is shown in Fig. 1.

In order to realize the function of recognition, the characteristics of the sEMG signals under these postures are discussed. The muscle which is responsible for providing the force of the movement is called the active muscle. During the movement of the upper limb, the biceps and triceps are the active muscles for elbow flexing, and the deltoid is the active muscles for shoulder movement. The brachioradialis is one of the active muscles for wrist rotation. Therefore, the ideal signal acquisition points are the muscles of the biceps, triceps, deltoid and brachioradialis, which are used in the experiments. The specific measurement position and the rehabilitation robot are shown in Fig. 2.

Figure 1.

Graphs of each motion. (a) elbow joint motion; (b) shoulder forward flexing; (c) shoulder abduction; (d) lifting trousers; (e) eating.

Figure 2.

Experiments of data selection.

Conditions for sEMG Signal Sampling. Before the sampling information about age, gender, weight and health status of subjects should be asked. Make sure they were notified what to do, clean the skin of the subjects carefully with alcohol, and the subjects are relaxed without vigorous exercise before. Two conditions should be followed by subjects. Firstly, the subjects need to remain as natural as possible before the experiments and strenuous exercise should not be taken. Secondly, in order to avoid the sudden change of muscle strength which could interfere with the subsequent analysis of the sEMG signal characteristics, it is necessary to ensure that the subjects move naturally, that is, the active muscle isometric contraction is not performed.

Motion Classification Experiment. First of all, the original data is collected this paper, part of them is shown in Fig. 3 for shoulder forward flexing (Fig. 1b). A total of 125 sets of experimental data for 5 types of actions, including 25 sets of each type of action are ready for the classification experiment. These data are the active segments of the signal that have been divided by the intelligent acquisition tool, and the length is 8000 points per channel. According to the sEMG signal characteristic analysis process, each set of data is transformed into a neural network model established by the 8-dimensional feature vector input ELM learning algorithm. Since the input dimension is not more, the number of hidden layer is set to 20.

The PCA was adopted as a comparison algorithm. The PCA method selects the feature dimension mainly by calculating the cumulative contribution rate of the principal, and the principal of the top ten in each channel and its contribution rate according to the test data are shown in the following Table 1.

Table 1

Contribution rate of components of PCA

Principal number	1	2	3	4	5	6	7	8	9	10
Channel 1	0.585	0.325	0.061	0.015	0.003	0.003	0.002	0.001	0.001	0.001
Channel 2	0.663	0.236	0.072	0.011	0.006	0.002	0.002	0.001	0.001	0.001
Channel 3	0.612	0.328	0.024	0.011	0.010	0.006	0.002	0.002	0.001	0.001
Channel 4	0.647	0.266	0.057	0.009	0.008	0.004	0.001	0.001	0.001	0.001

Figure 3.

The original signals collected from four channels.

Figure 4.

Comparison of different testing results of extraction methods.

It can be seen from Table 1 that the contribution rate of the first two principal elements of each channel is above 89%. So the PCA feature dimension is also 2 $\times$ 4, which is the same with the output of NMF. Since the feature dimension is unchanged, the network structure of the SLFNs is also unchanged.

The data under each type of action is randomly selected from 15 groups as training set and 10 groups as test set. The feature extraction method proposed in this paper is compared with the PCA and full-action features of input data. The training results are shown that no mater the training results of this paper or the PCA or the full-action are the 100%. It shows that the model has the same initial condition and if the testing results are better, the algorithm is better.

From the testing results in Fig. 4, the correct extraction rate of the feature extraction algorithm proposed in this paper is 95%, which is higher than 90% of the PCA. At the same time, the method of full-action feature is not ideal whose accuracy is only 66%. The input of the ELM is the low-dimensional feature vector extracted L ${}_{1/2}$ -NMF. So for the same ELM construction the construction and parameters of L ${}_{1/2}$ -NMF can affect the results. The fewer types of recognition, the better the recognition effect. So the algorithm of L ${}_{1/2}$ -NMF is very important and necessary. In another hand for particularly similar movements, the moving arm needs to do some weight-bearing exercises before training and testing in advance to enhance the signal strength. In general the proposed algorithm can describe the upper limb motion through low-dimensional features.

5. Conclusion

One of the most important premises for better results of mirror rehabilitation motion is the recognition method. A new method is proposed by combining L ${}_{1/2}$ -NMF and TSSVD-ELM. For L ${}_{1/2}$ -NMF it has fewer restrictions and matches the non-negative characteristics of sEMG signals. For TSSVD-ELM, it establishes a motion model between the characteristics of sEMG signals and rehabilitation robot. The results of experiments showed that the method is feasible and effective for the basic rehabilitation training of upper limb rehabilitation robot system, and the stability of the model and the recognition accuracy are improved.

Footnotes

Acknowledgments

This research is supported by the Natural Science Foundation of Liaoning Province, China (20170540641), (20170520386), (20180540143), and National Natural Science Foundation of China (71672117).

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