# EMG feature extraction and muscle selection for continuous upper limb movement regression

Lucas Quesada, Dorian Verdel, Olivier Bruneau, Bastien Berret, Michel-Ange Amorim, Nicolas Vignais

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Lucas Quesada, Dorian Verdel, Olivier Bruneau, Bastien Berret, Michel-Ange Amorim, et al., EMG feature extraction and muscle selection for continuous upper limb movement regression. Biomedical Signal Processing and Control, 2025, 103, pp.107323. 10.1016/j.bspc.2024.107323. hal-04871025

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# EMG feature extraction and muscle selection for continuous upper limb movement regression

Lucas Quesada<sup>a,b,c ID*</sup>, Dorian Verdel<sup>d ID</sup>, Olivier Bruneau<sup>c ID</sup>, Bastien Berret<sup>a,b ID</sup>, Michel-Ange Amorim<sup>a,b ID</sup>, Nicolas Vignais<sup>e ID</sup>

## ARTICLE INFO

Keywords:

Signal processing

Electromyography

Intent detection

Human-robot interaction

## ABSTRACT

Achieving a versatile control of exoskeletons or prostheses requires accurate, robust and fast predictions of upcoming human movements. Electromyographic (EMG) signals are increasingly being used for this purpose as they theoretically allow to estimate joint torques in advance due to the electromechanical delay. However, their performance in continuously predicting joint torques strongly depends on the location of the sensors and on the feature extracted from the signal, whose impact on the accuracy is little-known in this context. In the present paper, the influence of different EMG features and muscles on the performance to predict both multi- and single-joint torques have been analyzed, while moving in a parasagittal plane hindered by a viscous force field applied by an exoskeleton. The existence of an accuracy-latency tradeoff is first highlighted, whether with frequency or time-domain features, the latter providing the best tradeoff. Second, the impact of muscle selection on the quality of the joint torques prediction is illustrated. In particular, the anterior deltoid, the long triceps, the brachialis, and the brachioradialis muscles are shown to be the most important to record during movements in a parasagittal plane. The present results pave the path towards the design of reactive and accurate exoskeletons and prostheses controllers based on EMG signals

## 1. Introduction

Human-robot interactions for applications such as exoskeletons or prostheses control often rely on a human intention detection scheme to predict the movement [1,2], where providing accurate predictions compatible with human motion planning is a crucial step [3]. Two main approaches can be distinguished: discrete and continuous intention detection [4,5]. Discrete intention detection focuses on a high-level classification of intent, such as a direction (e.g., up/down, left/right), a target, or selecting the nearest candidate movement from a predetermined set of trajectories. Such intent classification can be obtained from multiple types of biological recordings, including EMGs [6–8], brain computer interfaces [9], or eye gaze [10]. Typically, discrete intention detection can be achieved with pattern recognition methods such as classifiers, often based on machine learning models and either utilizing kinematic [11,12], haptic [13] or EMG data [14,15]. However, these discrete methods for predicting movement are reactive and require a significant time window to predict the onset of a movement (i.e.,

several hundreds of milliseconds). Additionally, these methods often require prior knowledge of parameters such as an endpoint, probable trajectories, or inertial information on the object to interact with.

In contrast to the previous intent classification, continuous detection aims at continuously estimating or predict a movement's feature, such as joint torque, impedance, or kinematics. Like their discrete counterparts, continuous intent detection can be achieved from kinematic data by using movement primitives [16,17], Gaussian mixture models [18,19], and recurrent neural networks [20]. In contrast to kinematics based predictions that are necessarily reactive, EMG signals intrinsically contain a predictive information as they appear before movement onset thanks to the electromechanical delay [21]. This potentially allows to estimate the upcoming movement ahead of time. Additionally, it provides insight into the current dynamics of the limb as it relates to muscle activations, which is informative about human efforts, interaction forces, and kinematics. Therefore, this study will

<footnote><sup>a</sup> CIAMS, Université Paris-Saclay, Orsay, France</footnote>

<footnote><sup>b</sup> CIAMS, Université d'Orléan, Orléan, France</footnote>

<footnote><sup>c</sup> LURPA, École Normale Supérieure Paris-Saclay, Gif-sur-Yvette, France</footnote>

<footnote><sup>d</sup> Human Robotics Group, Department of Bioengineering, Imperial College of Science, Technology and Medicine, W12 OBZ London, United Kingdom</footnote>

<footnote><sup>e</sup> M2S, Université Rennes 2, Rennes, France</footnote>

<footnote>* Corresponding author at: CIAMS, Université Paris-Saclay, Orsay, France. E-mail address: lucas.quesada@ens-paris-saclay.fr (L. Quesada).</footnote>
focus on using EMG signals for continuous estimation of the joint torques of human participants.

While they present challenges pertaining to their cost and their processing, EMG signals have been increasingly used in the context of human-robot interactions during continuous movements [22–26]. For this type of application, continuous trajectory prediction relies on regression models, predicting either joint torques or kinematics based on EMG signals in real time. For this purpose, several models have been proposed in the past few years, ranging from complex neuro-musculoskeletal models [24,27,28] to simple linear regressions [22,29], neural network based [25,30–32] and other models [23,33]. Similarly, classification frameworks have been thoroughly tested for EMG-based neuroprosthetic control [34–36]. It is noteworthy that discrete intent detection, when carried out through pattern recognition methods, typically relies on a collection of features derived from the EMG signals [37–40], see [8] for a review. Each feature characterizes the mathematical procedure for extracting useful information from an EMG signal. Within this discrete framework, several studies compared existing EMG features and their combination to maximize classification accuracy [41, 42]. However, only a few studies take advantage of the concept of EMG features to improve movement prediction accuracy in a continuous framework [43].

Typically, classical feature extraction techniques such as low-pass filtering [27,44] or root mean square (RMS) [24,45] are commonly used. However, there is still a lack of a systematic investigation of feature extraction techniques and their impact on prediction accuracy. In previous works, Triwiyanto et al. found that the zero-crossing (ZC), slope sign change (SSC), and Waveform Length (WL) features had the best regression accuracy for the estimation of elbow angle [46]. Those features obtained correlation coefficients above 0.8 while concurrent features such as the root mean square (RMS), the variance (VAR), and the mean absolute value (MAV) were below 0.7. Likewise, Putro et al. [30] found that the median frequency (MDF) was more effective than other time-domain and frequency-domain features in estimating finger joint angles. The authors showed that this feature obtained a $R^2$ score of 0.97, with a root mean square error (RMSE) of 22.5°, which they deemed comparatively better than the mean frequency (MNF), which obtained a similar $R^2$ but a less precise RMSE of 23.4°. Importantly, although they provide valuable information about the effects of certain features on prediction accuracy, they did not consider the latency induced by the extraction process. However, this latency can generate slowness and delays in adapting to the user's movements, leading to unwanted energetic expenditure [3,47]. In particular, Smith et al. [47], measured the impact of window length and its associated latency on task completion with virtual prosthetics driven by EMG pattern recognition. They found that although a higher window length was associated with a higher pattern recognition accuracy, the increased latency negatively affected task completion. Specifically, using linear mixed models, they showed that reducing the window length from 550 ms to 50 ms led to a 15% increase in completion rate, which highlights the crucial importance of minimizing the delay associated with the feature extraction process. Therefore, all the analyses of the present paper will not only consider maximizing accuracy but also focus on optimizing a tradeoff between accuracy and latency.

Furthermore, performing skin preparation and installing EMG sensors is a time-consuming and demanding process, which can be particularly complex for large sets or measuring small muscles. Such complexity is an important obstacle to the ecological use of EMG-driven robots. Hence, minimizing the tradeoff between the number of muscles and the prediction error is crucial [1]. A thorough search of the literature showed that this major issue has only been tackled under some very limited conditions, which do not cover joints torques estimation during multi-joints dynamic motion. Specifically, Camardella et al. [48] have shown that a set of eight relevant muscles allowed to decrease the RMSE to less than 4 N with no significant accuracy improvement above eight muscles during upper limb isometric contractions. Similarly, Ziai

et al. [49] showed the diminishing returns of increasing the number of measured muscles from two ($R^2$ = 0.69±0.18), to five ($R^2$ = 0.81±0.12), to eight ($R^2$ = 0.82 ± 0.09), for isometric wrist joint torque regression using a neural network. Finally, Liu et al. [50] provided a similar conclusion considering knee joint moment, where going from seven to ten sensors did not significantly improve the estimation error. In the current study, these previous results were significantly extended by considering the impact of the measured muscle set on the accuracy of multi-joints torques predictions during dynamic movements.

The present paper provides a comprehensive analysis of two trade-offs: accuracy versus latency and measurement set versus complexity. It aims at optimizing them to improve the usability of EMG-based controllers in ecological conditions. The analysis is conducted on a public dataset that was previously collected [33,51]. In what follows, the dataset and the EMG-to-torque model are first introduced, then the tested EMG features and muscles sets are detailed. The results and discussion sections present the findings, including their limitations and future perspectives.

# 2. Methods

## 2.1. Dataset

The analyses of the present paper were performed using a dataset that was collected during a previous work [33], and which is openly available on Zenodo [51]. While this section quickly describes the material and protocol, more insights and details can be found in the corresponding publications.

### 2.1.1. Participants

A total of 17 participants (11 males, 6 females) with the following anthropometric characteristics: age 28.2 ± 7 years, height 175.4 ± 7 cm, weight 70 ± 11 kg took part in the experiment. The protocol was approved by the ethics committee of Université Paris-Saclay (CER-PS-2021-048/A1), and written informed consent was provided by each participant.

### 2.1.2. Material

Kinematics were recorded using an optoelectronic motion capture system (Qualisys, Göteborg, Sweden) with a 100 Hz sampling rate. Reflective markers were placed on anatomical landmarks to capture the upper limb and upper torso movements (see supplementary material S1 for details). After a skin shaving and cleaning, MiniWave EMG sensors (MiniWave, Cometa, Bareggio, Italy) were placed on 12 muscle heads following SENIAM recommendations [52] (see supplementary material S2 for details): long and short biceps (BL and BS), brachioradialis (BRD), brachialis (BRA), long, lateral and medial triceps (TLO, TLA, and TM), anterior, posterior and medial deltoids (DA, DP, and DM), pectoralis major (PM) and latissimus dorsi (LD). EMG signals were captured at a 2 kHz sampling rate and synchronized with the motion capture system using the Qualisys Track Manager (QTM) software. The shoulder and elbow joints of the ABLE exoskeleton [53] were controlled at 1 kHz to apply a visco-resistive force field on the participant's wrist, the intensity of which was adjusted for each participant to normalize the level of effort [33]. Participants were attached to the exoskeleton via an ergonomic orthosis to minimize discomfort and hyperstatism [54,55]. The interaction forces and torques were measured via a 6-axis F/T sensor (ATI, Apex, North Carolina, USA) at a 1 kHz sampling rate. A screen was positioned near the participant to display instructions and tasks.
<figure><img src="image_4.png" /><figcaption>Fig. 1. Setups of single-joint (left) and multi-joint (right) tasks. Participants were connected to the exoskeleton via the orthosis represented in green; interaction forces are measured via the F/T sensor represented in red. During the tasks, the yellow and white dots represented the current and target positions, respectively.</figcaption></figure>

### 2.1.3. Protocol

Reflective markers were first placed on the participant, and a static motion capture frame was recorded for anthropometric measurements. EMG sensors were placed on the muscle heads, and participants performed maximum voluntary contraction (MVC) trials for muscle activity normalization. Specifically, they were instructed to exert maximal upward or downward force on a horizontal bar through four contraction types: elbow flexion, elbow extension, shoulder flexion, and shoulder extension. During elbow contractions, the arm was along the body with the forearm horizontal, and the bar was set at elbow height. For shoulder contractions, the upper limb was fully extended horizontally, with the bar at shoulder height (see supplementary material S3 for a figure). Each contraction was held for three seconds and repeated twice, with a 30 s rest interval between each trial.

Participants performed two series of trials under different conditions: single-joint (SJ) and multi-joint (MJ). In SJ, participants only performed flexion and extension of the elbow to track a trajectory displayed on the screen, while the shoulder joints of the exoskeleton were mechanically locked. Due to the nature of this movement, only the flexor and extensor muscles of the elbow were recorded during this condition: BL, BS, BRD, BRA, TLO, TLA, and TM. In the MJ condition, participants were asked to move both their upper and lower arms, and all the muscles previously introduced were recorded. In the SJ condition, the participant's position relative to the target trajectory was determined by the angle of their elbow. In contrast, in the MJ condition, it was determined by the cartesian position of their wrist (see Fig. 1). A viscous force field hindered the participants' movements during trajectory tracking, creating interaction forces with the exoskeleton. In total, the experiment consisted in two series of ten trials, one serie in each condition. To avoid muscle fatigue, a 1-min resting period was respected after each trial. Both conditions took advantage of randomly generated target trajectories maximizing the mechanical work and ensuring a movement distribution representative of daily life tasks [33].

### 2.1.4. Data processing

Before feature extraction, EMG signals were filtered using a 50 Hz notch filter, a 20–450 Hz fourth-order band-pass Butterworth filter [52, 56], and normalized using MVC data. The resulting filtered signals are referred to as $s(t) \in \mathbb{R}^K$ throughout the paper, with $K$ the number of muscles.

OpenSim's [57] tool was used to compute human kinematics through a musculoskeletal model [58] that was scaled using anthropometric measurements. Similarly, human dynamics were computed via OpenSim's inverse dynamics tool such that for J joints:

$$ \tau_h = M_h(q_h)\ddot{q}_h + c(q_h, \dot{q}_h) + g_h(q_h) + \tau_i \quad (1) $$

were $\tau_h \in \mathbb{R}^J$ represents the reference torque vector exerted by the human, $q_h$ denotes the joint positions, $M_h \in \mathbb{R}^{J \times J}$ stands for the inertia matrix, $c \in \mathbb{R}^J$ and $g_h \in \mathbb{R}^J$ are respectively the Coriolis and gravity terms, and $\tau_i \in \mathbb{R}^J$ corresponds to the human-exoskeleton interaction torque. $\tau_i$ was computed as

$$ \tau_i = J_h^T(q_h)\ddot{f}_s + \tau_s \quad (2) $$

with $\ddot{f}_s$ and $\tau_s$ the measured force and torque vectors, and $J_h$ the human jacobian matrix.

### 2.2. EMG-to-torque estimation model

In the present paper, the investigations were limited to torque predictions based on an explicit mapping of EMG activity to joint torques, excluding machine learning-based approaches. It has to be noted that the dataset being public [51], further analyses of the impact of features extraction and muscle selection for such methods are possible but beyond the scope of the present paper. For the rest of the present paper, the focus will be on obtaining an estimation of the human torque $\hat{\tau}_h$ that closely matches the reference torque $\tau_h$ derived from inverse dynamics.

#### 2.2.1. Regression model

In a previous work [33], using filtered EMG signals, a non-linear mapping (NLMap) model was shown to be able to significantly improve the accuracy of linear mapping models [22,29], even outperforming the heavy and hard to calibrate neuro-musculo-skeletal modeling for multi-joints movements [24,59,60]. This model stems from a common multivariate linear regression (MVLR) formulation [29]:

$$ \hat{\tau}_h(t) = H_c \cdot m(t) \quad (3) $$

with $K$ the number of muscles, $H_c \in \mathbb{R}^{J \times K}$ the mapping matrix, $\hat{\tau}_h(t)$ the estimated torque, and $m(t)$ the vector of processed EMG signals. Nonlinearities are then introduced in the formulation by incorporating the shape factor [61], such that it becomes:

$$ a_k(t) = \frac{e^{A_k m_k(t)} - 1}{e^{A_k} - 1} \quad (4) $$

with $a_k(t) \in \mathbb{R}^K$ the vector of nonlinear muscle activations (and $a_k$ its components), $A_k$ the shape factors, and $H_{n\ell} \in \mathbb{R}^{J \times K}$ the nonlinear mapping matrix.

To calibrate this model, a single objective genetic algorithm [62] is used to identify the optimal shape factor parameters, minimizing the quadratic mean of degrees of freedom's root mean square error:

$$ C(\tau_h, \hat{\tau}_h) = \sqrt{\sum_{j=1}^{J=J} \frac{1}{N} \sum_{n=0}^{N} (\tau_{h,j}(t_n) - \hat{\tau}_{h,j}(t_n))^2} \quad (5) $$
<figure><img src="image_5.png" /><figcaption>Fig. 2. Cross validation workflow [63]. Data are split in two folds, and two validation iterations follow. The first iteration I0 uses the fold F0 as calibration data and F1 as validation. The second iteration, I1, does the opposite. Once the EMG feature is computed, the model is calibrated from the calibration fold, and a score is computed from the torque estimated from the validation fold.</figcaption></figure>

For each new iteration of the algorithm, a chromosome of shape factors is generated via mutation and crossover, the nonlinear activations are computed accordingly, and the $H_{n\ell}$ matrix is then computed via Matlab's `mvregress` function (v2021b, MathWorks, Natick, Massachusetts, USA) to solve the following equation:

$$T = H_{n\ell} \cdot A \qquad (6)$$

with $A \in \mathbb{R}_{+}^{K \times N}$ holding nonlinear activations samples and $T \in \mathbb{R}_{+}^{J \times N}$ the references torque samples of the calibration dataset. After rounds of generations, the algorithm is stopped when attaining a maximum number of generations or when the cost function is stalling.

### 2.2.2. Regression accuracy criterion

Features and muscle sets were tested using a 2-fold cross-validation framework (see Fig. 2). First, the dataset was divided into two folds, each alternatively having the role of calibration and validation data, yielding two iterations. Restricting the number of folds to two prevented to introduce an overfitting bias while limiting the computational cost of the analysis. After performing the calibration, torques from the validation fold were estimated with the benchmark model for each iteration, yielding $\hat{\tau}_h$. The torque estimation accuracy was then evaluated with the normalized root means square error (NRMSE) and the Pearson correlation coefficient ($r$). The NRMSE was computed separately for each joint $j$ as follows:

$$NRMSE_j = \frac{\sqrt{\frac{1}{N} \sum_{i=0}^{I=N} (\tau_{h,j}(t_i) - \hat{\tau}_{h,j}(t_i))^2}}{\max(\tau_{h,j}) - \min(\tau_{h,j})} \qquad (7)$$

with $N$ the number of samples in the validation fold and $\tau_{h,j}$ the reference torque computed from Eq. (1). Likewise, the $r$ coefficient was computed as:

$$r_j = \frac{\text{cov}(\tau_{h,j}, \hat{\tau}_{h,j})}{\sigma_{\tau_{h,j}} \sigma_{\hat{\tau}_{h,j}}} \qquad (8)$$

with $\sigma$ representing the standard deviation, and $\text{cov}(\cdot, \cdot)$ denoting the covariance operator.

## 2.3. EMG features

Since raw EMG signals are noisy and hardly exploitable as is [56], features are computed to extract information from them. Several feature extraction methods can be categorized: filtering, time-domain, and frequency-domain features. Filtering features are recursive; they result from the application of an infinite impulse response (IIR) filter to either the raw signal or a full-wave rectified version of it. Time-domain features are directly computed from the temporal signal, and frequency-domain features necessitate a Fourier transform. In this section, $s(t)$ corresponds to the pre-processed EMG signal (see Section 2.1.4), and the signal resulting from feature extraction is referred to as $\tilde{m}(t)$. The feature extraction process was first applied to the MVC signal, yielding a corresponding normalization factor $\tilde{m}_0$:

$$\tilde{m}_0 = \max(\tilde{m}_{MVC}(t)) \qquad (9)$$

where $\tilde{m}_{MVC}(t)$ is the feature signal extracted from EMG data of the MVC trial. The final normalized extracted EMG feature was then computed as follows:

$$\tilde{m}(t) = \frac{\tilde{m}(t)}{\tilde{m}_0} \qquad (10)$$

### 2.3.1. Infinite impulse response filtering baselines

The filter feature, which has been used in a previous work [33], involves performing a full wave rectification, followed by a third-order low-pass Butterworth filter with a 3 Hz cutoff frequency [64]. Two versions of this feature are being considered: the forward and forward-backward filters. Forward-backward filters are applied in both the forward and backward directions, which eliminates any phase delay caused by the filtering process and nullifies latency. Although this type of filtering scheme is not suitable for real-time applications because it requires the whole signal, it was used in this study as a reference signal to evaluate the latency of other features. Additionally, the forward-only version of this filter was employed as an EMG feature and used as a baseline for $r$ and NRMSE scores.

### 2.3.2. Time-domain features

Time domain features are extracted by applying their formula on a rolling window of the signal. The window length is referred to as $W$ in this paper, and while it corresponds to a number of EMG samples, it will rather be expressed in terms of milliseconds. Likewise, because features are formulated in their numerical form, $t$ corresponds to the index of the most recent data point. Typically, certain features are expressed using a fixed multiplicative factor, which is often related to the length of the window (e.g., $\frac{1}{W}$). However, in this paper, these factors are disregarded because they are suppressed by the normalization through the MVC, from which the feature is also extracted.

Among popular features, the root mean square (RMS) is often used to perform offline analysis as well as real-time intention detection [22, 30, 65]. It is formulated as:

$$\text{RMS}: \quad \tilde{m}(t) = \sqrt{\sum_{i=t-W}^{t} s_i^2} \qquad (11)$$

The integrated EMG (INT) and the mean absolute value (MAV) have a similar formulation, corresponding to a rolling average of the rectified signal, with a constant multiplicative factor being the only difference between the two. However, as the normalization of the signal absorbs this constant factor, INT and MAV produce the same resulting feature in this study.

$$\text{INT}: \quad \tilde{m}(t) = \sum_{i=t-W}^{t} |s_i| \qquad (12)$$

While the above feature was computed by attributing the same importance to each sample of the window, the linearly weighted average (LWAVG) aims at prioritizing the most recent samples:

$$\text{LWAVG}: \quad \tilde{m}(t) = \sum_{i=t-W}^{t} \frac{i-t+W}{W} |s_i| \qquad (13)$$
<figure><img src="image_6.png" /><figcaption>Fig. 3. Latency computation (top) and feature extraction workflows (bottom). For the latency computation, the baseline and the feature of interest are computed and normalized by their respective MVCs. Then, the latency is computed by maximizing the correlation between the baseline and the feature signals. The EMG feature is computed by performing the same normalization step and applying the latency previously computed to the signal.</figcaption></figure>

In this equation, the weight of each sample is set so that the oldest sample is weighted to zero and the most recent one is weighted to one, with a linear evolution between the two.

The simple square integral (SSI), while seeming similar to the RMS feature, has the difference of not applying the square root operator after the mean square. This results in a feature analogous to the signal energy [65], and for which the amplitude is nonlinearly impacted, contrary to the RMS. Similar to IEMG and MAV, the SSI feature has analogous formulations in the form of the EMG variance (VAR). Due to the normalization, these two features will also produce the same output.

$$SSI: \quad \tilde{m}(t) = \sum_{i=t-W}^{t} s_i^2 \qquad (14)$$

Some features, such as the waveform length (WL), and average amplitude change (AAC), exploit the rectified time differential of the EMG signal [65,66]:

$$WL: \quad \tilde{m}(t) = \sum_{i=t-W}^{t} |s_i - s_{i-1}| \qquad (15)$$

Similarly, the differential absolute standard deviation value (DASDV) is expressed as the root mean square of the time differential [65,66]:

$$DASDV: \quad \tilde{m}(t) = \sqrt{\sum_{i=t-W}^{t} (s_i - s_{i-1})^2} \qquad (16)$$

### 2.3.3. Frequency-domain features

Frequency domain features are computed by first applying a Fourier transform to the signal to obtain its power spectral density (PSD), and using it as the base information. While EMG frequency is mainly used for fatigue analysis [67,68], features relative to the frequency domain have been proposed to drive intention detection models [41,69]. In this study, the PSD was obtained using the `scipy.signal.spectrogram` function from SciPy [70], with a Hamming window of length W, and a W-1 overlapping. With a 2kHz EMG sampling frequency, the function yielded a PSD ranging from 0 to $f_{max}$ = 1kHz. For a given instant t, the PSD is thus computed using the W previous samples and is noted $P(t, f)$, with f as the frequency.

The total power (TTP) corresponds to the aggregate of the power spectrum [65]. This feature is also named energy or first spectral moment. Due to the normalization, it is also equivalent to the mean power (MNP). It is defined as:

$$TTP: \quad \tilde{m}(t) = \sum_{f=0}^{f_{max}} P(t, f) \qquad (17)$$

Spectral moments can also be used to extract information from EMG frequency. It can be written, depending on its order i, as:

$$SMi: \quad \tilde{m}(t) = \sum_{f=0}^{f_{max}} P(t, f)^i \qquad (18)$$

### 2.3.4. Latency computation

The latency induced by the feature extraction process is a crucial factor when considering real-time applications, which was assessed in several steps. First, a latency-free baseline signal $b(t)$ of the BL muscle was computed from a low-pass forward-backward filter (see Section 2.3.1). Then, the cross-correlation between the extracted feature $\tilde{m}(t)$ and the baseline signal is computed:

$$c(\delta_i) = \int_0^{T_{max}} b(t + \delta_i) \tilde{m}(t) dt \qquad (19)$$

with $\delta_i$ the time lag and $T_{max}$ the duration of the tested signal. Latency is then calculated by finding the time lag maximizing the correlation:

$$\delta_i^{opt} = \underset{\delta_i}{\operatorname{argmax}} c \qquad (20)$$

In order to reduce uncertainty, the latency of a specific feature was calculated by combining the BL signal from all trials for each subject and then taking the average. Before their testing for regression accuracy, EMG features were first time-shifted to compensate for their latency:

$$m(t) = \hat{m}(t - \delta_i^{opt}) \qquad (21)$$

This operation was performed to avoid any bias related to latency-induced score deterioration. Thus, in this paper, the ability of a feature to predict joint torque is decoupled from the latency associated with doing so. The final latency computation and feature extraction workflows are summed up in Fig. 3.

### 2.3.5. Analyses

For each subject and feature, two score values for r and NRMSE were obtained from the 2-fold cross-validation, which were then averaged. The difference between the features and the forward IIR filter's baseline scores was computed, resulting in $\Delta r$ and $\Delta$NRMSE values for each subject, feature, and window length, such that:

$$\begin{aligned} \Delta \text{NRMSE}(S, F, W) &= \text{NRMSE}(S, F, W) - \text{NRMSE}(S, \text{Baseline}) \\ \Delta r(S, F, W) &= r(S, F, W) - r(S, \text{Baseline}) \end{aligned}$$

where S, F, and W designate a subject, a feature, and a window length. Additionally, the previously described workflow was used to compute
<table><caption>**Table 1**
Contribution of muscles to the movements of the upper limb in the sagittal plane [58,59].</caption><thead><tr><th>Movement</th><th>BL</th><th>BS</th><th>BRA</th><th>BRD</th><th>TLO</th><th>TLA</th><th>TM</th><th>DA</th><th>DM</th><th>DP</th><th>PM</th><th>LD</th></tr></thead><tbody><tr><td>Elbow flexion</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Elbow extension</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Shoulder flexion</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Shoulder extension</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

a latency value for each participant, feature, and window length (see Fig. 3). These were then averaged across subjects to obtain the mean latency $\delta_t^{opt}$ of every feature and window length combination.

In order to perform statistical analyses, accuracy-latency curves were fitted for each subject and feature with an exponential model:

$$r(\delta_t^{opt}) = o_r + g_r e^{r_c(\delta_t^{opt} - t_{s,r})}$$

$$\text{NRMSE}(\delta_t^{opt}) = o_e + g_e e^{r_c(\delta_t^{opt} - t_{s,e})}$$

where, among the parameters, $o$ represent the offset, $g$ the gain, $t_c$ the time constant and $t_s$ the time shift. Although comparing features based on gain and time constant is less informative, the offset value directly represents an accuracy performance with respect to latency, and the time shift value represents a latency performance with respect to accuracy. Thus, a difference in latency depending solely on window size will not necessarily translate into a difference in time shift. Conversely, a difference in offset means that the feature is more accurate for a given latency. After fitting these parameters, a statistical analysis was performed on their values using JASP (v0.17.1, University of Amsterdam, Netherlands). A one-way repeated measurements analysis of variance (rm-ANOVA) was conducted for each parameter, with the feature serving as the within-subject factor. The sphericity of the data was evaluated using Mauchly's test [71], and a Greenhouse-Geisser correction was utilized for adjustment if necessary (i.e. $\epsilon < 0.75$). Post hoc comparisons between features were carried out employing a Holm-Bonferroni correction to account for multiple comparisons. The Shapiro-Wilk [72] test was employed to evaluate normality, and Conover's post hoc test was used in case of assumption violation.

## 2.4. Muscle sets

An optimal set of muscles must be determined for intention detection to encourage the use of EMG-based interaction systems by reducing the number of sensors used. Finding the optimal set of muscles is a combination of objective and contextual criteria: how well does a set allow to estimate the intention in a given task, and how practical the number of sensors and their locations are for this same task? With this consideration, two analyses are presented in this paper. Initially, an assessment was carried out to analyze how the number of measured muscles affected the accuracy of torque estimation, aiming to identify the minimum number required to achieve a specific estimation accuracy. Then, for a given number of muscles, each muscle was individually assessed to determine its impact on the quality of the estimation. These analyses were carried out using the low-pass forward-backward filter as an EMG feature (see Section 2.3).

### 2.4.1. Sets definitions

Because each muscle group is responsible for a particular movement (see Table 1), the collection of candidate muscle sets is heuristically generated by ensuring that every set can produce every movement. For instance, sets that did not contain at least one flexor and one extensor for each joint were not considered valid and, therefore, not included in the analyses. Likewise, sets where bi-articular muscles were used as the sole predictor for two movements were not considered as they do not ensure a decoupling. This approach resulted in 105 muscle sets for the SJ condition and 1890 for the MJ condition.

<table><caption>**Table 2**
Latency ($\delta_t^{opt}$) and accuracy (NRMSE and $r$) results using the baseline low-pass IIR filter as EMG feature [33]. $\pm$ corresponds to the standard deviation.</caption><thead><tr><th rowspan="2"></th><th>SJ</th><th colspan="2">MJ</th></tr><tr><th>Elbow</th><th>Elbow</th><th>Shoulder</th></tr></thead><tbody><tr><th>NRMSE [%]</th><td>4.7 ± 0.5</td><td>6.6 ± 0.7</td><td>6.9 ± 1.4</td></tr><tr><th>r</th><td>0.97 ± 0.01</td><td>0.91 ± 0.02</td><td>0.86 ± 0.03</td></tr><tr><th>δ<sub>t</sub><sup>opt</sup> [ms]</th><td colspan="3">-114 ± 1.1</td></tr></tbody></table>

### 2.4.2. Statistical analysis

A statistical analysis was performed to compare the performance of the measured muscle configurations. Similar to the feature comparison, score values were averaged over the two iterations of cross-validation. Prior to performing the analysis, Fisher's transform was applied to the $r$ scores, and values with a z-score greater than three were removed as outliers [73]. For the comparison of muscle number, the sphericity of the data was assessed using Mauchly's test prior to statistical analysis. A one-way rm-ANOVA was then performed with muscle number as the within-subject factor. A Greenhouse-Geisser correction was applied in case of sphericity violation. Post hoc tests between muscle numbers were performed using the Holm-Bonferroni correction.

For a given number of muscles, the influence of each muscle was assessed by first calculating the score difference on a subject-by-subject basis between sets of muscles where it was present or not. This computation accounted for the muscle role by only considering the positive or negative part of the error (e.g., the brachioradialis muscle score was computed only using the positive torques, i.e., corresponding to the flexion of the elbow):

$$\Delta \text{NRMSE}(S, k, M) = \text{NRMSE}(S, k, M_{\text{present}}) - \text{NRMSE}(S, k, M_{\text{absent}})$$

$$\Delta r(S, k, M) = r(S, k, M_{\text{present}}) - r(S, k, M_{\text{absent}})$$

with $S, k$, and $M$, respectively, designating the subject, the number of muscles, and a given muscle. Then, a two-factor rm-ANOVA was performed for each muscle, using the number of muscles and the muscle presence as between-subject factors. Again, post hoc tests were performed using the Holm-Bonferroni correction to account for multiple comparisons.

## 3. Results

Using the baseline low-pass IIR filter resulted in the accuracy and latency results presented in Table 2.

### 3.1. EMG features comparison

#### 3.1.1. Latency

Latencies were initially calculated following the method shown in Fig. 3, producing a latency value for each feature, participant, and window size (see Fig. 4.c). In general, extending the window size led to an increase in latency. Although some variations among participants were noted, they did not impact the significance of the differences in window size latencies. While the main effect for latency came from window size ($p < 0.001$ and $\eta^2 = 0.963$), features had a significant impact on the latency, albeit with a small effect ($p < 0.001$ and $\eta^2 = 0.02$). Overall, the LWAVG feature had a significantly lower latency for a given window size ($p < 0.001$) with a large effect size ($d > 1$).
<figure><img src="image_7.png" /><figcaption>Fig. 4. (a), (d) and (e) Regression score difference as a function of mean latency. (a) Represents the SJ condition while d) and (e) respectively represent the elbow and shoulder joints for the MJ condition. Above is Pearson's correlation coefficient, and below is the normalized root mean square error. Each dot represents a time window. The vertical gray dashed line represents the mean latency induced by the forward IIR filtering; the horizontal one represents its score. $\delta_t^{opt}$ is the mean latency across subjects for a given feature and window length. (b) Fitted parameters of the exponential model for SJ condition. From top to bottom: offset, gain, time constant, and time shift. Confidence intervals are computed using the method from Morley et al. [74]. (c) Latency values for each feature and window length. Boxes represent the variability across the subjects. The colormap differentiates Windows lengths. The horizontal dashed gray line represents the mean baseline latency from the IIR filter.</figcaption></figure>

### 3.1.2. Accuracy

Following the analysis outlined in Section 2.3.5, the results were used to create Fig. 4.a for the SJ condition. This visual representation illustrates the difference in performance compared to the baseline score at various latency levels while also showing the parameter fit of the exponential model (see Fig. 4.b). For the *r* score, the rm-ANOVA showed a significant effect of the feature on offset and time constant (respectively *p* < 0.001 and *p* < 0.05). Concerning the NRMSE score, feature selection significantly impacted the offset and the gain (respectively *p* < 0.001 and *p* < 0.05). Using the offset value of the fit, the INT and WL features were associated with a better mean accuracy score overall, albeit without statistical significance, compared to LWAVG, RMS, and

DASDV. A notable distinction could be made between time-domain and frequency-domain features that seemed to underperform in terms of accuracy. However, the variability associated with frequency-domain features and SSI prevented conclusive statistical confirmation. Overall, for an equivalent latency (i.e., $\delta_t^{opt} = -114 \pm 1.1$ ms), none of the features had significantly better accuracy than the IIR filter baseline. As shown in Fig. 4.d and e, in the MJ condition, similar trends were observed. In sum, time-domain features offered improved accuracy compared to frequency-domain features.

Interestingly, every feature followed a common pattern: a higher accuracy was associated with a higher latency, with an asymptotic trend.
## 3.2. Muscle sets comparison

### 3.2.1. Muscle number

As shown in Fig. 5.a, increasing muscle number resulted in a better score for the SJ condition. With the Greenhouse-Geisser correction, the repeated measures ANOVA confirmed this result, with the number of muscles having a significant effect on the NRMSE and *r* scores (*p* < 0.001). According to the post hoc tests, increasing the number of muscles from two to three and from three to four muscles had a significant impact on both scores (*p* < 0.001) with a strong effect (*d* > 1.3 and *d* > 0.75, respectively). Although the significance remained (*p* < 0.001), the impact lessened when the number of muscles increased from four to five, leading to a moderate effect with effect sizes of *d* = 0.63 for NRMSE and *d* = 0.61 for *r*. Likewise, the NRMSE and *r* scores were significantly impacted from five to six muscles with *d* = 0.45 and *d* = 0.46 with *p* < 0.05 and *p* < 0.001, respectively. For the final increase from six to seven muscles, no significant difference was found for the NRMSE score, while the *r* score showed a significant increase but with a small effect (*p* < 0.05 and *d* = 0.32). In sum, the main improvements were observed when including up to six muscles, and further inclusion only led to minor improvement.

A similar pattern was observed for the MJ condition (see Fig. 5.c and d). The rm-ANOVA showed a significant effect of muscle number on both scores and for both joints (*p* < 0.001). Specifically, for the elbow joint, each successive increase in muscle number led to a significant improvement in the *r* score (*p* < 0.05), but with a decreasing effect size (from *d* = 0.92 to *d* = 0.18). The NRMSE score increased significantly (*p* < 0.05) up to the ten to eleven muscle number increase, again with a decreasing effect size (from *d* = 0.89 to *d* = 0.25). The shoulder joint showed a different pattern: the score increased significantly up to seven muscles (*p* < 0.05, from *d* = 0.47 to *d* = 0.18 for NRMSE, and from *d* = 0.84 to *d* = 0.34 for *r*), then each subsequent increase did not produce a significant difference. In sum, the main improvements were observed when including up to eleven muscles for the elbow and seven for the shoulder, and further inclusion only led to minor improvement.

### 3.2.2. Muscle contribution

Considering the SJ condition, as depicted in Fig. 5.b, only the presence of the brachioradialis muscle significantly impacted the resulting score (*p* = 0.011 for NRMSE and *p* = 9.3 × 10⁻³ for *r*). More precisely, apart from the configuration with six muscles, the presence of the brachioradialis always contributed to improving the scores (*p* < 0.05), albeit with a higher effect size with a lower number of muscles. Accordingly, as shown in Fig. 5.b, subjects tended to have varying recruitment strategies. However, a clearer pattern emerged from the MJ condition. Considering the elbow joint, first, the presence of the brachialis and brachioradialis muscles both contributed to improving the scores for any number of muscles (*p* < 0.001). Conversely, long and short biceps globally had a negative impact (*p* < 0.001). The NRMSE score improved significantly with the median triceps presence (*p* < 0.01) and worsened with long triceps (*p* < 0.01), but there was no effect on the *r* score. The presence of lateral triceps did not lead to a significant difference in scores. Considering the shoulder joint (see Fig. 5.e and f), the median and anterior deltoid presence had a significative positive impact on both scores (*p* < 0.001). Conversely, the pectoralis major presence had a significant negative impact (*p* < 0.001). The latissimus dorsi did not have a significant effect, and neither did the long biceps. The posterior deltoid presence had a significative negative impact on both scores (*p* < 0.05), while the long triceps had a significant positive effect on the *r* score.

## 4. Discussion

The present paper introduced a methodology to evaluate and compare EMG feature extraction techniques as well as muscle sets to optimize continuous EMG-based torque prediction. The computations

were based on a previously established dataset, including SJ and MJ upper limb movements across random target trajectories [33]. This paper presented several commonly used EMG features, their computation methods and investigated their suitability to predict human torques in terms of accuracy and latency. Finally, the results showed the effect of the number of recorded muscles on the accuracy of the prediction and further showed which muscles impacted the prediction quality. These results pave the way towards the optimization of measurement and processing strategies to make EMG-driven robots a plausible daily-life scenario.

### 4.1. Feature extraction

Two important considerations for intention detection techniques are their ability to produce accurate detection and their induced latency. EMG feature extraction techniques have been extensively tested for movement classification [40,41] but not much for movement regression. Additionally, their induced latency has not been measured. As two main criteria are considered (i.e. latency and accuracy), there is no definitive answer as to which feature is best overall. Similarly to Tri-wiyanto et al. [46], the current study found that the waveform length was one of the most accurate features regarding Pearson's correlation coefficient and normalized root mean square, while the SSI performed poorly. However, contrary to their findings, the INT and RMS features did not show significantly different accuracies. As their study focused on angle estimation, this difference suggests that torque estimation may be less sensitive to the choice of these features. Furthermore, while WL and INT features were more accurate, they performed similarly to the baseline 3 Hz low-pass filter in terms of accuracy when considering a higher latency. Indeed, rather than showing an improvement, the estimation precision stalled for window lengths above 256 ms, showing no benefits despite a higher latency. This suggests that a low-pass filter is adequate for applications that do not require high reactivity. Smith et al. [47] highlighted a trend for EMG-driven pattern recognition that seems to apply to every continuous movement regression feature: a longer time window leads to a more accurate intention detection. Additionally, as illustrated in Fig. 4.a and b, the variations between the top features (e.g., INT, WL, RMS, and LWAVG) are minimal. This implies that the selection of any of these features will not notably affect the regression outcome. However, the window length remains a crucial factor, drawing a tradeoff between latency and accuracy. Each EMG-driven application has unique requirements for reactivity and precision. Thus, it is not possible to recommend a specific window length in a general sense. These findings rather suggest that the selection process first requires identifying the specific need of the application to tailor the window length accordingly. In preparing hardware for a specific application, it is crucial to consider that EMG sensor brands possess different specifications. For example, some sensors implement pass-band filters during data collection (e.g., Delsys), whereas others do not (e.g., Cometa). Furthermore, variations in the transfer protocol and acquisition method can contribute to differing transmission delays, affecting overall latency. Consequently, although the relative performance of feature extraction methods should remain the same, a shift in the overall latency and precision can be observed when employing different EMG sensors.

### 4.2. Muscle selection

EMG sensors can be costly, and their placement requires expertise. Therefore, to streamline and accelerate the overall process for in-field applications, reducing the number of EMG electrodes to a minimum and, consequently, the number of measured muscles is necessary. This present study showed that increasing the number of recorded muscles above 5 did not lead to better regression scores for the SJ condition. Similarly, the elbow joint benefited from each new muscle up to eleven for the MJ condition, and the shoulder joint stagnated above seven.
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** For each subfigure, above is Pearson's correlation coefficient, below is the normalized root mean square error, gray lines represent individual subjects, and colored lines represent the mean. (a), (c) and (d) Regression scores as a function of the number of measured muscles. (a) Represents the SJ condition, while (c) and (d) respectively represent the elbow and shoulder joints for the MJ condition. Error bars are the 95% confidence interval computed following Morey [74]. (b), (e) and (f) Regression scores difference as a function of the number of measured muscles and individual muscle presence. (b) Represents the SJ condition while (e) and (f) respectively represent the elbow and shoulder joints for the MJ condition. The difference is calculated in terms of the presence of the muscle versus its absence (see Section 2.4.2). The error bars are the usual 95% confidence interval. Data points should be interpreted such that changing a given muscle from absent to present will affect the score by the $\Delta$ value on average for a given number of muscles.</figcaption></figure>

However, because the number of available muscles for each joint is not the same (e.g., elbow flexion is actuated by four measured muscles while shoulder extension is actuated by two), the optimal number of sensors might depend on the available surface muscles for a given joint and application. Overall, while each new muscle was associated with a better score, the effect size became small, resulting in more and more diminishing returns, as also shown by Camardella et al. [48] and Ziai et al. [49]. Similar to window length selection, these results suggest that a tradeoff must be made between the expected regression accuracy and the resources allocated to achieve it for a given application. Looking at the individual muscle contributions, the results showed that with the

exception of the brachioradialis, no muscle had a preferential role in the regression accuracy of the elbow in the SJ condition. While this conclusion was reached when averaging over all subjects, a subject-by-subject analysis, as shown in Fig. 5.b, painted a different picture. Each muscle showed a high variability across subjects in its effect on regression scores. This variability excluded the possibility of extracting a general set of muscles allowing for overall better estimation performances for this condition. As such, when considering the elbow flexion/extension movement, there seems to be strong evidence that the optimal muscle set should be tailored to the participant. However, this was only partially true for the MJ condition, where muscle roles appeared more
consistent across subjects. Some previous works suggest the existence of inter-individual variability in muscle recruitment strategy employed by the central nervous system [75,76]. Also, the optimality of the recruitment strategy can be affected by physiological parameters such as limb lengths and muscles' moment arms. Nonetheless, it is unclear whether this recruitment variability is responsible for the observed between-subject difference in the effect of muscle presence. In addition, the ability of muscle activation to predict movement is largely due to the quality of information that can be extracted from the surface EMG. A thinner skin interface, less skin motion artifact, and less cross talk from surrounding muscles are critical to obtaining a cleaner EMG signal [4,68,77]. Similarly, multi-articular muscle activations result from potentially multiple simultaneous joint actuations, making it difficult to extract information selectively. From these considerations, while an optimal muscle set must be tailored to each participant in an SJ application, an upper limb sagittal MJ application would benefit from prioritizing the measure of the anterior deltoid, the long triceps, the brachialis, and the brachioradialis.

### 4.3. Limitations and future work

Some limitations restrict the scope of these findings. First, only features that did not require an *ad hoc* parameter fitting were selected. Some time-domain features such as zero-crossing or slope sign change [65], while being promising [46], require an a priori knowledge of ambient noise that was not recorded for the dataset. Second, the elbow and shoulder extension were underrepresented in the MJ conditions due to gravity. This could lead to exaggerated variability in the roles of extensor muscles, such as the posterior deltoid and the triceps heads. As such, the role of these muscles in improving intention detection might have been underestimated in this study. The frequency-domain feature relies on a spectrogram computation that requires windowing to emulate signal periodicity. While the Hamming window has been used in this study, other types of windows were not tested and might impact both latency and accuracy. Finally, the latency computation relies on the hypothesis that the baseline IIR-filtered EMG signal presents similarities with other EMG features. While this is generally true, as most features result in an envelope extraction of some sort, it may add variability to the measured latency.

Several extensions of this work can be envisioned to extend the findings presented in this study. First, movements in the sagittal plane, while encompassing a wide variety of daily tasks, are not representative of the full range of motions that the upper limb covers. Thus, extending this analysis to a higher number of degrees of freedom, including internal/external rotations and adduction/abduction of the shoulder, is essential. This is especially important when considering that individual muscle evaluation leads to sensibly different results when comparing SJ and MJ conditions. Second, using an artificial neural network-based EMG-to-torque benchmark model would allow testing multi-feature bundling as this framework was used for movement classification [41, 78] but not for movement regression.

## 5. Conclusion

In this study, several time- and frequency-domain features were tested for induced latency and their ability to perform accurate EMG-to-torque estimation. The results showed a Pareto front between accuracy and latency. Features performed similarly or worse than the 3 Hz low-pass filtering for high accuracy with high latency. The waveform length (WL) and integrated EMG (INT) features demonstrated good performances for other low-latency applications. Various muscle sets were tested to determine their impact on regression accuracy. The results showed that increasing the number of measured muscles improved accuracy but with diminishing returns after five muscles for elbow-only movement and eleven and seven muscles for the shoulder and elbow, respectively, during upper limb parasagittal plane movements.

The brachioradialis muscle was found to be the most critical choice for elbow-only movement, while other muscles showed high inter-subject variability. The anterior deltoid, long and median triceps, brachialis, and brachioradialis muscles were found to be more effective for elbow and shoulder movements in the sagittal plane.

### CRediT authorship contribution statement

**Lucas Quesada:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Do-rian Verdel:** Writing – review & editing, Software, Methodology, Data curation, Conceptualization. **Olivier Bruneau:** Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization. **Bastien Berret:** Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization. **Michel-Ange Amorim:** Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization. **Nicolas Vignais:** Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization.

### Funding

This work was funded by the French National Agency for Research (grant ANR-19-CE33-0009) and the H-Code program.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.bspc.2024.107323.

### Data availability

The data used for this study is openly available on Zenodo [51].

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