# Human Joint Torque Estimation Based on Mechanomyography for Upper Extremity Exosuit

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- The measuring device can be used directly without touching the skin, which simplifies the preparation before data collection;
- the signal has strong anti-interference ability and will not be affected by environmental variables such as sweat, humidity, or electromagnetics;
- the equipment cost is pretty low because the data collection task can be completed by using an acceleration sensor that meets the accuracy requirements.

- We have attempted to use the MMG signal as the medium for the exosuit to understand human intentions, and to demonstrate the feasibility and effectiveness of this approach.
- A series of MMG-related methods for signal acquisition, filtering, and feature extraction have been developed.
- A regression model reflecting the nonlinear relationship between muscle activation and joint output is constructed.
- A torque estimation-based control algorithm is designed and applied to the multi-joint motion assistance of upper extremity exosuit, which can significantly amplify the limb strength.

## 2. Data Sets Acquisition

#### 2.1. Raw Information Collection

_{x}and F

_{y}) as input, the joint torque (${\overrightarrow{T}}_{\mathit{elbow}}$) can be calculated by a certain mathematical relation. The mechanical model of the elbow is shown in Figure 1b, where $\overrightarrow{A}$, $\overrightarrow{F}$, and L, respectively, represent the current posture vector of human arm, the resultant force vector at the end, and the length of forearm. Then, we can dynamically obtain the joint torque values during elbow static flexion and extension through the following formulas.

_{x}, ACC

_{y}, and ACC

_{z}), and take its modulus as the original MMG signal (MMG(t)), which can be expressed as the following equation.

#### 2.2. MMG Signal Processing

_{i}(t) = x(t), otherwise it is necessary to let MMG(t) = x(t), and repeat the above steps until these two conditions are met. Next, we remove the obtained IMF

_{i}(t) from MMG(t) and repeat all the above steps again with the remaining part (r

_{i}(t)) to get other IMF components until r

_{i}(t) is a constant or monotonic function. As shown in Figure 3a, the original MMG signal is decomposed into 9 IMFs and 1 residual (res(t)) according to the signal frequency, which can be expressed as follows.

_{IMF}(t

_{1},t

_{2})), which reflects the correlation degree of signal values at different times (t

_{1}and t

_{2}). Its normalized expression form, (ρ

_{IMF}(τ)), can be obtained with the following formula, where τ = t

_{1}− t

_{2}.

#### 2.3. Feature Extraction

_{i}) and energy (E

_{i}). Then, MPF can be calculated through the following equation.

## 3. Off-Line Torque Estimation

#### 3.1. Regression Model Design

- Randomly extract any number of samples from the training set to form multiple new sub-training sets;
- use each sub-training set to train a CART separately. During this process, it is necessary to randomly obtain any number of features from all the features, and then select the optimal segmentation point to cut the subtree;
- repeat step 2 to obtain multiple trained CARTs;
- calculate the average of all the CARTs’ prediction results and use it as the final estimated value.

#### 3.2. Off-Line Training and Testing

^{2}) are introduced as evaluation indexes. The RMSE is a commonly used method to express numerical errors, representing the sample standard deviation of the difference between the predicted value and the actual one. It can be calculated by using the following formula.

^{2}reflects how much the regression relationship can account for changes to the dependent variable. A higher value indicates that the regression model can produce better prediction results. The corresponding calculation process is shown below.

## 4. Test Platform Construction

#### 4.1. Overview of the Upper Extremity Exosuit

#### 4.2. Torque Estimation-Based Control Strategy

## 5. Experiment on Exosuit

#### 5.1. Reliability Analysis Experiment for Torque Estimation

^{2}introduced above to quantitatively describe the identification effect for different subjects. It can be seen from Table 1 that the RMSE of the experimental group is lower than that of the control group, indicating that the error between the actual and estimated value is smaller for the joint torque of Subject 1 and Subject 2. Moreover, the R

^{2}in the experimental group comes up to 100%, which, when closely compared with the control group, means that the trained RFR model can perform better when utilizing the biological signals of Subject 1 and Subject 2.

- If we have collected a person’s MMG signal for training the RFR model offline, the reliability of the online torque estimation will remain at a pretty high level when they wear the exosuit that uses the trained model;
- utilizing a trained model to estimate the joint torque of unknown subjects online may significantly weaken the effectiveness of identification.

#### 5.2. Efficiency Evaluation Experiment for Power Assistance

_{exosuit}to ASUM

_{total}.

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Information collection process during elbow static flexion/extension: (

**a**) measurement platform; (

**b**) joint torque calculation model for elbow.

**Figure 2.**The IMU data during elbow dynamic flexion/extension with low strength: (

**a**) three-axis euler angles; (

**b**) three-axis accelerations.

**Figure 3.**MMG signal processing: (

**a**) decomposing result through EMD; (

**b**) autocorrelation function curves of the first four IMFs.

**Figure 4.**Comparison between the filtered MMG of the brachioradialis muscle and the corresponding elbow joint torque: (

**a**) the change curve of joint torque; (

**b**) the change curve of filtered MMG.

**Figure 6.**Machine learning effect of shoulder static adduction/abduction: (

**a**) iterative training process with training set; (

**b**) verification result of test set.

**Figure 9.**Elbow joint torque estimation results: (

**a**) experimental result of Subject 1; (

**b**) experimental result of Subject 2; (

**c**) experimental result of Subject 3.

**Figure 10.**Actual power-assisted experiments: (

**a**) experiment for elbow static flexion/extension; (

**b**) experiment for shoulder static flexion/extension; (

**c**) experiment for shoulder static adduction/abduction.

**Figure 11.**Variations of different torques in each motion mode: (

**a**) torque curves for elbow static flexion; (

**b**) torque curves for shoulder static flexion; (

**c**) torque curves for shoulder static abduction.

Groups | Participants | RMSE | R^{2} |
---|---|---|---|

Experimental group | Subject 1 | 1.9812 | 0.9532 |

Subject 2 | 1.7008 | 0.8620 | |

Control group | Subject 3 | 3.4261 | 0.6824 |

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**MDPI and ACS Style**

Shi, Y.; Dong, W.; Lin, W.; He, L.; Wang, X.; Li, P.; Gao, Y. Human Joint Torque Estimation Based on Mechanomyography for Upper Extremity Exosuit. *Electronics* **2022**, *11*, 1335.
https://doi.org/10.3390/electronics11091335

**AMA Style**

Shi Y, Dong W, Lin W, He L, Wang X, Li P, Gao Y. Human Joint Torque Estimation Based on Mechanomyography for Upper Extremity Exosuit. *Electronics*. 2022; 11(9):1335.
https://doi.org/10.3390/electronics11091335

**Chicago/Turabian Style**

Shi, Yongjun, Wei Dong, Weiqi Lin, Long He, Xinrui Wang, Pengjie Li, and Yongzhuo Gao. 2022. "Human Joint Torque Estimation Based on Mechanomyography for Upper Extremity Exosuit" *Electronics* 11, no. 9: 1335.
https://doi.org/10.3390/electronics11091335