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Citation: Ma, Y.; Liu, D.; Yan, Z.; Yu,
L.; Gui, L.; Yang, C.; Yang, W.
Optimizing Exoskeleton Assistance:
Muscle Synergy-Based Actuation for
Personalized Hip Exoskeleton Control.
Actuators 2024,13, 54. https://
doi.org/10.3390/act13020054
Academic Editor: Steve Davis
Received: 5 January 2024
Revised: 24 January 2024
Accepted: 29 January 2024
Published: 31 January 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
actuators
Article
Optimizing Exoskeleton Assistance: Muscle Synergy-Based
Actuation for Personalized Hip Exoskeleton Control †
Yehao Ma 1,‡ , Dewei Liu 2, ‡, Zehao Yan 2, Linfan Yu 3, Lianghong Gui 2, Canjun Yang 4and Wei Yang 2,4,*
1Robotics Institute, Ningbo University of Technology, Ningbo 315100, China; mayehao@nbut.edu.cn
2Ningbo Innovation Center, Zhejiang University, Hangzhou 310058, China; 22260405@zju.edu.cn (D.L.);
yanzehao@zju.edu.cn (Z.Y.); glh000@zju.edu.cn (L.G.)
3Beijing Institute of Precision Mechatronics and Control, Beijing 100190, China; yulf@zju.edu.cn
4College of Mechanical Engineering, Zhejiang University, Hangzhou 310058, China; ycj@zju.edu.cn
*Correspondence: simpleway@zju.edu.cn
†
This paper is an extended version of our published paper Yang, W.; Yan, Z.; Yu, L.; Feng, L.; Gui, L.; Yang, C.
Muscle Synergy-Based Human-in-the-Loop Optimization for Personalized Hip Exoskeleton Control. In
Proceedings of the 2023 International Conference on Advanced Robotics and Mechatronics (ICARM), Sanya,
China, 8–10 July 2023.
‡These authors have contributed equally to this work.
Abstract: Exoskeleton robots hold promising prospects for rehabilitation training in individuals
with weakened muscular conditions. However, achieving improved human–machine interaction
and delivering customized assistance remains a challenging task. This paper introduces a muscle
synergy-based human-in-the-loop (HIL) optimization framework for hip exoskeletons to offer more
personalized torque assistance. Initially, we propose a muscle synergy similarity index to quantify the
similarity of synergy while walking with and without the assistance of an exoskeleton. By integrating
surface electromyography (sEMG) signals to calculate metrics evaluating muscle synergy and itera-
tively optimizing assistance parameters in real time, a muscle synergy-based HIL optimized torque
configuration is presented and tested on a portable hip exoskeleton. Iterative optimization explores
the optimal and suboptimal assistance torque profiles for six healthy volunteers, simultaneously
testing zero torque and predefined assistance configurations, and verified the corresponding muscle
synergy similarity indices through experimental testing. In our validation experiments, the assistance
parameters generated through HIL optimization significantly enhance muscle synergy similarity
during walking with exoskeletal assistance, with an optimal average of 0.80
±
0.04 (mean
±
std),
marking a 6.3% improvement over prior assistive studies and achieving 96.4% similarity compared
with free walking. This demonstrates that the proposed muscle synergy-based HIL optimization can
ensure robotic exoskeleton-assisted walking as “natural” as possible.
Keywords: human-in-the-loop optimization; hip exoskeleton; muscle synergy; surface
electromyography;
assist torque profile
1. Introduction
Wearable devices, such as exoskeleton robots and exosuits, have garnered significant
attention in fields such as rehabilitation [
1
], augmentation [
2
], and elderly care [
3
] owing
to their potential to offer timely movement guidance or torque assistance to users [
4
].
Recent advancements in portable walking-assist exoskeletons demonstrate considerable
potential in improving the wearers’ mobility, for instance, by reducing metabolic costs [
5
–
8
]
or muscular activity [
9
,
10
]. Simultaneously, mechanical adaptations, e.g., serial elastic
actuator [
11
] and quasi-direct driver [
12
], along with cognitive adaptations, such as admit-
tance control [
13
], have been extensively researched to foster improved human–exoskeleton
interactions. Despite the innovations, determining the exertion of forces and torques on the
human body and understanding and predicting individual adaptation or response remain
Actuators 2024,13, 54. https://doi.org/10.3390/act13020054 https://www.mdpi.com/journal/actuators
Actuators 2024,13, 54 2 of 16
unresolved challenges [
14
,
15
]. Even for an exoskeleton that applies assistive torques to a
single joint during highly cyclic motions such as walking, forecasting variations in an indi-
vidual’s muscle recruitment and movement patterns poses challenges [
16
]. Enhancements
in somatic sensation due to optimized torque configurations based on human-in-the-loop
(HIL) optimization have made significant strides [
6
,
8
], thereby garnering increased atten-
tion for walking-assist exoskeletons. Beyond metabolic costs and muscular activity, user
preferences [
17
], transferred work [
9
], and several other physical and physiological signals
are also considered cost functions in HIL optimization. However, during the acceptance of
the assistance of an exoskeleton, users’ neuromuscular control might undergo alterations.
Understanding how users adapt their neuromuscular control in response to external assis-
tance is crucial for guiding the high-level control of wearable devices [
18
]. In other words,
considering the higher-level control of users’ neuromuscular patterns is more likely to
achieve a more “natural” gait.
The hypothesis of muscle synergy was initially proposed by Bernstein [
19
] as an
appropriate way to explain the mechanisms of the motor nervous system under multi-
degree-of-freedom control. This hypothesis suggests that the central nervous system (CNS)
tends to combine muscle groups within low-dimensional modules to achieve efficient and
precise motor control, thereby reducing the complexity of CNS control over the muscu-
loskeletal system [
20
]. Characteristics of muscle synergy have been observed in various
movements, such as walking [
21
], running [
22
], and turning [
23
]. Muscle synergy has
been employed to investigate the impact of exoskeletons on users, providing guidance for
the design of these devices. Exoskeletons can alter muscle recruitment patterns during
walking and other tasks. Li et al. [
24
] quantitatively analyzed the muscle synergy of the
lower limbs during walking with hip-knee exoskeleton assistance. The results showed
significant alterations in muscle synergy when there was assistance from the exoskeleton.
Liu et al. [
25
] used muscle synergy to identify transitions between different movement
patterns, which are crucial for adjusting exoskeleton control to ensure safe and comfortable
support for users. Steele et al. [
18
] demonstrated the feasibility of exoskeleton application
in rehabilitation by comparing synergy weights and activations of ankle exoskeletons under
different torque and operation modes. Current research primarily focuses on variations in
muscle synergy under various exoskeleton assist modes. However, the means of adjusting
assistive torque configurations to influence user muscle synergy remains unknown. This
work proposes a similarity index to quantify the degree of similarity between muscle
synergy patterns, based on which a muscle synergy-based human–exoskeleton interaction
optimized hip exoskeleton assistive torque configuration is designed and experimentally
validated to guide “natural” walking.
The objective of this study is to establish a HIL optimization framework grounded in
muscle synergy for exoskeleton control. This framework aims to offer personalized torque
assistance while concurrently minimizing the exertion involved in walking. The baseline
muscle synergy, i.e., synergy during free “natural” walking of one subject, can be referred
to as a synergy dataset that could be developed by researchers based on statistical analysis.
Our contributions are outlined as follows:
On the one hand, we devised a muscle synergy similarity index to quantify the
resemblance of synergy between walking with and without exoskeleton assistance. On
the other hand, we proposed a human–exoskeleton interaction optimized assistive torque
configuration based on muscle synergy and experimentally validated it on a portable
hip exoskeleton. Under the personalized optimal torque configurations provided by hip
exoskeleton assistance, an enhancement in muscle synergy similarity during walking
was observed. To our knowledge, this is the first work to use muscle synergy as a cost
function in HIL optimization for assistive torque generation and to investigate it. The
findings of this study will contribute to future human–machine collaboration optimization
and a better understanding of human neuromuscular control responses under external
robotic assistance.
Actuators 2024,13, 54 3 of 16
In the remaining sections of this paper, Section 2introduces the experimental platform
and the proposed HIL optimization framework, and Section 3presents the experimental
results of walking with exoskeletal assistance and detailed data analysis. The discussion
and conclusions are presented in Sections 4and 5, respectively.
2. Methods
2.1. System Overview
The total mass of the hip exoskeleton was 4.95 kg, comprising the powered joint
module, interface modules (cuffs and frames), and electrical components (control board
and battery), as illustrated in Figure 1A [
26
]. It was secured to the human body by straps,
fixing it around the waist and thighs. The waist’s fixation structure serves to secure the
exoskeleton and motor positions, while the leg’s structure connects with the leg link, secur-
ing it to the wearer’s thigh for torque transmission. The leg link is constructed from carbon
fiber, aiming to minimize the exoskeleton’s weight while ensuring torque transmission,
with personalized adjustments in link length to accommodate varying body sizes.
Actuators 2024, 13, x FOR PEER REVIEW 3 of 16
In the remaining sections of this paper, Section 2 introduces the experimental plat-
form and the proposed HIL optimization framework, and Section 3 presents the experi-
mental results of walking with exoskeletal assistance and detailed data analysis. The dis-
cussion and conclusions are presented in Section 4 and Section 5, respectively.
2. Methods
2.1. System Overview
The total mass of the hip exoskeleton was 4.95 kg, comprising the powered joint mod-
ule, interface modules (cuffs and frames), and electrical components (control board and
battery), as illustrated in Figure 1A [26]. It was secured to the human body by straps, fixing
it around the waist and thighs. The waist’s fixation structure serves to secure the exoskel-
eton and motor positions, while the leg’s structure connects with the leg link, securing it
to the wearer’s thigh for torque transmission. The leg link is constructed from carbon fiber,
aiming to minimize the exoskeleton’s weight while ensuring torque transmission, with
personalized adjustments in link length to accommodate varying body sizes.
Figure 1. Exoskeleton and sEMG sensors: (A). Hip exoskeleton; (B). sEMG sensors attached to the
muscles (RF: rectus femoris, VM: vastus medialis, VL: vastus lateralis, BF: biceps femoris, GL: glu-
teus maximus, GM: gastrocnemius, TA: tibialis anterior, SOL: soleus); (C). sEMG sensors.
The powered joint module consisted of servo motors (Maxon EC 90 Flat, Maxon Mo-
tor Co., Ltd., Sachseln, Switzerland), customized planetary gear reducers (31.6:1), and mo-
tor drivers (ESCON 50/5 module, Maxon Motor Co., Ltd., Switzerland) positioned on the
left and right sides of the hips, providing assistance torque ranging from 0 to 23 Nm for
hip flexion and extension. Two inertial measurement units (IMU) (Shenzhen Witte Intel-
ligent Technology Co., Ltd., Shenzhen, China), depicted in Figure 1A, were mounted on
the front of both thighs, measuring hip flexion/extension angles and velocities. Surface
electromyography (sEMG) signal sensors (Customized by College of Biomedical Engi-
neering & Instrument Science, Zhejiang University) were used in the experiments, with a
sampling frequency of 2 kHz [27]. Data of real-time transmission to the computer were
achieved using WIFI. Multiple threads were employed to receive data from several sen-
sors, parsing the communication data to obtain multi-channel sensor data. As shown in
Figure 1B, sEMG sensors were used to capture sEMG signals from eight muscle sites on
the left leg of the human body, including rectus femoris (RF), vastus medialis (VM), vastus
lateralis (VL), biceps femoris (BF), gluteus maximus (GL), gastrocnemius (GM), tibialis
anterior (TA), and soleus (SOL).
Figure 1. Exoskeleton and sEMG sensors: (A). Hip exoskeleton; (B). sEMG sensors attached to the
muscles (RF: rectus femoris, VM: vastus medialis, VL: vastus lateralis, BF: biceps femoris, GL: gluteus
maximus, GM: gastrocnemius, TA: tibialis anterior, SOL: soleus); (C). sEMG sensors.
The powered joint module consisted of servo motors (Maxon EC 90 Flat, Maxon
Motor Co., Ltd., Sachseln, Switzerland), customized planetary gear reducers (31.6:1), and
motor drivers (ESCON 50/5 module, Maxon Motor Co., Ltd., Switzerland) positioned
on the left and right sides of the hips, providing assistance torque ranging from 0 to
23 Nm
for hip flexion and extension. Two inertial measurement units (IMU) (Shenzhen
Witte Intelligent Technology Co., Ltd., Shenzhen, China), depicted in Figure 1A, were
mounted on the front of both thighs, measuring hip flexion/extension angles and velocities.
Surface electromyography (sEMG) signal sensors (Customized by College of Biomedical
Engineering & Instrument Science, Zhejiang University) were used in the experiments,
with a sampling frequency of 2 kHz [
27
]. Data of real-time transmission to the computer
were achieved using WIFI. Multiple threads were employed to receive data from several
sensors, parsing the communication data to obtain multi-channel sensor data. As shown in
Figure 1B, sEMG sensors were used to capture sEMG signals from eight muscle sites on
the left leg of the human body, including rectus femoris (RF), vastus medialis (VM), vastus
lateralis (VL), biceps femoris (BF), gluteus maximus (GL), gastrocnemius (GM), tibialis
anterior (TA), and soleus (SOL).
2.2. Human-in-the-Loop Optimization Platform
The experimental setup comprises sEMG sensors, a hip exoskeleton, and an upper-
level computer housing a human-in-the-loop optimization algorithm. The workflow of the
experimental setup is illustrated in Figure 2[26].
Actuators 2024,13, 54 4 of 16
Actuators 2024, 13, x FOR PEER REVIEW 4 of 16
2.2. Human-in-the-Loop Optimization Platform
The experimental setup comprises sEMG sensors, a hip exoskeleton, and an upper-
level computer housing a human-in-the-loop optimization algorithm. The workflow of
the experimental setup is illustrated in Figure 2 [26].
Figure 2. Human-in-the-loop optimization platform: (A). The subject wearing the hip exoskeleton;
(B). Angle and sEMG signal sampling; (C). Signals segmentation and normalization; (D). NMF-
based synergy calculation. (E). Synergy similarity calculation. (F). HIL optimization based on syn-
ergy similarity; (G). Hermite interpolation for assist torque profile generation.
The sEMG signals and lower-limb kinematic data were transmitted to the upper-level
computer via WIFI and Bluetooth, respectively, where all data processing tasks were con-
ducted using MATLAB (MatlabR2020b, MathWorks Inc., Natick, MA, USA). Referring to
the data preprocessing method of Zhang et al. [28], parameters were adjusted to prepro-
cess the original sEMG signals. This involved second-order 20–300 Hz Butterworth band-
pass filtering, full-wave rectification, and second-order 10 Hz Butterworth low-pass filter-
ing. Subsequently, using kinematic data, such as angles and phases, collected by IMUs,
the sEMG signals were segmented based on gait cycles and processed through an opti-
mized Non-negative Matrix Factorization (NMF) method to compute muscle synergy,
which is discussed further in Section 2.3. Finally, various gait evaluation parameters were
obtained through a comparison with predefined standard assessment metrics in HIL op-
timization. The mean of the evaluation parameters obtained from multiple gait calcula-
tions was considered the evaluation metric for this iteration. In Python, using HIL opti-
mization, iterative calculations yielded eight key parameters for the assistive configura-
tion file. In Section 2.5, these parameters were then used to generate the assistive config-
uration file for torque control.
2.3. Evaluation Index Based on Muscle Synergy
In this study, the process of analyzing synergies based on human experimental data
is illustrated in Figure 3. The raw sEMG signal during walking (Figure 3A) underwent
filtering (Figure 3B), and after gait segmentation and normalization, the preprocessed
sEMG signal was obtained (Figure 3C), NMF was employed for extracting muscle syner-
gies, ensuring the non-negative attributes of the decomposition matrix [29,30], thereby
granting it greater physical interpretability compared with alternative decomposition
methodologies. The expression is as follows:
𝑴× =𝑾× ×𝑯× +𝑬×, (1)
Figure 2. Human-in-the-loop optimization platform: (A). The subject wearing the hip exoskeleton;
(B). Angle and sEMG signal sampling; (C). Signals segmentation and normalization; (D). NMF-based
synergy calculation. (E). Synergy similarity calculation. (F). HIL optimization based on synergy
similarity; (G). Hermite interpolation for assist torque profile generation.
The sEMG signals and lower-limb kinematic data were transmitted to the upper-
level computer via WIFI and Bluetooth, respectively, where all data processing tasks were
conducted using MATLAB (MatlabR2020b, MathWorks Inc., Natick, MA, USA). Referring to
the data preprocessing method of Zhang et al. [
28
], parameters were adjusted to preprocess
the original sEMG signals. This involved second-order 20–300 Hz Butterworth bandpass
filtering, full-wave rectification, and second-order 10 Hz Butterworth low-pass filtering.
Subsequently, using kinematic data, such as angles and phases, collected by IMUs, the
sEMG signals were segmented based on gait cycles and processed through an optimized
Non-negative Matrix Factorization (NMF) method to compute muscle synergy, which is
discussed further in Section 2.3. Finally, various gait evaluation parameters were obtained
through a comparison with predefined standard assessment metrics in HIL optimization.
The mean of the evaluation parameters obtained from multiple gait calculations was
considered the evaluation metric for this iteration. In Python, using HIL optimization,
iterative calculations yielded eight key parameters for the assistive configuration file. In
Section 2.5, these parameters were then used to generate the assistive configuration file for
torque control.
2.3. Evaluation Index Based on Muscle Synergy
In this study, the process of analyzing synergies based on human experimental data
is illustrated in Figure 3. The raw sEMG signal during walking (Figure 3A) underwent
filtering (Figure 3B), and after gait segmentation and normalization, the preprocessed
sEMG signal was obtained (Figure 3C), NMF was employed for extracting muscle synergies,
ensuring the non-negative attributes of the decomposition matrix [
29
,
30
], thereby granting
it greater physical interpretability compared with alternative decomposition methodologies.
The expression is as follows:
Mm×n=Wm×k×Hk×n+Em×n, (1)
where
Mm×n
incorporates sEMG signals sampled across all eight channels (where
m
denotes
the number of muscles, and
n
signifies the time frames used to extract muscle synergies).
Wm×k
signifies the muscle weight distribution, reflecting the relative contributions of
each muscle to the synergies, while
Hk×n
embodies the activation profiles, elucidating the
temporal dynamics of muscle synergy activation throughout the gait cycle.
Em×n
denotes
the reconstruction error, depicting the disparity between the reconstructed and original
sEMG signals. The number of muscle synergies,
k
, is determined using the activation profile
Actuators 2024,13, 54 5 of 16
matrix variability accounted for (VAF) criterion [
31
], which is defined as the reconstruction
error over the original sEMG signals:
VAF = (1−∑n
i=1∑n
j=0Ei,j2
∑n
i=1∑n
j=1Mi,j2)(2)
In accordance with previous studies, the quantity of muscular synergy effects is determined
by two conditions: when adding new muscular synergy effects, the total VAF exceeds
90%, while each additional synergy effect does not exceed 5% [
32
]. In the present study,
as illustrated in Figure 4, when the number of synergies was 3, the VAF exceeded 90%,
meeting the first condition. However, when the number of synergies increased to 4, the
rise in VAF surpassed 5%. Ultimately, the number of synergies was determined to be 4,
indicating that four sets of synergies could describe the muscular activity of the lower limbs
during human walking.
Actuators 2024, 13, x FOR PEER REVIEW 5 of 16
where 𝑴× incorporates sEMG signals sampled across all eight channels (where 𝑚 de-
notes the number of muscles, and 𝑛 signifies the time frames used to extract muscle syn-
ergies). 𝑾× signifies the muscle weight distribution, reflecting the relative contribu-
tions of each muscle to the synergies, while 𝑯× embodies the activation profiles, eluci-
dating the temporal dynamics of muscle synergy activation throughout the gait cycle.
𝑬× denotes the reconstruction error, depicting the disparity between the reconstructed
and original sEMG signals. The number of muscle synergies, 𝑘, is determined using the
activation profile matrix variability accounted for (VAF) criterion [31], which is defined as
the reconstruction error over the original sEMG signals:
𝑉𝐴𝐹=(1− ∑
∑
𝑬,
∑
∑
𝑴,) (2)
In accordance with previous studies, the quantity of muscular synergy effects is deter-
mined by two conditions: when adding new muscular synergy effects, the total VAF ex-
ceeds 90%, while each additional synergy effect does not exceed 5% [32]. In the present
study, as illustrated in Figure 4, when the number of synergies was 3, the VAF exceeded
90%, meeting the first condition. However, when the number of synergies increased to 4,
the rise in VAF surpassed 5%. Ultimately, the number of synergies was determined to be
4, indicating that four sets of synergies could describe the muscular activity of the lower
limbs during human walking.
Figure 3. The flow chart of muscle synergy analysis. (A). Raw sEMG signals; (B). Filtered sEMG
signals; (C). The mean value (black line) of preprocessed sEMG signals of different gaits (gray line);
(D). Muscle synergy weights.
Figure 3. The flow chart of muscle synergy analysis. (A). Raw sEMG signals; (B). Filtered sEMG
signals; (C). The mean value (black line) of preprocessed sEMG signals of different gaits (gray line);
(D). Muscle synergy weights.
Actuators 2024, 13, x FOR PEER REVIEW 6 of 16
Figure 4. Total variability accounted for (VAF) versus the number of synergies based on NMF. NE
and Exos stand for walking trials without and with exoskeleton, respectively. VAF gradually in-
creased, with an increase in the number of synergies.
To quantify the similarity among human muscle synergies across different condi-
tions, an evaluative measure termed 𝜂 was introduced. 𝜂 was calculated as the summa-
tion of the product between the proportion of the s-th synergy and its corresponding Pear-
son correlation coefficient 𝑟: 𝜂=∑
∑
, (3)
where 𝑐 signifies the correlation coefficient between the s-th synergy and its matched
reference synergy, and 𝑟 denotes the activation ratio of the s-th synergy vector. 𝑐 is de-
fined as follows: 𝑐=(1−∑
∑
(𝑴,𝑹,
)
∑
∑
𝑴,)×100%, (4)
where 𝑹×
is the product of the k-th column vector of 𝑾 and the k-th row vector of 𝑯.
𝑹×
=𝑾×
×𝑾×
(5)
2.4. Assistive Torque Profile Generation
The assistive torque configuration was generated using a parameterized approach
that allows for online adjustments. The gait cycle serves as the horizontal axis, while the
assistive torque represents the vertical axis, with the moment of maximum hip flexion
angle set as the starting point of a gait cycle. Previous studies configured the assistive
torque within a cycle using four parameter points [33]. However, in the normal human
walking process, hip joint flexion and extension torques are not symmetrical. To ensure
accuracy in calculating the assistive torque profile and convergence speed, this study de-
termined the assistive torque configuration for each gait cycle using eight parameters.
These parameters included peak torque during flexion 𝜏 and extension 𝜏, peak time of
flexion 𝜑 and extension 𝜑, rise time of flexion 𝜑 and extension 𝜑, and fall time of
flexion 𝜑 and extension 𝜑.
The segmented cubic Hermite interpolation polynomial was employed to interpolate
each profile, thereby linking each parameter to generate the desired torque assistance pro-
file s. The interpolation polynomials can be represented as follows:
𝑆(𝑥)=𝑦𝛼(𝑥)+𝑦𝛼(𝑥)+𝑦
𝛽(𝑥)+𝑦
𝛽(𝑥), (6)
where 𝛼(𝑥), 𝛼(𝑥), 𝛽(𝑥), and 𝛽(𝑥) represent the basis functions of interpolation.
The expressions for these basis functions are as follows:
Figure 4. Total variability accounted for (VAF) versus the number of synergies based on NMF. NE and
Exos stand for walking trials without and with exoskeleton, respectively. VAF gradually increased,
with an increase in the number of synergies.
Actuators 2024,13, 54 6 of 16
To quantify the similarity among human muscle synergies across different conditions,
an evaluative measure termed
η
was introduced.
η
was calculated as the summation of
the product between the proportion of the s-th synergy and its corresponding Pearson
correlation coefficient rs:
η=∑k
s=1csrs
∑k
s=1cs
, (3)
where
cs
signifies the correlation coefficient between the s-th synergy and its matched
reference synergy, and
rs
denotes the activation ratio of the s-th synergy vector.
cs
is defined
as follows:
cs= (1−
∑m
i=1∑n
j=1Mi,j−Rs
i,j)2
∑m
i=1∑n
j=1Mi,j2)×100%, (4)
where Rk
m×nis the product of the k-th column vector of Wand the k-th row vector of H.
Rs
m×n=Ws
m×1×Ws
1×n(5)
2.4. Assistive Torque Profile Generation
The assistive torque configuration was generated using a parameterized approach
that allows for online adjustments. The gait cycle serves as the horizontal axis, while the
assistive torque represents the vertical axis, with the moment of maximum hip flexion angle
set as the starting point of a gait cycle. Previous studies configured the assistive torque
within a cycle using four parameter points [
33
]. However, in the normal human walking
process, hip joint flexion and extension torques are not symmetrical. To ensure accuracy in
calculating the assistive torque profile and convergence speed, this study determined the
assistive torque configuration for each gait cycle using eight parameters. These parameters
included peak torque during flexion
τp
and extension
τn
, peak time of flexion
φp
and
extension
φn
, rise time of flexion
φpr
and extension
φnr
, and fall time of flexion
φpr
and
extension φnr.
The segmented cubic Hermite interpolation polynomial was employed to interpolate
each profile, thereby linking each parameter to generate the desired torque assistance
profile s. The interpolation polynomials can be represented as follows:
S(x)=ykαk(x)+yk+1αk+1(x)+y’
kβk(x)+y’
k+1βk+1(x), (6)
where
αk(x)
,
αk+1(x)
,
βk(x)
, and
βk+1(x)
represent the basis functions of interpolation. The
expressions for these basis functions are as follows:
αk(x)=1+2x−xk
xk+1−xk x−xk+1
xk−xk+12
αk+1(x)=1+2x−xk+1
xk−xk+1 x−xk
xk+1−xk2
βk(x)=(x−xk)x−xk+1
xk−xk+12
βk+1(x)=(x−xk+1)x−xk
xk+1−xk2
(7)
For the sake of simplifying the function expressions, we defined the following:
hk=xk+1−xk(8)
Substituting Equations (7) and (8) with Equation (6) yields the cubic polynomial of
this segment of the profile:
S(x)=1−2x−xk
−hkx−xk+1
−hk2yk+1−2x−xk+1
hkx−xk
hk2yk+1
+(x−xk)x−xk+1
−hk2y’
k+(x−xk+1)x−xk
hk2y’
k+1
(9)
Actuators 2024,13, 54 7 of 16
In this study, the expression can be simplified since the derivatives at all connecting
points of the profile s are zero:
S(x)=(hk+2(x−xk))(x−xk+1)2yk
h3
k
+(hk−2(x−xk+1))(x−xk)2yk+1
h3
k
(10)
Considering safety and comfort during assistance, these parameters are only allowed
to vary within predefined suitable ranges established through prior testing:
τp=[0 Nm, 10 Nm]
φp=[20%, 30%]
φpr =[10%, 20%]
φpr =[10%, 20%]
τn=[−10 Nm,0 Nm]
φn=[20%, 30%]
φnr =[10%, 20%]
φnr =[10%, 20%]
(11)
Figure 5illustrates the interpolation of the configuration files and spatial coverage
achieved by generating different parameters’ configuration files.
Actuators 2024, 13, x FOR PEER REVIEW 7 of 16
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
𝛼(𝑥)=1+2 𝑥−𝑥
𝑥−𝑥𝑥−𝑥
𝑥−𝑥
𝛼(𝑥)=1+2𝑥−𝑥
𝑥−𝑥 𝑥−𝑥
𝑥−𝑥
𝛽(𝑥)=(𝑥−𝑥)𝑥−𝑥
𝑥−𝑥
𝛽(𝑥)=(𝑥−𝑥)𝑥−𝑥
𝑥−𝑥
(7)
For the sake of simplifying the function expressions, we defined the following:
ℎ=𝑥−𝑥 (8)
Substituting Equations (7) and (8) with Equation (6) yields the cubic polynomial of
this segment of the profile:
𝑆(𝑥)=1−2𝑥−𝑥
−ℎ𝑥−𝑥
−ℎ𝑦+1−2𝑥−𝑥
ℎ𝑥−𝑥
ℎ𝑦
+(𝑥−𝑥)𝑥−𝑥
−ℎ𝑦
+(𝑥−𝑥)𝑥−𝑥
ℎ𝑦
(9)
In this study, the expression can be simplified since the derivatives at all connecting
points of the profile s are zero:
𝑆(𝑥)=ℎ+2(𝑥−𝑥)(𝑥−𝑥)𝑦
ℎ
+ℎ−2(𝑥−𝑥)(𝑥−𝑥)𝑦
ℎ
(10)
Considering safety and comfort during assistance, these parameters are only allowed
to vary within predefined suitable ranges established through prior testing:
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
𝜏=0 𝑁𝑚, 10 𝑁𝑚
𝜑=20%,30%
𝜑 =10%,20%
𝜑 =10%,20%
𝜏=−10 𝑁𝑚, 0𝑁 𝑚
𝜑=20%,30%
𝜑 =10%,20%
𝜑 =10%,20%
(11)
Figure 5 illustrates the interpolation of the configuration files and spatial coverage
achieved by generating different parameters’ configuration files.
Figure 5. Parametric assistance profile generation, including assistance profile, control parameters,
and the space that profiles can traverse.
2.5. Iterative Process for Optimizing Assistive Torque
The optimization process of HIL employs the Bayesian optimization algorithm [
34
],
achieving a twofold increase in convergence speed compared with traditional gradient
descent methods [35]. Table 1presents the pseudocode for the optimization process.
Table 1. Optimization process for assistive torque based on the Bayesian optimization algorithm.
Iterative Process for Optimizing Assistive Torque
Input:F,S,A,M
D←Initial Assistive Profile Parameters (F,S)
Fori←Nto Tdo
p(y|x,D)←Fit Assistive Profile—Human Musculoskeletal Synergy Similarity Model (M,D);
xi←argmax
x∈SA(x,p(y|x,D)); // Determine the next sampling point based on the maximum
value of the acquisition function
yi←f(xi); // Measure sEMG to calculate lower limb muscular synergy
Similarity
D←D∪(xi,yi);
end for
Actuators 2024,13, 54 8 of 16
The variables involved include
x
as the parameters of the exoskeleton assistive torque
profile, which is presented in the form
hτp,φp,φpr,φp f ,τn,φn,φnr,φn f i
, and
y
as the op-
timization target, representing the similarity of human muscle synergy.
D
stands for the
dataset,
F
denotes the model for the assistance profile and human muscle synergy similar-
ity,
S
represents the hyperparameter search space,
A
signifies the acquisition function,
M
represents the model fitted to dataset
D
,
N
is the initial number of sampling points, and
Trefers to the number of algorithm iterations. This approach aims to explore the region
where the maximum value of the function is expected. After a certain number of iterations,
the assistance torque profile parameter values corresponding to the highest attained muscle
synergy similarity evaluation index represent the optimal torque.
2.6. Testing Protocol
Six healthy male participants took part in this experiment, and their basic characteris-
tics are presented in Table 2. The experiment comprised two sessions.
Table 2. Participants information.
Subject Height (cm) Weight (kg) Age (Year) BMI (kg/m2)
S1 168 64 22 22.7
S2 173 73 24 24.4
S3 173 62 22 20.7
S4 182 71 23 21.4
S5 178 61 24 19.3
S6 170 70 35 24.2
Mean ±std 174 ±4.7 66.8 ±4.7 25.0 ±4.5 22.1 ±1.9
The first session involved the HIL optimization experiment. Initially, participants
walked for 90 s on a treadmill at a speed of 1 m/s without wearing the exoskeleton (NE)
to establish a baseline using data collected from sEMG sensors and IMUs. Subsequently,
participants walked on the treadmill at a speed of 1 m/s while wearing the exoskeleton,
and tests were randomly conducted according to the conditions outlined in Table 3. Be-
fore the experiment, participants had a period of time to acclimatize to the exoskeleton,
ensuring no resistance to the assistive torque provided by the exoskeleton during walking.
Based on prior experimental findings and testing experiences, each iteration was set for a
duration of 90 s [
32
], with the evaluation metrics calculated using the data from the last
30 s
(approximately 20 steps). Additionally, the data processing and synergy analysis using
NMF took approximately 3 s, which was compensated for at the beginning of each iteration
and did not impact the experimental results. To mitigate the impact of muscle fatigue
during human walking on the produced sEMG signals, participants rested for a certain
period after completing 10 cycles of optimization, equivalent to 15 min of walking. To
expedite the exploration process, the experiment commenced with four sets of different
predefined parameters.
Table 3. The assist torque profile used in the experiment.
No. Walking Speed Assist Torque Profile
1 1 m/s Zero Torque (ZT)
2 1 m/s Predefined Profile (PD)
3 1 m/s Optimal result of Bayesian Optimization (BO1)
4 1 m/s Sub-optimal result of Bayesian Optimization (BO2)
The second session involved the evaluation of muscle synergy optimization, scheduled
concurrently with the HIL optimization experiment, aiming to minimize the influence of
additional factors by requiring participants to maintain a lifestyle consistent with the day
of the HIL optimization experiment. Before the experiment, participants had a period to
Actuators 2024,13, 54 9 of 16
adapt to the exoskeleton. To mitigate the impact of different sensor placements on the
experimental results, the surface sEMG sensors were positioned as close as possible to their
locations in the previous experiment. Initially, participants walked freely on a treadmill at
a speed of 1 m/s in NE mode, and the collected sEMG data were used to calculate a new
synergy baseline. Subsequently, participants wore the exoskeleton and were subjected to
randomized tests according to the conditions outlined in Table 3[
26
]. Finally, participants
walked freely on the treadmill at a speed of 1 m/s in NE mode as well, and these data
were compared with the baseline data obtained at the beginning of the experiment. The
initial and final 10-step data from each experimental condition were removed, and the
remaining sEMG data from the gait cycles were used for synergy analysis and similarity
calculations. Statistical analysis was conducted using the similarity data obtained from
multiple gait cycles.
3. Results
3.1. Human-in-the-Loop Optimization Experiment
The process of HIL optimization based on muscular synergy is depicted in Figure 6.
Figure 6A delineates the specifics of the iterative refinement of eight parameters.
Figure 6B
exhibits auxiliary configuration files generated for each iteration, illustrating the explo-
ration of the optimal auxiliary torque configuration throughout the process. The muscular
synergy-based evaluation metrics computed in each iteration are presented in Figure 6C.
Taking Subject 2 as an example, a total of 64 iterations were conducted, and at the 35th
iteration, the evaluation metric reached its highest value, stabilizing thereafter, thereby
establishing it as the optimal parameter set. The optimal auxiliary parameters were de-
termined to be
hτp,φp,φpr,φp f ,τn,φn,φnr,φn f i
= [2.38, 0.28, 0.19, 0.16, 4.85, 0.76, 0.16,
0.13], with a synergy similarity of 0.84. Of the six participants, the peak assist torque
value of Subject 2 was the lowest. During the experiment, when assist torque increased,
the gait of Subject 2 slightly changed, leading to an unnatural feeling during walking;
thus, the synergy similarity would decrease. After HIL optimization, he felt more natural
during the low-assist peak torque pattern. In contrast, the subsequent analysis identified a
sub-optimal parameter set at the 53rd iteration, yielding
hτp,φp,φpr,φp f ,τn,φn,φnr,φn f i
= [4.43, 0.29, 0.17, 0.18, 3.46, 0.73, 0.18, 0.13], with a synergy similarity of 0.82. The itera-
tive optimization results of the assistive parameters for the six subjects are presented in
Table 4. The difference between the similarity achieved by all subjects under the optimal
assistive torque configuration and the similarity under the sub-optimal configuration was
less than 0.015, indicating convergence, despite Subjects 3 and 5 reaching only 35 and
48 iterations, respectively. Compared with the optimal strategy, their similarity decrease
was merely 1.33% and 2.17%, respectively. The average similarities for the optimal group
(BO1) and the sub-optimal group (BO2) of the six subjects were 0.83
±
0.09 and 0.81
±
0.08
(mean ±std), respectively.
Subjects 4 and 5 showcased notable synergy similarities when using hip exoskeleton
assistance, reaching 0.91 and 0.92, respectively, in the BO1 mode and surpassing 0.9 even
in the BO2 mode. This theoretically suggests a minimal impact of exoskeleton assistance
on the muscular synergy structure under the current iterative torque configuration and
aligns closely with the “natural” walking of these subjects. S2 and S6 maintained synergy
optimization configurations around 0.84. However, Subjects 1 and 3 exhibited lower
synergy similarities after assistive optimization, with S1 registering the lowest at 0.69 and
0.69 under the two parameter sets, indicating a substantial impact on the muscular synergy
structure despite being optimal assistive parameter configurations. Comprehensive torque
configuration data for each iteration are provided in Appendix A.
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53rd iteration, yielding 𝜏,𝜑,𝜑,𝜑,𝜏,𝜑,𝜑,𝜑 = [4.43, 0.29, 0.17, 0.18, 3.46, 0.73,
0.18, 0.13], with a synergy similarity of 0.82. The iterative optimization results of the assistive
parameters for the six subjects are presented in Table 4. The difference between the similar-
ity achieved by all subjects under the optimal assistive torque configuration and the simi-
larity under the sub-optimal configuration was less than 0.015, indicating convergence, de-
spite Subjects 3 and 5 reaching only 35 and 48 iterations, respectively. Compared with the
optimal strategy, their similarity decrease was merely 1.33% and 2.17%, respectively. The
average similarities for the optimal group (BO1) and the sub-optimal group (BO2) of the six
subjects were 0.83 ± 0.09 and 0.81 ± 0.08 (mean ± std), respectively.
Figure 6. Human-in-the-loop optimization results: (A) Variation of each parameter with iteration.
(B) The assistive torque profiles; (C) Evaluation index calculated in each iteration and optimization
of evaluation index.
Table 4. Iterations of Assistive Parameters to Optimal and Sub-optimal for Six Participants.
Subject Total
Iterations
Iterations of
Optimal
Iterations of
Sub-Optimal Optimal Sub-Optimal
S1 64 50 1 0.69 0.69
S2 64 35 53 0.84 0.82
S3 35 10 13 0.75 0.74
S4 64 27 26 0.91 0.90
S5 48 4 34 0.92 0.90
S6 64 42 46 0.84 0.83
Mean ± std 56.5 ± 11.3 28.0 ± 16.5 28.8 ± 18.0 0.83 ± 0.09 0.81 ± 0.08
Subjects 4 and 5 showcased notable synergy similarities when using hip exoskeleton
assistance, reaching 0.91 and 0.92, respectively, in the BO1 mode and surpassing 0.9 even
in the BO2 mode. This theoretically suggests a minimal impact of exoskeleton assistance
on the muscular synergy structure under the current iterative torque configuration and
aligns closely with the “natural” walking of these subjects. S2 and S6 maintained synergy
optimization configurations around 0.84. However, Subjects 1 and 3 exhibited lower syn-
ergy similarities after assistive optimization, with S1 registering the lowest at 0.69 and 0.69
under the two parameter sets, indicating a substantial impact on the muscular synergy
structure despite being optimal assistive parameter configurations. Comprehensive
torque configuration data for each iteration are provided in Appendix A.
Figure 6. Human-in-the-loop optimization results: (A) Variation of each parameter with iteration.
(B) The
assistive torque profiles; (C) Evaluation index calculated in each iteration and optimization of
evaluation index.
Table 4. Iterations of Assistive Parameters to Optimal and Sub-optimal for Six Participants.
Subject Total
Iterations
Iterations of
Optimal
Iterations of
Sub-Optimal Optimal Sub-Optimal
S1 64 50 1 0.69 0.69
S2 64 35 53 0.84 0.82
S3 35 10 13 0.75 0.74
S4 64 27 26 0.91 0.90
S5 48 4 34 0.92 0.90
S6 64 42 46 0.84 0.83
Mean ±std 56.5 ±11.3 28.0 ±16.5 28.8 ±18.0 0.83 ±0.09 0.81 ±0.08
3.2. Optimized Muscle Synergy
Figure 7displays the validation outcomes of the HIL optimization experiments.
Figure 7A
conducts a significant analysis of the experimental similarity among the six
subjects, while Figure 7B presents the mean similarity results and their distribution. With
the exception of Subject 4, the muscular synergy similarity indices in the two sets of NE
mode for all subjects were highest when compared with their own, averaging above 0.83.
This suggests that human muscle coordination remains generally consistent in the short
term after assistance, making free walking a viable reference. The similarity index for
the ZT group was notably lower, averaging only 0.68
±
0.03. Comparatively, the mean
similarity index in the BO1 mode exhibited an increase of approximately 18.0%, averaging
0.80
±
0.04. Similarly, the BO2 mode demonstrated a 12.3% increase, averaging
0.76 ±0.03.
In contrast to the PD mode, the similarity indices increased by 6.3% and 1.2% for optimal
and sub-optimal parameters, respectively. Moreover, when compared with free walking,
the mean similarity index of the BO1 mode decreased by only 3.6%, demonstrating an
80.3% improvement over the ZT mode and a 61.5% enhancement over the PD mode, in-
dicating a better alignment of the iteratively optimized assistive torque profile with the
human muscular synergy structure. Furthermore, the similarity indices obtained from
the validation experiments closely mirrored the average optimal and sub-optimal sim-
ilarity indices obtained from the HIL optimization experiments, differing by only 2.5%
and 6.2%, respectively, signifying good overall stability in the assistive torque parameter
configurations derived from the HIL optimization process.
Actuators 2024,13, 54 11 of 16
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3.2. Optimized Muscle Synergy
Figure 7 displays the validation outcomes of the HIL optimization experiments. Fig-
ure 7A conducts a significant analysis of the experimental similarity among the six sub-
jects, while Figure 7B presents the mean similarity results and their distribution. With the
exception of Subject 4, the muscular synergy similarity indices in the two sets of NE mode
for all subjects were highest when compared with their own, averaging above 0.83. This
suggests that human muscle coordination remains generally consistent in the short term
after assistance, making free walking a viable reference. The similarity index for the ZT
group was notably lower, averaging only 0.68 ± 0.03. Comparatively, the mean similarity
index in the BO1 mode exhibited an increase of approximately 18.0%, averaging 0.80 ±
0.04. Similarly, the BO2 mode demonstrated a 12.3% increase, averaging 0.76 ± 0.03. In
contrast to the PD mode, the similarity indices increased by 6.3% and 1.2% for optimal
and sub-optimal parameters, respectively. Moreover, when compared with free walking,
the mean similarity index of the BO1 mode decreased by only 3.6%, demonstrating an
80.3% improvement over the ZT mode and a 61.5% enhancement over the PD mode, in-
dicating a better alignment of the iteratively optimized assistive torque profile with the
human muscular synergy structure. Furthermore, the similarity indices obtained from the
validation experiments closely mirrored the average optimal and sub-optimal similarity
indices obtained from the HIL optimization experiments, differing by only 2.5% and 6.2%,
respectively, signifying good overall stability in the assistive torque parameter configura-
tions derived from the HIL optimization process.
Figure 7. Evaluation of muscle synergy optimization: (A) Analysis of similarity indices under vari-
ous individual conditions and their significance differences. Significance levels are denoted by
Figure 7. Evaluation of muscle synergy optimization: (A) Analysis of similarity indices under various
individual conditions and their significance differences. Significance levels are denoted by asterisks:
ns (p
≥
0.05), * (p< 0.05), ** (p< 0.01), *** (p< 0.001), and **** (p< 0.0001); (B) Average similarity
results among the subjects.
In Figure 7A, aligned with the HIL optimization experiments at an individual level, S4
and S5 exhibited relatively high similarity, while S1 and S6 demonstrated comparatively
lower similarity. In the validation experiment results, a significant difference analysis was
conducted between the similarity of each subject under the optimal assistive configuration
and under other conditions, demonstrating significant differences for p< 0.05. Apart from
Subject 6, there were almost no significant differences between the optimal and sub-optimal
configurations in terms of similarity values, indicating the convergence of the HIL iterative
optimization. It is worth noting that S6 did not perform well in the BO2 mode during the
evaluation session. This may be caused by a difference in sEMG sensor location between
the optimization session and the evaluation session, which could lead to a difference in
sEMG signals, making the synergy similarity of BO2 poor. S1, S2, S4, and S5 showed
significantly lower similarity in the BO1 mode compared with free walking. Despite S3
and S6 exhibiting significant differences in free walking, their overall similarity was higher
than that of the other groups. This suggests that HIL optimization enables subjects to walk
more naturally under the primary assistance of an exoskeleton. For each subject, synergy
similarities of the two NE modes were different to a certain extent. In particular, for S1,
S3, S4, and S5, the differences were negligible. This confirmed that the synergy in this
experiment was relatively stable.
Actuators 2024,13, 54 12 of 16
4. Discussion
4.1. Strategy for Torque Generation
While torque assistance based on a database seems straightforward [
34
,
35
], its stability
in accommodating external condition changes is poor. Mere scaling of biomechanical
joint torques proves insufficient in achieving convincing torque assistance. Ding et al.
parameterized the timing and values of assistive torque peaks, showcasing the superiority
of their approach [
35
]. Collins et al. introduced metabolism as a feedback signal, creating
cubic spline profiles for torque assistance based on four configuration parameters: rise
time, fall time, peak time, and peak torque. This significantly reduced human energy
consumption, albeit with a longer optimization convergence time [
28
]. In our previous
research, we employed sEMG as a metabolic representation for feedback, using Bayesian
and Covariance Matrix Adaptive Evolution Strategy to optimize the same four parameter
configurations and enhance the convergence speed of the optimal torque profile [
33
].
Considering potential differences in amplitude and phase between torque profiles during
flexion and extension, this study expanded the torque configuration parameters to eight and
used Hermite interpolation to generate assistive profiles. Despite several trials, participants
did not notably report increased comfort compared with the assistive profiles used in the
previous study. Nevertheless, in this study, the optimal similarity index surpassed the
predefined similarity, indicating that the four parameters—rise time, fall time, peak time,
and peak torque—adequately characterized the torque assistance profile.
4.2. Evaluation Index Based on Muscle Synergy
The NMF algorithm exhibits greater robustness in extracting muscle synergies com-
pared with ICA and FA [
36
,
37
]. Collins et al. employed NMF to compute synergistic effects
in each experiment, requiring 64 min of walking time to optimize four control parameters
based on metabolic consumption [
18
]. In this study, the algorithm was refined by imple-
menting a faster updating iterative method using the projected gradient approach for NMF.
Additionally, sEMG was employed to swiftly characterize metabolism as the evaluation
function for the HIL optimization process. These optimizations allowed for convergence in
a shorter duration (less than 1 h) despite doubling the number of parameter configurations.
To quantify the similarity of human muscle synergy under different conditions, a novel
evaluation index,
η
, was introduced, providing a more detailed representation than the
evaluation metrics proposed by Collins et al. [18].
4.3. The Experiments and Evaluation of Human-in-the-Loop Optimization
The preliminary analysis of both the HIL optimization and validation experiments
was conducted to obtain the aforementioned results. The similarity under the ZT condition
appears to be consistently lower, potentially due to the exoskeleton acting as an additional
load on the human body in this mode. Moreover, achieving an ideal zero torque mode
without torque sensors is challenging due to the reliance on exoskeleton-driven joint friction
compensation. Consequently, walking experiments under this condition altered the human
body’s synergy pattern, resulting in decreased similarity.
S1, S2, S4, and S5 displayed significant differences between BO1 and ZT, indicating
that the synergy structures of these subjects are susceptible to external factors (unpowered
exoskeletons here) but can be restored to high synergy similarity by wearing exoskeletons,
highlighting the superiority of HIL optimization. In contrast, the similarity of S3 and S6
under the optimal configuration did not significantly differ from ZT and closely resembled
PD, potentially linked to the high sensitivity of locomotion control to external robotic
assistance of these subjects.
Subject 4 achieved the highest similarity of 0.9054 under the optimal assistive parame-
ters, close to the similarity in the HIL optimization experiments and significantly higher
than the unassisted mode. Even the sub-optimal assistive profile reached a similarity
of 0.8899, both surpassing the similarity in free walking. However, this contradicts the
theoretical similarity of S4 being highest in free walking, possibly due to the minimal torque
Actuators 2024,13, 54 13 of 16
variations throughout the optimization process (with a maximum peak of only 3.6744 Nm
with optimal configuration, in Table A1, and 3.19 Nm with sub-optimal configuration, in
Table A2). This suggests that Subject 4 may be more accustomed to walking with lower
torque, resulting in minimal or even improved impact on the muscular synergy structure.
Subject 2 did not achieve the highest muscular synergy similarity with the optimal torque
configuration, showing a decrease of 2.2% compared with the sub-optimal configuration,
despite generally having the highest similarity with the BO1 mode across subjects after ex-
cluding the NE group. This discrepancy might be attributed to oscillations in the muscular
synergy similarity under a particular assistive torque configuration observed during the
experiment and arising from unstable physiological signals, specifically sEMG. Subject 6
displayed significantly lower similarity under the sub-optimal assistive configuration than
ZT and PD, potentially due to the stochastic nature of collaborative computation during
the closed-loop optimization experiment, resulting in some outlier data.
Table 5illustrates a comparison of HIL optimizations for exoskeleton assist torque
profile generation. Both the Collins group [
28
] and the Walsh group [
6
] used metabolic
cost as a cost function, which would take 2~4 min to estimate the metabolic cost for each
iteration. Our former work adopted muscle activity as a cost function to reduce muscle
effort during exoskeleton-assisted walking, making a reduction of rectus femoris muscle
activation to 33.5%. The presented work used muscle synergy as a cost function, which
reduced time cost per iteration to 30 s and sped up the whole HIL optimization. Meanwhile,
an average synergy similarity increase of 18.3% compared with ZT mode shows a promising
solution for natural robotic walking assistance.
Table 5. Comparison of HIL optimizations for exoskeletons.
Collins Group [28] Walsh Group [6] Former Work [33] This Work
No. of para. 4 3 8 8
Time/iter. (s) 120 120 25 30
Target index metabolic cost metabolic cost muscle activity synergy
CF reduction 24.2% 9.3% 33.5% 18.3%
4.4. Study Limitations
One major limitation of this study is that, despite the positive findings obtained from
the participation of six volunteers with homogeneous gender and age in the experiment,
the inclusion of more subjects, especially female participants and participants with a wider
range of ages, is necessary to establish more detailed patterns. Moreover, due to the
prolonged duration of HIL optimization, some participants experienced sweating while
wearing the exoskeleton, which affected the quality of the sEMG signal to some extent,
although this phenomenon was observed only during the experiment of S6. Structural
and algorithmic optimizations of the exoskeleton are needed to improve breathability and
shorten convergence time. Moreover, free walking trials should be conducted instead of
treadmill walking with a constant speed since, in real life, humans would constantly adjust
their walking speed and perform more natural and relaxed musculoskeletal states.
5. Conclusions
This study proposes a quantification method for muscular synergy similarity, investi-
gating the degree of similarity in muscular synergy during walking both with and without
exoskeleton assistance. Moreover, based on this quantification, it introduces a human–
machine collaborative optimization framework grounded in muscular synergy to generate
personalized torque assistance configurations validated on a portable hip exoskeleton
platform. The research findings indicate that incorporating quantified human physiological
signals and neuromuscular control into robot feedback control and subsequently obtain-
ing optimal torque configurations through iterative optimization significantly enhance
muscular synergy during exoskeleton-assisted walking. This achievement allows for a
more rational and “natural” torque assistance, presenting a novel, feasible approach for
exoskeleton-assisted strategies.
Actuators 2024,13, 54 14 of 16
Author Contributions: Conceptualization, D.L. and Y.M.; methodology, Y.M. and D.L.; software, L.Y.;
validation, D.L., L.G. and W.Y.; formal analysis, L.G. and Z.Y.; investigation, W.Y.; resources, L.Y.; data
curation, Z.Y.; writing—original draft preparation, Y.M. and D.L.; writing—review and editing, Y.M.,
D.L. and W.Y; visualization, L.Y.; supervision, C.Y.; project administration, W.Y.; funding acquisition,
W.Y. and C.Y. All authors have read and agreed to the published version of the manuscript.
Funding: This work was funded by the Key Research and Development Project of Zhejiang Province
(No. 2022C03029), in part by the Ningbo Public Welfare Project (No. 2021S082), in part by the
Scientific Research Fund of Zhejiang Provincial Education Department (No. Y202353520), in part by
the Scientific Research Fund of Zhejiang University (No. XY2023046), and in part by the Zhejiang
Public Welfare Project (No. LTGY23H170002).
Data Availability Statement: All data for this study have been included in this paper, and there are
no other unpublished data.
Acknowledgments: We appreciate the invaluable contributions of the volunteers involved in dataset
preparation and our experimental work.
Conflicts of Interest: The authors declare no conflicts of interest.
Appendix A
This section provides a detailed account of the optimal and sub-optimal torque as-
sistance profiles obtained from the HIL optimization for six participants. S1, S2, and S4
exhibited peak values (
τp
and
τn
) lower than 5 Nm for both optimal and sub-optimal
torques. This indicates a preference for lower levels of assistive torque among these three
participants. Conversely, S3, S5, and S6 demonstrated a preference for higher levels of
assistance, with Subject 3 notably displaying a peak extension torque (
τn
) at the hip joint of
9.5760 Nm.
Table A1. Optimal assistive parameters of six participants.
Subjects φpτpφpr φpf φnτnφnr φnf
S1 0.25 4.54 Nm 0.17 0.14 0.73 3.42 Nm 0.10 0.14
S2 0.28 2.38 Nm 0.19 0.16 0.76 4.85 Nm 0.16 0.13
S3 0.24 7.85 Nm 0.16 0.13 0.79 9.58 Nm 0.18 0.13
S4 0.30 3.67 Nm 0.10 0.18 0.80 2.40 Nm 0.20 0.10
S5 0.25 7.95 Nm 0.15 0.15 0.75 6.81 Nm 0.15 0.15
S6 0.25 6.28 Nm 0.18 0.15 0.75 5.98 Nm 0.19 0.17
Table A2. Sub-Optimal assistive parameters of six participants.
Subjects φpτpφpr φpf φnτnφnr φnf
S1 0.25 4.54 Nm 0.15 0.15 0.75 3.41 Nm 0.15 0.15
S2 0.29 4.25 Nm 0.17 0.18 0.73 3.46 Nm 0.18 0.13
S3 0.25 5.13 Nm 0.20 0.19 0.71 6.83 Nm 0.14 0.18
S4 0.25 3.19 Nm 0.14 0.13 0.75 3.37 Nm 0.16 0.17
S5 0.28 9.27 Nm 0.12 0.19 0.78 6.64 Nm 0.18 0.10
S6 0.26 2.79 Nm 0.13 0.13 0.72 9.75 Nm 0.14 0.14
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