Associating Endpoint Accuracy and Similarity of Muscle Synergies

Liming Cai

1,2 a

, Shuhao Yan

2,3

, Chuanyun Ouyang

2,3

, Tianxiang Zhang

2,3

, Jun Zhu

1 b

, Li Chen

1,4,∗

and Hui Liu

5,∗ c

Academy for Engineering&Technology, Fudan University, Shanghai, 200433, China

Suzhou Institute of Biomedical Engineering and Technology Chinese Academy of Sciences, Jiangsu,215163, China

School of Biomedical Engineering (Suzhou), Division of Life Sciences and Medicine University of Science and Technology

of China, Suzhou, China

Department of Orthopedics, Huashan Hospital, Fudan University, Shanghai, China

Cognitive Systems Lab, University of Bremen, Bremen, Germany

∗ ∗

Keywords:

Muscle Synergy Extraction, Muscle Synergy Similarity, Accuracy, Manipulate, Electromyography, EMG,

sEMG.

Abstract:

Recently, extracting the muscle synergy from surface electromyographic (sEMG) signals has become a stan-

dard method for evaluating motor control strategies during exercise. The synergy of the upper extremity in

various stretch and reach tasks has been described in many studies, but few of them have analyzed the relation-

ship between task performance and muscle synergy. This study provides an experimental device and analysis

method for muscle coordination in the joystick task for the speciﬁc action of the pilots’ joystick manipulation.

Eight healthy subjects performed the joystick manipulation. For upper limbs, the task content included iso-

tonic tasks with three load levels and recorded ten muscles’ EMG and acceleration information. The muscle

synergy effect was extracted and the correlation between muscle synergy similarity and manipulation per-

formance and interaction load was studied. The experiment data showed that the manipulation performance

varied under different loading conditions, but did not show signiﬁcant changes in synergistic muscle structure.

We found signiﬁcant correlations between the similarity of some synergistic muscle structures and manipula-

tion performance. However, between single-action performance and the average of their likeness, there was

no strong correlation. Through the analysis of muscle synergy, we can determine that there is a ﬁxed muscle

synergy pattern during rocker manipulation, of which the structure is independent of the rocker load level,

and muscle synergy similarity was negatively correlated with manipulation performance. The ﬁndings of this

study signiﬁcantly contribute to enhancing the ergonomic design of the ﬂight stick, offering speciﬁc insights

for its optimization. Additionally, they pave the way for developing specialized muscle training techniques,

which are tailored to augment the accuracy and precision of executing complex ﬂight maneuvers.

1 INTRODUCTION

Fine manipulation is one of the basic abilities of pi-

lots, and it is a necessary and preferred ability in the

selection and training process (Franklin et al., 2003).

Fine manipulation refers to the power of the phys-

iological reﬂex conducted by the optic nerve to re-

ﬂect on the action quickly. The visual system uses

the reﬂection and conduction of many visual func-

tions to input the information obtained from observ-

https://orcid.org/0000-0003-2952-0109

https://orcid.org/0000-0003-1311-4333

https://orcid.org/0000-0002-6850-9570

∗

Correspondence E-mails

ing the surrounding environment into the center of the

brain. Then it transmits and drives the neuromuscu-

loskeletal motor system and reﬂects it in the center of

the brain on delicate movements of the hands or feet

(Sepehrikia et al., 2023). The joystick manipulation

is one of the main contents of the ﬂight action; ma-

nipulation’s accuracy and stability are essential.

The joystick manipulation is a multi-joint-

coordinated movement. In motion control of the hu-

man body, the corresponding control modes are nu-

merous for multi-joint motion. Actions are inher-

ently variable, and professional athletes can use repe-

tition to make them as consistent as possible. Mus-

cle synergy has been used to study complex motor

control patterns in recent years. Numerous studies

Cai, L., Yan, S., Ouyang, C., Zhang, T., Zhu, J., Chen, L. and Liu, H.

Associating Endpoint Accuracy and Similarity of Muscle Synergies.

DOI: 10.5220/0012586800003657

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2024) - Volume 1, pages 683-694

ISBN: 978-989-758-688-0; ISSN: 2184-4305

683

have indicated that the CNS generates motor com-

mands through synergistic combinations of muscles

(d’Avella and Bizzi, 2003; Bizzi et al., 2008; Bizzi

and Cheung, 2013), which is called muscle synergy.

Applications of muscle synergy triggers studying the

effects of nerve damage (Tang et al., 2017; Roh

et al., 2013), human posture control (Torres-Oviedo

and Ting, 2007; Robert and Latash, 2008; Asaka

et al., 2011), robot-assisted technology (Miyazaki,

2011; Salman et al., 2010; C et al., 2021; Wang et al.,

2021), and locomotion (A et al., 2019).

In isometric tasks, against speed changes, the

module structures of muscle synergies were robust;

the neural commands to muscle synergies changed in

response to speed changes (Kojima et al., 2017). The

motor control strategy might be modiﬁed depending

on the requirement of the accuracy of the isometric

reaching task considered (Tsubasa et al., 2020; Et-

tema et al., 2005). In the isotonic contraction task,

previous studies have shown that the CNS could ac-

quire knowledge between stiff-ness level and size of

targets in some way (Osu et al., 2004; Sangwan et al.,

2015), and change the mechanical impedance of the

human body through the simultaneous activation of

antagonist muscle groups (Burdet et al., 2001; Feld-

man and Levin, 1995), which reveals the critical role

of co-contraction in upper limbs accuracy movement.

In addition to co-contraction indices, inter- and

intra-subject similarity have previously been a hotspot

in motor coordination (Alnajjar, 2017; Barnamehei

et al., 2018a; Esmaeili and Maleki, 2020). Stud-

ies have shown that expertise did not cause signiﬁ-

cant differences in muscle synergy in controlled ex-

periments between elites and non-elites (Barnamehei

et al., 2018b). Although many studies support the

similarity of synergistic components between differ-

ent subjects under task conditions (K et al., 2021;

Choi et al., 2019; Curado et al., 2015; Taborri et al.,

2017; Velden et al., 2022), only a few studies have

compared the relationship between intra-subject sim-

ilarity and motion accuracy under different conditions

(Choi et al., 2019). In comprehensive studies, the re-

searchers have not assessed the within-subject vari-

ability in detail, and data are often averaged across

trials to obtain average patterns without detailed anal-

ysis of individual manipulations (A et al., 2019; Zhao

et al., 2019; Mira et al., 2021).

The extraction of muscle synergy holds great po-

tential for enhancing ﬁne motor skills. In this context,

this study explores an objective and effective method

to investigate the relationship between muscle syn-

ergy similarity, manipulation performance, and inter-

action load. Speciﬁcally, the study designs isotonic

manipulation tasks with three different load levels.

From these tasks, muscle synergy structure and sim-

ilarity are extracted from sEMG data. Subsequently,

the manipulation performance, muscle synergy struc-

ture, and their likeness are thoroughly analyzed and

compared. Finally, the study delves into the relation-

ship between manipulation performance and muscle

synergy, offering insights into their interplay.

2 MATERIALS AND METHODS

2.1 Subjects and Experimental

Apparatus

In this study, a sample population of 8 healthy sub-

jects (all males, ages from 22 to 24, with heights of

170 ± 5 cm, and weighted 68 ± 5kg) volunteered to

participate. The experiment procedure was informed

to the subjects.

The joystick manipulation experimental apparatus

was self-developed by the project team. As shown

in Figure 1, it can realize the X and Y direction joy-

stick manipulation and record the space position of

the stick in real-time through the data from the en-

coder all of the subjects manipulated the experimental

apparatus according to the upper computer interface,

as shown in Figure 2A, and after completing the prac-

tical record of a single task, the description is shown

in Figure 2B.

2.2 Three Tasks

Joystick manipulation was usually done by coordinat-

ing the shoulder, elbow, wrist, and ﬁngers. This study

designed the reciprocating motion under three loading

conditions( Figure 2B). The study performed internal

rotation and external rotation during the experiment.

At the same time, the elbow joint was ﬂexed and ex-

tended on the sagittal plane and retracted on the coro-

nal plane. For the convenience of discussion, the en-

tire experimental action was described by supination

and pronation.

The subjects carried out simple manipulation

learning under guidance before the start of the tests.

All issues were asked to sit upright on a chair through-

out the investigation. The issues held the joystick and

moved back and forth along the X-axis ( Figure 2A).

The joystick moved to the right along +X, and the blue

ball rolled to the B circle synchronously Figure 2B).

The initial position of the blue ball was in the mid-

dle. Meanwhile, The black circle (diameter 2cm) was

symmetrical on both sides of the blue ball. The joy-

stick load was set to 3 levels (task 1, drag torque 0.72

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684

Nm; task 2, drag torque 2.16 Nm; task 3, drag torque

6 Nm).

The subjects were required to 1) keep a distance

between the elbows and the thighs, 2) exert force on

the upper limbs, 3) blue balls reciprocate between the

black circles, and 4) speed up while giving priority to

accuracy.

Operating Procedures. Each set of 16 reps, then rest

for 5 minutes before doing the next set. In this way,

there were 24 sets of trials, and each set of trials con-

tained 16 cyclic actions.

Data Induction. There were 24 clusters of experi-

ments for eight subjects, each completed three tasks.

The data includes the manipulation accuracy of the

left and right positions and the similarity of the mus-

cle synergy.

2.3 EMG Data Acquisition

Manipulation performance was recorded by the self-

made joystick manipulation experimental prototype

(position sampling frequency: 200Hz). Meanwhile,

while subjects performed the movement tasks, A sur-

face EMG system (Diese Trigno, USA DELSYS.

Inc)was used to measure EMG and acceleration from

10 muscles of the upper arm ( Figure 1A) includ-

ing brachioradialis (BRAD), the short head of biceps

(BICS), long head of biceps (BICL), anterior deltoid

(DA), long head of triceps (TRIL), lateral head of

triceps (TRILA), pectoralis major (PM), infraspina-

tus (INF), teres minor (T.M.), and posterior deltoid

(D.P.). Electrodes are shown in Figure 1B/C, and the

placement of electrodes follows the guidelines of sur-

face EMG (Hermens et al., 2000). The sampling fre-

quency of surface EMG is 1249Hz, and the sampling

frequency of acceleration is 149Hz. The acquired sig-

Figure 1: Placement and sensing muscles of sEMG sensors.

Top right: self-adhesive electrodes. BRAD: brachioradi-

alis; BICS: the short head of biceps; BICL: the long head of

biceps; PM: pectoralis major; DA: anterior deltoid; TRIP:

the long head of triceps; TRILA: the lateral head of triceps;

INF: infraspinatus; T.M.: teres minor; D.P.: posterior del-

toid (Cai et al., 2023b).

nals were recorded and imported into Matlab 2017

(The Mathworks, Natick, MA) to be processed by

means of custom routines.

2.4 Manipulation Performance Data

The data of manipulation was derived from the motor

encoder( Figure 2C), which was pre-processed in the

following way:

a. Perform absolute value and normalization process-

ing on the original data in order to detect the setting

of the threshold;

b. Perform median ﬁltering on the data obtained in

(a) to ﬁlter out noise (abnormal burr) interference;

c. Analyze the data, set the detection threshold, obtain

the position index of the data more signiﬁcant than

this threshold, and take the maximum and minimum

value of the position index to obtain 4: the start and

end position indexes of the valid data segment.

d. Calculate and obtain valid data in the original data

according to the detection results in (c), and calculate

the mean and variance.

e. Quantiﬁcation of Manipulation Performance:

Positon deviation (P.D.): the difference between the

mean of all data and the value of the ideal position.

Positon accuracy (P.A.): the difference between the

value of the actual and the ideal position

Positon repeatability (P.R.): variance of all actual

values.

Positon stability (P.E.): inferior for all manipulation

data.

2.5 Muscle Synergies Extraction and

Analysis

2.5.1 EMG Preprocessing

The custom routines were used for the sEMG Pre-

processing in Matlab. The EMG pretreatment was in

the following way:

a. Removes drifts: A mean shift was used to elimi-

nate baseline shifts caused by trial or subject electrode

shifts.

b. Band-pass (B.P.): ﬁltering (40-250Hz), Removing

high-frequency noise and motion artifacts.

c. Notch: 50Hz, 150Hz notch, removed ﬁxed fre-

quency noise.

d. Rectiﬁcation: it is a standard method used for an

envelope of non-negative sEMG signals

e. Low-pass (L.P.) ﬁltering (20Hz), applied to the

rectiﬁed sEMG signals, Cutoff frequency of 0.5Hz

ensured smooth envelope and affected NMF results

(Kieliba et al., 2018; Ouyang et al., 2023).

f. Normalization: normalized by the maximum value

Associating Endpoint Accuracy and Similarity of Muscle Synergies

685

Figure 2: Self-developed experimental device and software interface. (A) Top view of the device for experiments; (B) A

screenshot of the software interface; (C) An exemplar result record. PD: position deviation; PE: extreme range of the position

(Cai et al., 2023b).

of the data itself during the trials.

g. Segmentation: The ACC signal was obtained syn-

chronously with the EMG signal, but the sampling

frequency of the ACC signal was lower than that of

the EMG signal, so the ACC signal should be interpo-

lated ﬁrst to ensure that the length of the ACC signal

was consistent with the sEMG signal, after median

ﬁltering the ACC signal was used to divide the EMG

signal. This paper extracted data from the ﬁrst 14 cy-

cles, each containing one supination and one prona-

tion.

2.5.2 Extraction of Muscle Synergies

A Non-negative Matrix Factorization (NMF) algo-

rithm was employed to extract muscle synergies (Lee

and Seung, 1999). The pre-processed signal (V

m×t

where m represents the muscle channels and t denotes

time, was decomposed into two matrices: W

m×n

and

n×t

. Here, n is the number of extracted muscle syn-

ergies, W is the basis matrix representing muscle acti-

vation patterns, and H is the matrix of activation coef-

ﬁcients for the muscle activations across m channels.

m×t

≈ W

m×n

× H

n×t

= W

× H

+ · · · +W

× H

(1)

is a vector from the Muscle synergy matrix, spec-

ifying the muscle activity pattern deﬁned by mus-

cle synergy. Each element of W

was between 0 and

1 (Cai et al., 2023a). Muscle synergy formed by

these is functionally activated by the activation co-

efﬁcient matrixH

. The activation coefﬁcient repre-

sented the purported neural command from CNS, and

determined the relative contribution for establishing

the muscle synergy matrix (Torres-Oviedo and Ting,

2007; Cai et al., 2023c).

The number of muscle synergies n was between

1 and 10. The reconstructed matrix V

′

m×t

has been

expressed as (2). Then, the minimum number of syn-

ergies was selected that could adequately reconstruct

the pre-processed signals V

m×t

in all trials, as the vari-

ability accounted for (VAF shown in formula 3) >

90% in each muscle data vector (Tang et al., 2017).

′

m×t

= W

m×n

× H

n×t

VAF = 1 −



m×t

− V

′

m×t



m×t

(2)

2.5.3 Quantitative Similarity of Muscle

Synergies

To determine the synergies’ similarity among the

tasks between the clusters, we used the intraclass cor-

relation coefﬁcient (ICC) analysis (Choi et al., 2019;

Curado et al., 2015; Taborri et al., 2017; Velden et al.,

2022; McGraw and Wong, 1996), each subject per-

formed 14 round trips in a single task. First, indi-

vidual synergies from a single subject were collected

in one cluster. Then, we examined the similarity of

the synergies within the cluster by using the R

icc−wi

as formula (4), wi= [w

,..w

], wi is the synergy

matrices. In the formula (4), m represents the number

of trips which was 14, and i ranges from 1 to n.

icc−wi

= ICC (W

,. ..,W

) (3)

In the single cluster, the likeness between two mus-

cle synergies matrices was assessed by r (Pear-

son’s correlation coefﬁcients). Assume the num-

ber of trials was S for each subject, Sub ject 1

correlation coefﬁcients were expressed as R

i−wi

,. . . r

i−1

i+1

,. . . r

], with the ri has represented

the likeness of wi from the data of i-th trial and other

trials. Then the dispersion of all the averaged Ri

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686

was analyzed using the quartile method (Tang et al.,

2017). After ﬁltrating data, muscle synergies for each

subject R

task

were averaged.

i−wi

S − 1

∑

i=1

.. . + r

i−1

+ r

i+1

+ r

)

task−wi

∑

i=1

1−wi

+ R

2−wi

.. . + R

S−wi

)

(4)

2.5.4 Statistics Methods

This study’s descriptive statistics included the mean

and standard deviation of experiment data. One-way

ANOVA was used to evaluate between-cluster and

within-cluster R

icc−wi

differences between differ-

ent loadings and subjects. Coefﬁcients were consid-

ered signiﬁcant for p < 0.1 and p < 0.05 in this study.

3 RESULTS

3.1 Muscle Synergy Analysis

Muscle synergies extracted from three tasks of 8

healthy subjects are shown in Figure 3. Four muscle

synergies were recruited in three tasks. W1 mainly

reﬂected the activation of BRAD, INF, and DA; W2

contained the activation of DA, PELA, TRILA, and

TRIL; W3 was mainly BICL and BICS; W4 was com-

posed of D.P., T.M., INF, TRIAL, TRAIL, BRAD.

When the load increased, the effect of INF decreased,

and the effect of A.D. increased in the synergy (W1).

As a small muscle group, BRAD was lowered in all

four synergistic modes as the load increased.

Within the cluster, a pronounced structure was

observed among the eight subjects. The average of

icc−wi

across all tasks and subjects was 0.87 ± 0.05

icc−w2

= 0.97 ± 0.02, R

icc−w3

= 0.89 ± 0.09, R

icc−w4

= 0.96 ± 0.03), as shown in Figure 4. A one-way

analysis was conducted to evaluate the subjects and

tasks for R

icc−w1

. There was a signiﬁcant differ-

ence in R

icc−w2

among different subjects (F = 3.674,

p = 0.015), and no statistical difference was found

in the level of R

icc−w1

, which is affected by different

tasks. The table 1 presents all the ICC results of mus-

cle synergies in all trials.

In the cluster, One-way analysis was used to as-

sess R

icc−w1

of the subjects and tasks of. There

was a signiﬁcant difference in R

icc−w1

among differ-

ent subjects: R

icc−w1

(F = 10.754, p = 0); R

icc−w2

(F = 16.675, p = 0); R

icc−w3

(F = 43.418, p = 0);

icc−w4

(F = 25, p = 0), and statistical differences in

the level of R

icc−w1

(F = 5.903, p = 0.003) affected

by task.

3.2 Manipulation Accuracy Analysis

During pronation, six subjects exhibited smaller ma-

nipulation errors in task 2 compared to the other two

tasks. Furthermore, seven subjects had smaller ma-

nipulation errors in task 2 than in task 1, and the same

seven subjects had smaller errors in task 2 than in

task 3, as shown in Figure 5A. Regarding supination,

as depicted in Figure 5B, ﬁve subjects experienced

smaller manipulation errors in task 2 than in the other

two tasks, and ﬁve subjects had greater errors in task

1 compared to the other tasks.

The average similarity ri of a single trial in the

whole process was calculated. Meanwhile, the ri

with low similarity was proposed according to the

four-class classiﬁcation method. According to this

method, the experimental results left by each subject

are shown in Figure 5 and Figure 6, during pronation,

there are seven subjects whose manipulation error of

task 2 was smaller than the other two tasks. During

supination, the manipulation error of task 2 with six

subjects was smaller than that of the other two tasks.

The number of the subjects with this characteristic

was higher than before the treatment.

One-way analysis was used in the cluster to as-

sess manipulation accuracy P.A.–L, P.A.–R. There

was a signiﬁcant difference in P.A.–L among different

subjects (F = 3.374, p = 0.002), and different loads

(F = 5.143, p = 0.006).

3.3 Analysis of Correlation

Between the cluster, View Table 2, as shown in Figure

7 The correlation between P.D.–L and load is -0.29 (p

= 0.168), the r between P.D.–R and load is -0.41*(p

= 0.05), the r between P.R.–L and load is -0.3 (p =

0.15), the r between P.D.–R and load is -0.24 (p =

0.261), and r between P.E.–L and load is -0.32 (p =

0.12). The load correlation between the P.E.–R load

correlation is -0.27 (p = 0.2).

In the cluster, the relationship between the perfor-

mance of a single manipulation and ri (the similarity

of the muscle synergy from the single manipulation)

was shown in Table 3. Among the 96 groups of corre-

lation indicators, 18 were signiﬁcant, W

was signif-

icant six times, W

and W

appeared four times each,

and W

appeared three times (p < 0.1).

4 DISCUSSION

In this study, the muscle activity of 10 channels was

measured by EMG when a rocker manipulated the

upper limb, and the muscle synergy was extracted.

Associating Endpoint Accuracy and Similarity of Muscle Synergies

687

Figure 3: Muscle synergies extracted from 8 subjects (A), (B), (C)Y-axis is the muscle synergies under the different task (D)

the mean muscle synergies from all subjects, The horizontal axis is all corresponding to the selected ten muscles.

The results showed that approximately four individ-

ual synergistic effects were extracted from separate

EMG datasets with a 90% VAF criterion. Under dif-

ferent load conditions, the similarity between the ma-

nipulation performance and muscle synergy of each

action was collected for analysis, and the research be-

tween the manipulation performance and the muscle

synergy effect was clariﬁed from the perspective of

manipulation performance.

4.1 The Load and the Structure of

Muscle Synergy

In this study, we found that changes in loading did

not cause differences in muscle synergy, and mus-

cle synergy was substantially similar in each subject.

This is consistent with previous studies that changes

in loading have a limited effect on synergistic struc-

ture (Nicolas A et al., 2020). Giving the arm a certain

amount of assistance or resistance did not alter the

composition of the muscle synergy used by the sub-

jects during the stretch but instead changed the magni-

tude of the activation spectrum of the muscle synergy.

(Coscia et al., 2014)Previous studies have found that

3 to 5 muscles work together in the three-dimensional

force generation of the upper extremity (Roh et al.,

2012). The four muscle synergies we found in our

study can be analyzed, and the extracted muscle syn-

ergy is inﬂuenced by biomechanics and task con-

straints (Todorov et al., 2005). During pronation, the

muscle further weights of D.P., PM, BICL, and BICS

in the W2 synergistic effect are louder, which means

that these muscles work coordinately in pronation.

In the supination action, the muscle weights of D.P.,

T.M., INF, TRILA, and TRIL, synergistic effects of

W4, are more signiﬁcant. We found that small muscle

groups like BRAD have lower weights in all 4 syner-

gistic modes when the load was increased.

Muscle synergy similarity (R

icc−w2

) per cluster

was not signiﬁcantly correlated with load (r = 0 ∼

0.17). A study of three-digit force generation re-

ported that the EMG–EMG coherence was not sig-

niﬁcantly affected by force, suggesting that the dis-

tribution of neural drive to multiple hand muscles is

force-independent (Santos et al., 2010). Manipulation

performance has a certain correlation with the load

(r = -0.41, p < 0.05). Several studies have investi-

gated how the motor system modulates limb stiffness

to achieve accurate movements in the presence of un-

stable force loads (Burdet et al., 2001; Franklin and

Theodore E., 2007).

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688

Figure 4: Intragroup correlation coefﬁcients of muscle synergy in three tasks, (A)W 1, (B)W 2, (C)W3, (D)W 4.

The horizontal axis represents eight subjects; The vertical axis represents the intra-group correlation coefﬁcient of muscle

synergy in the three tasks of the subjects.

Figure 5: Results of manipulation for three tasks, the hori-

zontal axis represents eight subjects (A) P.D. during prona-

tion, (B) P.E. during Supination.

4.2 Manipulation Performance and the

Structure Similarity of Muscle

Synergy

Many studies have shown that there are usually many

compensatory solutions for any motor task, and these

Figure 6: Filtered results of manipulation for three tasks,

the horizontal axis represents eight subjects (A) P.D. during

pronation, (B) P.E. during Supination.

different solutions can achieve the same movement

(McKay and Ting, 2008; L. H. Ting, 2004). In our

study, all three tasks were isometric, and the position

distribution at the end of the exercise changed with the

load, which was similar to the previous study (Kojima

et al., 2017). We found that among the three tasks,

Associating Endpoint Accuracy and Similarity of Muscle Synergies

689

Table 1: ICC of muscle synergies and results of manipulation for all trials.

W1 W2 W3 W4 PD-L PD-R Task PR-L PR-R PE-L PE-R

Subject1 0.96 0.96 0.94 0.99 4.02 0.74 1 5.85 2.25 20.74 6.98

Subject1 0.89 0.97 0.98 0.99 1.02 0.32 2 3.47 3.65 15.31 11.4

Subject1 0.76 0.97 0.93 0.94 0.57 0.71 3 2.88 2.53 9.9 8.91

Subject2 0.85 0.98 0.92 0.93 4.06 1.57 1 4.02 5.35 14.12 20.76

Subject2 0.8 0.98 0.81 0.94 2.34 0.02 2 3.57 2.58 14.53 8.6

Subject2 0.74 0.99 0.93 0.95 1.76 0.29 3 3.74 3.81 14.12 14.54

Subject3 0.83 0.97 0.8 0.97 0.24 3.17 1 3.85 7.16 14.1 27.19

Subject3 0.87 0.99 0.83 0.99 0.63 0.94 2 4.44 2.77 15.19 9.74

Subject3 0.89 0.96 0.89 0.99 0.78 0.61 3 3.46 3.56 11.63 11.92

Subject4 0.87 0.97 0.97 0.98 1.49 0.77 1 4.33 4.41 17.09 15.7

Subject4 0.82 0.99 0.98 0.99 2.22 1.49 2 3.25 2.99 11.08 9.62

Subject4 0.94 0.99 0.98 0.98 2.39 1.4 3 4.15 4.07 15.43 16.31

Subject5 0.82 0.97 0.94 0.95 4.61 3.63 1 7.58 9.15 27.05 34.2

Subject5 0.85 0.96 0.94 0.96 0.78 0.67 2 3.65 6.31 13.42 27.54

Subject5 0.86 0.99 0.9 0.86 1.07 0.86 3 6.51 6.7 26.28 20.69

Subject6 0.87 0.96 0.89 0.89 1.36 0.59 1 5.63 3.71 25.03 10.41

Subject6 0.91 0.94 0.65 0.96 0.59 0.81 2 2.86 4.52 9.84 12.96

Subject6 0.95 0.97 0.67 0.96 1.56 0.64 3 3.71 5.07 14.16 18.29

Subject7 0.92 0.95 0.93 0.97 0.93 1.37 1 5.02 7.42 18.8 32.69

Subject7 0.87 0.95 0.86 0.98 1.28 0.99 2 4.02 3.51 17.04 13.3

Subject7 0.86 0.91 0.88 0.97 2.65 0.22 3 5.7 5.72 17.55 20.7

Subject8 0.95 0.98 0.94 0.94 2.86 0.48 1 4.25 3.06 14.13 12.46

Subject8 0.93 0.97 0.94 0.97 1.06 0.39 2 3.03 2.78 10.63 11.48

Subject8 0.92 0.96 0.86 0.96 2.14 1.01 3 3.39 2.62 11.97 9.05

Table 2: Pearson correlation of ICC and results of manipulation.

W1 W2 W3 W4 PD-

PD-

Task PR-

PR-

PE-

W1 1 -0.22 -0.14 0.23 0.08 -0.14 -0.13 0.04 -0.12 0.02 -0.09

W2 1 0.28 -0.18 0.06 0.13 0 -0.11 -0.18 -0.02 -0.17

W3 1 0.08 0.29 0.03 -0.17 0.21 -0.05 0.2 0.04

W4 1 -0.04 0.05 -0.02 -0.37 -0.24 -

.48*

-0.13

PD-

1 0.26 -0.29 .501* 0.1 0.36 0.1

PD-

1 -

.41*

0.37 0.65** 0.3 0.63**

Task 1 -0.3 -0.24 -0.32 -0.27

PR-

1 0.55** 0.94** 0.46*

PR-

1 0.50* 0.97**

PE-

1 0.39

PE-

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Table 3: Pearson correlation between similarity and results of manipulation in the cluster.

PA-L PA-R

Task W1 W2 W3 W4 W1 W2 W3 W4

Subject1 1 0.223 255 0.022 0.36 -0.47* -0.512* -0.04 0.213

Subject1 2 0.341 0.345 0.33 -0.093 0.208 0.294 0.053 -0.502*

Subject1 3 0.343 0.254 -0.229 -0.197 -0.076 0.045 -0.356 0.05

Subject2 1 0.318 -0.133 0.093 -0.026 0.017 0.057 -0.215 -0.811***

Subject2 2 -0.245 0.137 -0.587** -0.362 -0.279 -0.158 0.136 0.089

Subject2 3 0.036 -0.267 0.195 -0.038 0.452* 0.279 0.322 -0.337

Subject3 1 0.057 0.383 -0.25 -0.525** -0.033 0.042 0.289 -0.491*

Subject3 2 -0.13 0.083 -0.219 -0.423 -0.288 0.395 0.232 0.235

Subject3 3 0.16 0.038 -0.253 0.403 -0.06 0.141 0.089 0.433

Subject4 1 -0.025 0.094 0.229 0.245 0.097 -0.186 0.229 0.295

Subject4 2 -0.33 -0.285 0.344 0.314 -0.015 0.091 0.17 -0.192

Subject4 3 0.371 0.284 0.018 -0.002 0.189 0.031 0.029 -0.379

Subject5 1 0.242 -0.083 0.024 -0.198 -0.128 -0.325 0.421 0.108

Subject5 2 -0.332 0.425 -0.314 0.059 -0.609** -0.22 0.043 -0.028

Subject5 3 -0.15 0.072 -0.279 -0.039 0.298 0.242 -0.186 -0.125

Subject6 1 -0.046 0.197 0.166 -0.033 0.073 -0.495* -0.429* -0.108

Subject6 2 -0.221 -0.014 -0.539** -0.356 0.102 -0.228 0.292 -0.573**

Subject6 3 0.072 0.434 -0.424 0.386 0.149 0.242 -0.006 -0.165

Subject7 1 0.159 0.322 0.371 -0.225 0.265 0.097 -0.282 0.36

Subject7 2 0.093 -0.017 0.061 0.336 -0.373 -0.332 0.156 0.016

Subject7 3 0.42 -0.482** 0.228 -0.2 0.121 0.209 -0.302 -0.461*

Subject8 1 -0.127 -0.161 -0.113 -0.507** 0.16 -0.258 0.185 0.335

Subject8 2 0.104 -0.484** -0.369 -0.056 -0.185 0.139 0.2 -0.004

Subject8 3 0.278 0.368 0.175 0.169 0.058 -0.182 0.424 0.366

***p < 0.01, **p < 0.05, *p < 0.1

the manipulation error of task 2 was smaller than that

of the other two tasks, and this rule was more evi-

dent when the experimental data was screened by the

quartile method. This means that manipulation per-

formance is not linearly related to loading. According

to the results of Figure 5 and Figure 6, the load causes

a decrease in the manipulation accuracy, but there is

an optimal value within a speciﬁc range.

We hypothesize that motion accuracy is re-

lated not only to loading, co-contraction index, and

impedance (Sangwan et al., 2015), but also to muscle

synergy similarity (Choi et al., 2019). This hypothe-

sis is supported by our macroscopic experimental re-

sults. As Table 2 shows, the intra-group correlation

coefﬁcient of W

was signiﬁcantly negatively corre-

lated with P.E.-L (r = -0.48, p < 0.05). In the prona-

tion action, D.P., T.M., INF, TRILA, and TRIL within

the W

synergy are antagonistic muscles. This ﬁnding

suggests that the CNS activates antagonistic muscles

to adjust motor impedance, minimizing load-induced

interference and improving movement accuracy (Ser-

res and Milner, 1991; Wong et al., 2009).

Further research on a single manipulation was

conducted to observe the correlation between its ac-

curacy and the average similarity of this manipulation

with other manipulations in 7. No apparent statistical

law was found, and the number of signiﬁcant correla-

tions between W2 and W4 was greater than that of the

other two. From the analysis of the results with signif-

icant correlations, W4 was negatively correlated with

bilateral manipulation errors like the previous results,

and W2 was also negatively correlated with bilateral

manipulation results, which proved the role of the an-

tagonist’s muscles in performing precision-targeted

movements. The manipulating error was smaller as

the synergistic similarity of the antagonistic muscle

groups increased.

5 CONCUSION

Our experiments and in-depth data analysis revealed

that the synergistic structure of muscles remained

strikingly constant across various load levels when

healthy subjects skillfully performed rocker manip-

ulations, the similarity of muscle synergy was then

negatively correlated with load level. Our interpreta-

tion of this result also highlights the body’s capacity

Associating Endpoint Accuracy and Similarity of Muscle Synergies

691

Figure 7: O.A. versus the R

of muscle synergy in the cluster

A(W

), B(W

), C(W

), D(W

to adapt to varying loading levels through the modi-

ﬁcation of biomechanical strategies, reﬂecting an in-

nate and efﬁcient adaptability mechanism. We also

observed the performance of joystick manipulation

was negatively correlated with the similarity of cer-

tain muscle synergy. These results also supported

the alternative hypothesis that the human body in-

creased the activation of antagonistic muscle groups

to achieve better manipulation outcomes. Our results

showed that the muscle coordination model was effec-

tive as an understanding of the effect of load on mus-

cle coordination and manipulation performance in

joystick manipulation. Such an understanding would

help in the ergonomic design of ﬂight joysticks and

the training methods for improving pilots’ upper limb

manipulation.

ACKNOWLEDGEMENTS

The authors sincerely express their gratitude for

the generous ﬁnancial support of ”National Key

R&D Program of China”(No.2020YFC2007402,

No.2020YFC2007401, No.2020YFC2007404,

No.2020YFC2007403, No.2020YFC2007405,

No.2020YFC2007400), Basic Research Program of

Suzhou (SJC2022011), and Special project of basic

research on frontier leading technology in Jiangsu

Province (BK20192004C).

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