Single-input adaptive fuzzy sliding mode control of the lower extremity exoskeleton based on human–robot interaction

Abstract

This article introduces a human–robot interaction controller toward the lower extremity exoskeleton whose aim is to improve the tracking performance and drive the exoskeleton to shadow the wearer with less interaction force. To acquire the motion intention of the wearer, two subsystems are designed: the first is to infer the wearer is in which phase based on floor reaction force detected by a multi-sensor system installed in the sole, and the second is to infer the motion velocity based on the multi-axis force sensor and admittance model. An improved single-input fuzzy sliding mode controller is designed, and the adaptive switching controller is combined to promote the tracking performance considering system uncertainties. Adaptation laws are designed based on the Lyapunov stability theorem. Therefore, the stability of the single-input adaptive fuzzy sliding mode control can be guaranteed. Finally, the proposed methods are applied to the lower extremity exoskeleton, especially in the swing phase. Its effectiveness is validated by comparative experiments.

Full text

Special Issue Article
Advances in Mechanical Engineering
2017, Vol. 9(2) 1–9
ÓThe Author(s) 2017
DOI: 10.1177/1687814016686665
journals.sagepub.com/home/ade
Single-input adaptive fuzzy sliding
mode control of the lower extremity
exoskeleton based on human–robot
interaction
Xinglai Jin
1
, Shiqiang Zhu
1
, Xiaocong Zhu
1
, Qingcheng Chen
2
and
Xuequn Zhang
1
Abstract
This article introduces a human–robot interaction controller toward the lower extremity exoskeleton whose aim is to
improve the tracking performance and drive the exoskeleton to shadow the wearer with less interaction force. To
acquire the motion intention of the wearer, two subsystems are designed: the first is to infer the wearer is in which
phase based on floor reaction force detected by a multi-sensor system installed in the sole, and the second is to infer
the motion velocity based on the multi-axis force sensor and admittance model. An improved single-input fuzzy sliding
mode controller is designed, and the adaptive switching controller is combined to promote the tracking performance
considering system uncertainties. Adaptation laws are designed based on the Lyapunov stability theorem. Therefore, the
stability of the single-input adaptive fuzzy sliding mode control can be guaranteed. Finally, the proposed methods are
applied to the lower extremity exoskeleton, especially in the swing phase. Its effectiveness is validated by comparative
experiments.
Keywords
Human–robot interaction, lower extremity exoskeleton, admittance model, floor reaction force, single-input adaptive
fuzzy sliding mode control
Date received: 16 October 2016; accepted: 2 December 2016
Academic Editor: Zheng Chen
Introduction
Lower extremity exoskeleton is a typical kind of inte-
grated human–robot system which is superior to any
autonomous robotic system in unstructured environ-
ments that demand significant adaptation.
1
It attempts
to combine the strength and endurance of modern
robotics with the intelligence and agility of a human
operator.
2,3
Obviously, it has many potential advan-
tages, such as allowing the user to carry more loads
and to traverse irregular terrain surfaces. So, the lower
extremity exoskeleton can help individuals employed in
particular recreational, occupational, and military
activities who often carry heavy loads; it can help fire
fighters and other emergency personnel to carry oxygen
tanks and other equipment; and it can assist impaired
man to walk.
4
In one word, the exoskeleton benefits
from the combination of the wearer intellect and
machine strength.
1
State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang
University, Hangzhou, China
2
Shanghai Institute of Special Equipment Inspection and Technical
Research, Shanghai, China
Corresponding author:
Xinglai Jin, State Key Laboratory of Fluid Power and Mechatronic
Systems, Zhejiang University, Hangzhou 310027, China.
Email: 21125069@zju.edu.cn
Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License
(http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without
further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/
open-access-at-sage).

To provide effective physical support according to
each wearer’s intention, it is necessary to strongly focus
on the control system. An important challenge in the
exoskeleton system is the ability to sense wearer’s
motion intention in time.
5
According to the measure-
ment of the human–robot interaction (HRI), exoskele-
ton system can be divided into cognitive human–robot
interaction (cHRI)-based system and physical human–
robot interaction (pHRI)-based system.
6
The cHRI-
based system measures the electric signals from the
central nervous system (CNS) to the musculoskeletal
system of the human and subsequently uses them as
input information for the robot controller, such as
HAL.
7
However, the pHRI-based system measures
change of force or position that result from the motions
of the human musculoskeletal system and uses them as
input information for the robot controller, such as
BLEEX and HEXAR.
8,9
The voluntary controller of
HAL is developed which uses the wearer’s bioelectrical
signals. These signals are based on the myoelectric sig-
nal detected on the skin surface of the supporting mus-
cles.
10,11
Kwon and Kim
5
proposed an upper limb
motion estimation method using surface electromyo-
graphy (SEMG) and joint angular velocities based on
artificial neural network. Although the EMG sensor is
generally used to measure muscular activity signals, it
is disadvantageous in which it must be directly attached
to the skin; it requires high sampling frequencies for
signal collection; and it is difficult to quantify the sig-
nals.
12,13
As a novel control method, sensitivity amplifi-
cation control (SAC) has been designed in BLEEX.
14
It
needs no direct measurements from the wearer or the
human–machine interface. However, the system perfor-
mance is proportional to the precision of the exoskele-
ton dynamic model which is difficult to depict.
15
Measuring the human–machine interaction force is an
intuitionistic and widely used method. Yu et al.
16
have
designed a model-free proportional–integral–derivative
(PID)-type admittance control for an upper limb exos-
keleton to infer the desired trajectory from the human–
machine interaction force. To generate the wearer’s
intension from the interaction, Lee et al.
6
have adopted
virtual impedance control to model the human–
machine interaction. Lee et al.
17
also adopted a PI con-
troller to simplify the system controller.
As far as we know, no current technologies can
directly measure and extract the human intentions.
However, we can infer human intentions from their
appearance or motion. In this article, we will design an
intention estimator based on floor reaction force (FRF)
and force sensor which detects the HRI force.
11,18
Impedance control and admittance control are widely
used in modeling the human–machine interaction rela-
tionship.
16,19
However, the former cannot guarantee
zero contact force which may cause wearer discomfort.
So, the latter is adopted to infer the wearer’s motion
intention. Sliding mode control has been used in many
kinds of electromechanical systems, such as linear
motor,
20,21
hydraulic actuator,
22,23
active suspension
systems,
24,25
and teleoperation systems.
26,27
Finally, to
design a controller which is independent of mathemati-
cal model and is easy to accomplish, a direct adaptive
fuzzy sliding mode controller based on single input is
proposed and a new nonlinear integral sliding surface is
introduced to deal with the system chattering. Because
the swing phase occupies the 40% of one cycle, effec-
tiveness of the proposed algorithms is verified by
experiments in swing phase.
A brief overview of the article is given as follows: in
section ‘‘Architecture,’’ the lower extremity exoskeleton
is introduced which is developed to enhance the wearer
strength. In section ‘‘Acquisition of human intent,’’ the
pHRI system is established which is essential to acquire
human intent. The relationship between the walking
phase and FRF is verified by experiment. In section
‘‘Human–machine interaction model,’’ the admittance
is recommended to model HRI and the parameters can
be designed based on human impedance properties. In
section ‘‘Controller design,’’ a novel direct adaptive
fuzzy sliding mode controller based on single input is
proposed. To reduce the complexity of the fuzzy rule
and decrease the input variables of the fuzzy controller,
traditional sliding mode surface s(t) and its derivative
_
s(t) are replaced by sliding mode switching surface s(t).
The adaptive regulation law is designed to enhance the
robustness of the system by the Lyapunov theory. In
section ‘‘Experiment,’’ comparative experiments are
performed to verify the effectiveness of the proposed
controller. Section ‘‘Conclusion’’ concludes this article.
Architecture
The lower extremity exoskeleton is shown in Figure 1,
and it comprised two powered anthropomorphic legs, a
pair of shoes, and a spine which is designed to carry
heavy load. The structure of the exoskeleton belongs to
pseudo-anthropomorphic architecture to ensure maxi-
mum safety and minimum collisions with the environ-
ment and operator which means the structure of
exoskeleton is designed by reference to human legs, but
does not include every degree of freedom (DOF) of
human legs. Overall, the exoskeleton has seven distinct
DOFs per leg: 3 DOFs at the hip, 1 DOF at the knee,
and 3 DOFs at the ankle. Since the human leg and exos-
keleton leg kinematics are merely similar, the wearer and
exoskeleton are rigidly connected at the feet, shanks,
and upper body. It is unnecessary to actuate all DOFs
because most of the power needed for normal walking is
in the sagittal plane according to some researches. So,
only the freedoms of hip and knee in sagittal plane are
actuated by hydraulic. The ankle joint is passive, and
the springs are placed to help the foot reset.
2Advances in Mechanical Engineering

Acquisition of human intent
An entire walking gait cycle can be divided into the
swing phase and the standing phase. Researches have
shown that the leg undergoes large motions but it needs
relatively small torques which only supports its own
weight in the swing phase; the leg executes a small
motion but supports the entire torso and payload in
the standing phase. Thus, most of the lower extremity
exoskeletons have designed hybrid control, such as
BLEEX and HAL.
28,29
We have uncoupled the acquisi-
tion system of human intent into two subsystems. The
first subsystem is designed to detect the walking phase,
and the second subsystem is designed to detect the HRI
force. Conventional researches on human transient
walking have made clear that a FRF shift in a sole to
one leg is a prior motion to a walk.
7
So, if we can sense
the FRF shift induced by the wearer’s intention, we
can infer the leg is in which phase. According to some
researches, the foot pressures on the front and rear
parts are larger than other parts. To detect the FRF in
a sole, we have designed the exoskeleton foot and its
sensor system as shown in Figure 2.
The FlexiForce A401 force-sensing resistor (FSR)
developed by Tekscan is selected because of its compact
size and wide measurement range. To ensure the output
voltage has linear relation with the pressure, an analog
circuit has been designed and the wearer can change the
maximum measurable force. Obviously, the output vol-
tage of the FSR can reflect FRF and the output voltage
variation can reflect the pressure change. Considering
the complexity of the application environment of the
exoskeleton, Ribbon Switch developed by AbleNet is
selected as footswitch which is a moisture-resistant
switch that is activated by moving the 4 30.3-in or
10.2 35-cm activation surface in either direction with
4 oz or 110 g of force. The controller records the foots-
witch’s status, and the current and previous values of
the FSR can infer the four possible states of each leg
including stance, swing, heel-strike, and toe-off. The
rules to infer the leg is in which phase have been formu-
lated and are listed as follows. The leg is considered to
be in heel-strike mode when foot contact condition is
satisfied
fh p =0\fh c.0\ft c =0\SWh=0ð1Þ
where fh p and fh c are the previous and current FRFs
of the foot heel side, respectively; ft c is the current
FRF of the foot toe side; and SWhis the state of the
footswitch of the foot heel side. It means before the
Figure 1. Lower extremity exoskeleton.
Figure 2. Exoskeleton foot and its sensor system:
(a) force-sensing resistor and (b) footswitch.
Jin et al. 3

footswitch of the foot heel side is on, the FRF of the
foot heel side will have a sudden change when the leg is
in the heel-strike mode. The leg is considered to be in
stance mode when foot contact condition is satisfied
fh c.a\SWh=1\SWt=1\ft c .bð2Þ
where SWtis the state of the footswitch of the foot toe
side. In addition, aand bare the thresholds to detect
whether the foot heel side and toe side are on the floor.
These values can be set by the wearer. The leg is consid-
ered to be in toe-off mode when foot contact condition
is satisfied
fh c =0\SWh=0\SWt=1\ft c\gð3Þ
where ft p is the previous FRF of the foot toe side, and
gis the threshold of the FRF and it is used to judge
whether the foot is going to leave the floor. The leg is
considered to be in swing mode when foot contact con-
dition is satisfied
fh c =0\SWh=0\ft c =0\SWt=0ð4Þ
As a sole prototype, we installed one FSR and two
footswitches. Figure 3 shows the experiment results. We
have identified the four walking phases even if the FRF
of the foot front part is omitted.
In Figure 3, we have defined that number 0 repre-
sents swing mode, number 1 represents heel-strike
mode, number 2 represents stance mode, and number 3
represents toe-off mode. Based on the first subsystem,
we have inferred the walking phase of the human–
machine system. To activate the exoskeleton to shadow
the wearer with minimum interaction force in swing
phase, the second subsystem needs to detect the interac-
tion force.
Human–machine interaction model
As a pHRI-based exoskeleton, force sensor is a com-
monly used method to detect the HRI force. Figure 4
illustrates that the interaction forces are generated from
the connected interface where two 6-axis force sensors
are installed and the pHRI is modeled as an admittance
relationship.
Many studies have modeled the HRI as an impe-
dance model because the impedance control is an excel-
lent controller in hybrid control of position and
force.
30,31
Theoretically, the input of the impedance is
position and its output is force. Admittance control is
always seen as the inverse of impedance control while
its input is force and output is velocity or position
which is more fit to this system. So, we apply the
admittance relation in exoskeleton system as follows
_
ud(s)= Mas+Ba+Da
s

f(s)ð5Þ
where f(s) represents the HRI force detected by the
force sensor; Ma,Ba, and Daare the parameters of the
admittance model.
16
Each joint of the lower limb can be modeled as a
second-order biomechanical system in the musculoske-
letal system.
32
Lee has defined the human impedance
model as follows
H(s)= 1
Mhs2+Bhs+Kh
ð6Þ
where Mh,Bh, and Khare the virtual impedance
parameters.
In order to find the value of parameters, experiment
can be designed to measure and analyze the motions of
a human leg using the joint angle and forward kine-
matics. Relationship has been deduced as follows
33
Ma=100MhBh
Kh
,Ba=10Bh,Da=4Kh
3ð7Þ
To improve the operation convenience, we have
designed input interface which permits the wearer to
Figure 3. (a) State of the footswitch installed in toe and heel
part, (b) voltage of the FSR installed in toe part, and (c) state of
the corresponding leg.
Figure 4. pHRI model using the admittance relationship.
4Advances in Mechanical Engineering

adjust the admittance parameters according to wearing
feeling.
Thus far, the block diagram to control the swing leg
of the lower extremity exoskeleton can be designed as
shown in Figure 5.
Controller design
Considering the model error and uncertainties of the
hydraulic exoskeleton system, the dynamics model of
the swing leg can be written as
(M+DM)€
u+(C+DC)_
u+(G+DG)=t+dð8Þ
where M2R232is the symmetric positive-definite iner-
tia matrix; C2R232represents the centripetal Coriolis
matrix; G2R2stands for the gravitational vector;
t2R2is the joint torques; DM,DC, and DGrepresent
the model error; u2R2is the position of the joints; and
drepresents the unknown disturbance.
Because of the difficulties in deriving an exact math-
ematical model and the complexity of traditional fuzzy
controller, we have combined the single-input fuzzy
logic controller and adaptive fuzzy sliding mode con-
troller.
34,35
An assumption should be pointed out that
the desired trajectory of every joint of the lower extre-
mity exoskeleton has been inferred. The tracking error
can be defined as follows
e=uudð9Þ
where udis the desired trajectory.
In traditional sliding mode control, the first step is to
select a sliding surface. We have used an improved slid-
ing surface as follows
s=ce +_
e+kSat(se)ð10Þ
where c=diag½c1 cn,ci.0, and k=diag
½k1 kn,ki.0, are the design parameters which
satisfy Hurwitz.
Obiviously, atan(x) is a nonlinear saturation func-
tion, so another class of quasi-potential function is
introduced in equation (11) and its derivative is written
in equation (12), where smeans an adjustable
parameter
Sat(sx)=(sx)atan sxðÞ
1
2ln 1+(sx)2

ð11Þ
sat(sx) = atan(sx)ð12Þ
The number of input variables directly decides the
complexity of a convertional fuzzy system. As the
dimension and complexity of a system increase, the size
of the rule base increases exponentially. By defining the
sliding surface as the input variable of fuzzy rules, the
fuzzy system is simplified effectively and is easier to
implement. The fuzzy rules are given in the following
form
36
Rule 1 : IF sis Fi
s, THEN uis aið13Þ
where ai,i=1,2,... is the singleton control actions
and Fi
sis the label of fuzzy set. The defuzzification of
the control output is accomplished by the method of
center of gravity
tfz =P
m
i=1
aimi
P
m
i=1
mi
ð14Þ
where miis the membership grade of the ith rule.
From the sliding surface equations (10)–(12) and the
dynamic model equation (8), we can infer
_
s=c_
e+€
e+katan(se)ð15Þ
Tradition sliding mode control law can be designed
as
t=M€
ud+c_
e+katan(se)

+C_
u+G^
fð16Þ
Since the system dynamics and the disturbance are
unknown, the traditional control law is difficult to
implement. So, the adaptive fuzzy sliding mode control
(AFSMC) is proposed. The control law in equation
(14) has been improved by choosing aias an adjustable
parameter. Equation (14) can be written as
$GPLWWD
QFH
PRGHO
,QYHUVH
MDFRELDQ
PDWUL[
*HQHUDWH
MRLQW
DQJOHV
&RQWU
ROOHU 5RERW
:HDUHU
θ
&
d
θ
τ
v,
θ θ
&
0
d
f=
hr
f
−
+
++
−
−
Figure 5. Block diagram of the controller for human–robot interaction exoskeleton.
Jin et al. 5

tfz(s,a)=aTzð17Þ
where a=½a1,a2,...,amTand z=½z1,z2,...,zmTis
a regressive vector and is defined as zi=miPm
i=1mi.
There exists an optimal fuzzy control system to
approximate tbased on the fuzzy approximation the-
orem. It is listed as
t=t
fz(s,a)+e=aTz+eð18Þ
where eis the approximation error and is assumed to
satisfy e
jj
\E. Now, we use a fuzzy control system to
approximate t
fz(s,a). Thus, we obtain
^tfz(s,^a)=t
fz(s,a)=^aTzð19Þ
where ^ais the estimator of a.
Considering the approximation error, switching con-
trol is introduced to compensate it. Finally, the control
law is listed in equation (20) and the block diagram of
AFSMC is depicted in Figure 6
t=^tfz(s,^a)+tsc (s)ð20Þ
From equation (18), we can get
~tfz =^tfz t=^tfz t
fz eð21Þ
To infer the control equation, we define ~a=^aa.
Then, equation (21) can be simplified as
~tfz =~aTzeð22Þ
Combining equations (15) and (16), we can obtain
t=M€
ud_
s+€
e

+C_
u+G^
f=tM_
sð23Þ
Substituting equation (20) into equation (23), a new
equation can be written as
_
s=M1(^tfz +tsc t)=M1(~aTz+tsc e)ð24Þ
Thus, the Lyapunov function can be designed as
V(s,~a)= 1
2s2+M1
2l~aT~að25Þ
where lis a positive constant.
Differentiating equation (25) and using equation
(24), we obtain
_
V(s,~a)=s_
s+M1
l~aT_
~a
=sM1(~aTz+tsc e)+ M1
l~aT_
~a
=M1~aTsz+
_
~a
l

+sM1(tsc e)
ð26Þ
To achieve _
V(s,~a)0, so that the system is stable,
the adaptive law and the switching controller are
designed as
_
~a=_
^a=lszð27Þ
tsc =Esgn(s)ð28Þ
where E=max(e
jj
)+d,d.0, and sgn( ) is a sign
function.
Then, equation (26) can be written as
_
V(s,~a)= M1Es
jj
M1es
M1Es
jj
+M1e
jj
s
jj
=M1(Eejj)sjj
0
ð29Þ
By Barbalat’s lemma, we can conclude that s!0as
t!‘.
In equation (28), it is difficult to measure the approx-
imation error E. If a too large Ehas been determined, a
large chattering may take place. To decrease the chat-
ting problem, we adopt fuzzy switching method
37
to
approximate eand the approximation of Eis written as
^
E=^
bTfð30Þ
Figure 6. Illustrative diagram of the single-input adaptive fuzzy sliding mode control.
6Advances in Mechanical Engineering

where fis the fuzzy vector and ^
badjusts with adaptive
law.
To obtain the adaptive law, we define that bis the
best value and ~
b=b^
bis the estimated error. A
Lyapunov function is defined as
V2(s,~a,~
b)= 1
2s2+M1
2l1
~aT~a+M1
2l2
~
bT~
bð31Þ
where l2.0. Differentiating equation (31) and using
equation (27)
_
V2(s,~a,~
b)=sM1(^
Esgn(s)e)+ M1
l2
~
bT_
~
b
=M1^
Es
jj
es+1
l2f(^
EE)_
~
b

ð32Þ
For achieving _
V20, the adaptive law is designed as
_
^
b=l2fsð33Þ
Equation (32) can be written as
_
V2(s,~a,~
b)=M1^
Es
jj
es+^
EE

s
jj

M1(e
jjs
jj
Es
jj
)
=M1(Ee
jj
)s
jj
0
ð34Þ
By Barbalat’s lemma, we can conclude that s!0as
t!‘. By applying this estimation law, the AFSMC
system with a simplified fuzzy switching can be guaran-
teed to be stable.
Experiment
To verify the effectiveness of the sensor system in the
sole and the proposed algorithm to estimate human
intentions based on admittance and single-input adap-
tive fuzzy sliding mode control (S-AFSMC), we per-
form experiment on the swing leg of the lower extremity
exoskeleton as shown in Figure 1. The lower extremity
exoskeleton is a typical HRI system. So, the wearer will
first move his leg as the desired trajectory in the swing
phase. The controller needs to infer the wearer motion
intention and moves the swing leg to shadow the
motion in time.
As shown in Figure 5, the human motion intention
is inferred based on the force sensor, so the HRI force
is measured by the six-axis pressure sensor. The con-
troller proposed in this article aims to minimize the
force vector and finally reduced the force vector to
zero. Thus we can justify the system’s performance by
the amplitude of the interaction force vector. We com-
pared the proposed controller with the conventional
fuzzy sliding mode control (FSMC). The parameters in
equations (15) and (20) are given as:
c=5,k=15,s=1:5,l=30, and l2=0:5:
As a human–machine system, our aim is to let the
swing leg shadow the wearer. So the tracking error and
interaction force are chosen to justify the controller.
Figure 7 shows the results of the experiment.
Through Figure 7, it is obvious that the new control-
ler has less interaction force and better tracking perfor-
mance. The switching control law can compensate the
difference between the fuzzy controller and the desired
controller. The adaptive law of the switching gain can
decrease the chattering problem. The interaction force
is obtained by force sensor installed between wearer
and exoskeleton and the tracking error is calculated by
admittance model and joint encoders. To evaluate the
performance of the controller, we have adopted two
evaluating indicator: the first is the root-mean-square
(RMS) residuals and the second is the maximum abso-
lute value which are defined as
Figure 7. (a) Interaction force along the X axis in S-AFSMC and FSMC; (b) Interaction force along the Y axis in INSM and CSM
controller; (c) Tracking error of the hip joint in S-AFSMC and FSMC; (d) Tracking error of the knee joint in S-AFSMC and FSMC.
Jin et al. 7

eRMS =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
NX
N
i=1
e2(i)
v
u
u
t
emax =max
0iNe(i)jjfg
ð35Þ
The evaluation results of the controller performance
are illustrated in Table 1. Obviously, the RMS value
and the maximum value of the two joints gained by
S-AFSMC are smaller than the ones gained by FSMC.
So the wearer needs less power to drive the swing leg
and feels more comfortable by using the S-AFSMC.
Conclusion
In this article, a sensor system to detect the centor of
force is designed in a sole. The estimation algorithm
based on FRF which can reflect wearer’s motion status
is investigated through the walking experiment. This
method can divide walking pace into four modes: heel-
strike mode, stance mode, toe-off mode and swing
mode. Admittance control is adopted to model the
HRI which is normally described by impedance model.
An input interface is designed to improve the wearer’s
feeling which permits the wearer to adjust the admit-
tance parameters. Further, considering the uncertain-
ties of the HRI system and the hydraulic system model,
an S-AFSMC is proposed with a novel nonlinear inte-
gral sliding surface. The whole controller contains
AFSMC and fuzzy switching control. Both adaptation
laws are designed based on Lyapunov stability theo-
rem. Therefore, the stability of the S-AFSMC can be
guaranteed. Finally, the proposed methods in this arti-
cle are verified on the lower extremity exoskeleton,
especially in the swing phase. Experiments prove the
effectiveness and reliability of the proposed controller
compared to traditional fuzzy sliding mode controller.
The wearer feels more comfortable to move the swing
leg. These methods can be applied in other HRI
system.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
article.
Funding
The author(s) disclosed receipt of the following financial sup-
port for the research, authorship, and/or publication of this
article: This research work was supported by the Science
Fund for Creative Research Groups of the National Natural
Science Foundation of China (no. 51521064) and Zhejiang
Provincial Natural Science Foundation of China (no.
LY13E050001), and Hangzhou Civic Significant
Technological Innovation Project of China (no.
20132111A04) and SANLIAN (ShangHai) Group (no.
H20131864).
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