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


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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.
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Special Issue Article
Advances in Mechanical Engineering
2017, Vol. 9(2) 1–9
ÓThe Author(s) 2017
DOI: 10.1177/1687814016686665
Single-input adaptive fuzzy sliding
mode control of the lower extremity
exoskeleton based on human–robot
Xinglai Jin
, Shiqiang Zhu
, Xiaocong Zhu
, Qingcheng Chen
Xuequn Zhang
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
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
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.
It attempts
to combine the strength and endurance of modern
robotics with the intelligence and agility of a human
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.
In one word, the exoskeleton benefits
from the combination of the wearer intellect and
machine strength.
State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang
University, Hangzhou, China
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.
Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License
( 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 (
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.
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.
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
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
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-
Kwon and Kim
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-
As a novel control method, sensitivity amplifi-
cation control (SAC) has been designed in BLEEX.
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.
Measuring the human–machine interaction force is an
intuitionistic and widely used method. Yu et al.
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.
have adopted
virtual impedance control to model the human–
machine interaction. Lee et al.
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.
Impedance control and admittance control are widely
used in modeling the human–machine interaction rela-
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
hydraulic actuator,
active suspension
and teleoperation systems.
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.
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
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.
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
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
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
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
where f(s) represents the HRI force detected by the
force sensor; Ma,Ba, and Daare the parameters of the
admittance model.
Each joint of the lower limb can be modeled as a
second-order biomechanical system in the musculoske-
letal system.
Lee has defined the human impedance
model as follows
H(s)= 1
where Mh,Bh, and Khare the virtual impedance
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
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
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
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-
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
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 +_
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
Sat(sx)=(sx)atan sxðÞ
2ln 1+(sx)2
sat(sx) = 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
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
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
Tradition sliding mode control law can be designed
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
θ θ
Figure 5. Block diagram of the controller for human–robot interaction exoskeleton.
Jin et al. 5
where a=½a1,a2,...,amTand z=½z1,z2,...,zmTis
a regressive vector and is defined as zi=miPm
There exists an optimal fuzzy control system to
approximate tbased on the fuzzy approximation the-
orem. It is listed as
where eis the approximation error and is assumed to
satisfy e
\E. Now, we use a fuzzy control system to
approximate t
fz(s,a). Thus, we obtain
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=^aa.
Then, equation (21) can be simplified as
~tfz =~aTzeð22Þ
Combining equations (15) and (16), we can obtain
Substituting equation (20) into equation (23), a new
equation can be written as
s=M1(^tfz +tsc t)=M1(~aTz+tsc e)ð24Þ
Thus, the Lyapunov function can be designed as
V(s,~a)= 1
where lis a positive constant.
Differentiating equation (25) and using equation
(24), we obtain
=sM1(~aTz+tsc e)+ M1
+sM1(tsc e)
To achieve _
V(s,~a)0, so that the system is stable,
the adaptive law and the switching controller are
designed as
tsc =Esgn(s)ð28Þ
where E=max(e
)+d,d.0, and sgn( ) is a sign
Then, equation (26) can be written as
V(s,~a)= M1Es
By Barbalat’s lemma, we can conclude that s!0as
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
approximate eand the approximation of Eis written as
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
To obtain the adaptive law, we define that bis the
best value and ~
bis the estimated error. A
Lyapunov function is defined as
b)= 1
where l2.0. Differentiating equation (31) and using
equation (27)
Esgn(s)e)+ M1
For achieving _
V20, the adaptive law is designed as
Equation (32) can be written as
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.
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 =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
emax =max
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.
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
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
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.
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... The design scheme of Lower Limb Exoskeleton Rehabilitation Robot (LLERR) has been decoupled by Zhu et al. [44] to analyze the domain parameters (DP) in accordance with Axiomatic Design (AD) theory of customized design scheme. Jin et al. [45] developed a THKAF lower extremity exoskeleton with two anthropomorphic legs, a spine and a pair of shoes. In each leg, the exoskeleton consists of seven DOFs i.e. three DOFs each at hip and ankle with one DOF at the knee. ...
... Rehabilitation exoskeleton Augmentation exoskeleton THKAF ATLAS [38], IHMC Mobility Assist Exoskeleton [39], Mina [12], MINDWALKER [11], eLEGS [16], ANKUR-LL II [51,52], BioComEx [53,54], Soft exosuit [56], ATALANTE [139] Lower Extremity Assistive Exoskeleton by Long et al. [41,42], CUHK-EXO [43], LLERR [44], Lower extremity exoskeleton by Jin et al. [45], XoR [46,47], CPWalker [48][49][50] BLEEX [27,28], BE [30], NAEIES [31], HUALEX [35], Nurse Robot Suit [32], CHPU [36], MIT Exoskeleton [34], HUALEX [35], CHPU [36,37] KAF exoskeleton system by Sawicki and Ferris [75], by Chen et al. [78] No information Content courtesy of Springer Nature, terms of use apply. Rights reserved. ...
... Saito et al. [118] developed a lower limb exoskeleton with a hybrid combination of hydraulic and electric actuators. [10], Mina [12], ReWalk™ [14], ATLAS [15,38], eLEGS [16], Lower Extremity Assistive Exoskeleton by Long et al. [41], CUHK-EXO [43], LLERR [44], Lower extremity exoskeleton by Jin et al. [45], Vanderbilt lower-limb orthosis [69,70], ABLE [72], AIT leg exoskeleton-I [66] HipBot [45], LOPES [18,81], ALEX II [80], One-DOF hip exoskeleton device by Ollinger [82], Parallel hip joint exoskeleton by Yu et al. [83], APO [86], PKO Lai et al. [92], TUPLEE [94], One DOF knee exoskeleton by Ollinger et al. [95], Robotic knee exoskeleton prototype by Gams et al. [96], SCKAFOs [97], Knee orthosis by Karavas et al. [99], EICoSI [102], Stewart-platform-type AFO [105], Honda Walking Assist [141], BELK [142], Keeogo [143], C-Brace [144] Pneumatic Nurse Robot Suit [32] Power assist wear by Sasaki et al. [55] Pneumatic active gait orthosis by Belforte et al. [73] KEA [100] Hydraulic CHPU [36], BLEEX [130] SEAs Lower-limb exoskeleton by Tagliamonte et al. [67] BioComEx [53,54] MINDWALKER [11], IHMC Mobility Assist Exoskeleton [39,120] RoboKnee [93], IPEC AFO [105], ...
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The basic routine movements for elderly people are not easily accessible due to the weak muscles and impaired nerves in their lower extremity. In the last few years, many robotic-based rehabilitation devices, like orthosis and exoskeletons, have been designed and developed by researchers to provide locomotion assistance to support gait behavior and to perform daily activities for elderly people. However, there is still a need for improvement in the design, actuation and control of these devices for making them cost-effective in the worldwide market. In this work, a systematic review is presented on available lower limb orthosis and exoskeleton devices, to date. The devices are broadly reviewed according to joint types, actuation modes and control strategies. Furthermore, tabular comparisons have also been presented with the types and applications of these devices. Finally, the needful improvements for realizing the efficacy of lower limb rehabilitation devices are discussed along with the development stage. This review will help the designers and researchers to develop an efficient robotic device for the rehabilitation of the lower limb.
... To deal with uncertainties, SMC-based techniques utilize two main approaches: disturbance observer-based SMCs [21,42] and intelligent methods, such as fuzzy SMCs [17,29,33,39] and neural network-based SMCs [9,40]. In [21], a disturbance observer-based backstepping sliding mode controller is designed for control of a lower-limb exoskeleton robot. ...
... The simulation results confirm the desirable performance. [17] has proposed an adaptive fuzzy SMC for a lower extremity exoskeleton. Experimental results have demonstrated the effectiveness and reliability of the proposed controller compared to traditional fuzzy sliding mode controller. ...
The paper investigates a novel fractional-order Lyapunov-based robust controller based on a fuzzy neural network (FNN) compensator for exoskeleton robotic systems. First, a finite-time fractional-order nonsingular fast terminal sliding mode control (FONFTSMC) method is designed. Second, a FNN algorithm is constructed to approximate the model uncertainty and external disturbances. Then, finite-time stability of the closed-loop control system is proved using Lyapunov stability theorem and adaptive law is derived through it. The proposed fuzzy neural network-based FONFTSMC (FNN-FONFTSMC) guarantees finite-time convergence and robustness against uncertainties for the exoskeleton robots trajectory tracking. Finally, to illustrate the effectiveness of the proposed control strategy, an upper-limb exoskeleton robot is provided as a case study in rehabilitation. The simulation results confirm the superiority of the proposed control method.
... Not stated [97] Assistive Knee Experiment with healthy subjects Five subjects [98] Not stated Full LEE Simulation Not applicable [99] Assistive Full LEE Experiment with healthy subjects Two subjects [100] Assistive Full LEE Experiment with healthy subjects One subjects [101] Assistive Full LEE Experiment with healthy subjects Not stated [102] Rehabilitation Knee Experiment with healthy subjects One subjects [103] Not stated Hip-knee Simulation Not applicable [104] Not stated Full LEE Simulation Not applicable [105] Rehabilitation and assistive Knee-ankle Simulation Not applicable [106] Not stated Knee Simulation Not applicable [107] Not stated Ankle-shank Simulation Not applicable [108] Assistive Ankle Experiment with healthy subjects Ten subjects [109] Assistive Full LEE Simulation Not applicable [110] Assistive Knee simulation and in experimentation with healthy subjects Six healthy subjects [21] Assistive Knee Experiments Five healthy subjects [111] Assistive Knee Experiments Five healthy subjects [112] Assistive Hip-knee Simulations and experiment One healthy subject [113] Rehabilitation Knee-ankle-foot Experiments Not stated [20] Rehabilitation Hip-knee Simulation Not applicable [114] Assistive Full LEE Simulations and experiment Five healthy subjects [115] Rehabilitation Knee-ankle Simulations and experiment One healthy subject [116] Rehabilitation Full LEE Experiment One healthy subject [117] Rehabilitation Full LEE Experiment One healthy subject [118] Not stated Full LEE Experiment Not stated [119] Rehabilitation and assistive Knee Experiment Three healthy subjects [120] Rehabilitation Knee Experiment Not stated b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g x x x ( 2 0 1 9 ) x x x -x x x optimal control law was found using GA. The closed-loop system was proved to be asymptotically stable using Lyapunov theory. ...
... The only difference is in the controller and the type of exoskeleton. Two parallel control methods for exoskeleton trajectory tracking were reported in [118]. The controllers can deal with human-exoskeleton interaction and disturbances. ...
The lower extremity exoskeletons (LEE) are used as an assistive device for disabled people, rehabilitation for paraplegic, and power augmentation for military or industrial workers. In all the applications of LEE, the dynamic and static balance, prevention of falling, ensuring controller stability and smooth human-exoskeleton interaction are of critical importance for the safety of LEE users. Although numerous studies have been conducted on the balance and stability issues in LEEs, there is yet to be a systematic review that provides a holistic viewpoint and highlights the current research challenges. This paper reviews the advances in the inclusion of falling recognition, balance recovery and stability assurance strategies in the design and application of LEEs. The current status of research on LEEs is presented. It has been found that Zero Moment Point (ZMP), Centre of Mass (CoM) and Extrapolated Center of mass (XCoM) ideas are mostly used for balancing and prevention of falling. In addition, Lyapunov stability criteria are the dominant methods for controller stability confirmation and smooth human-exoskeleton interaction. The challenges and future trend of this domain of research are discussed. Researchers can use this review as a basis to further develop methods for ensuring the safety of LEE’s users.
... To compensate for the exoskeleton model uncertainties, some works propose artificial intelligence using neural networks or fuzzy control as alternatives to reduce the problems of obtaining the parameters of the mathematical model. 68,69 This method is popular for solving problems with many nonlinearities. 70,71 It seeks to obtain the coordination between the mechanical leg and the user, while the interaction is minor. ...
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In the industrial and military sector, work activities are required transporting or supporting heavy loads manually, affecting this the human spinal column due to the weight of the loads or the repetition of this labor. In this regard, the use of force-enhancing exoskeletons is a potential solution to this issue. Therefore, this article summarizes the state of the art in relevant contributions to structural design, control systems, actuators, and performance metrics to evaluate the proper functioning of exoskeletons used for load support and transfer. This is essential to address current and new open problems in these applications, and this includes reducing the metabolic cost and enhancing the loading force in exoskeletons, in which challenges such as structural design and kinetic interactions between the human and the robot are presented. The systematic review of the strategies found in the literature helps addressing these challenges in an orderly way. The proposal of some alternative solutions could help to solving some of the challenges mentioned above, as well as further research to improve the design of these devices is necessary.
... According to Eqs. (14), (22), (24) and (26), the input vector is obtained as Eq. (31): u i (k) = 1 b 0i C 2 z 1 y mi (k + t d ) 1 z 1 ŷ i (k) 2 z 1 u i (k)+C 2 z 1 " i (k) ...
An accurate control algorithm for small satellites is critical to mission success. In this paper, a novel discrete-time Model Reference Adaptive Control (MRAC) algorithm is developed based on a uni ed approach for the attitude control of a three-axis stabilized nonlinear satellite model. The linearized model of a satellite with unknown dynamic parameters is derived and a Recursive Least Squares (RLS) algorithm is used to identify the linear model's unknown parameters. In order to take into account the nonlinear model of satellite dynamics, the proposed MRAC strategy is used considering the linear model, the estimation error; and the di erence between the actual nonlinear system and the linear model outputs. The actual nonlinear model of the satellite includes moments of inertia uncertainties, external disturbances, and sensor noise on the outputs. The introduced controller performance is compared with a conventional discrete-time MRAC which demonstrates excellent simultaneous regulation and tracking capabilities.
... SMC has two specific features of disturbance rejection and insensibility to uncertainties by designing the sliding mode surface [11]. Different types of SMC strategies are employed for robotic exoskeletons, such as terminal SMC [12], nonsingular terminal SMC [13] and fuzzy SMC [14]. Nevertheless, the performance of sliding mode control is susceptible to the existence of a chattering phenomenon, which may increase control effort and excite high-frequency oscillation [15]. ...
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This paper presents and experimentally demonstrates an extended state observer (ESO) - based nonlinear terminal sliding mode control strategy with feedforward compensation (ESO-F-NTSMC) for lower extremity exoskeleton. Since the lower extremity exoskeleton (LEE) is a coupled human-exoskeleton coordination system, the internal or external disturbances and uncertainties affect its performance. A nonlinear terminal sliding mode control with feedforward compensation (F-NTSMC) is proposed to drive the lower extremity to shadow the target human gait trajectory. An ESO is employed to estimate the total disturbances including these caused by the chattering phenomenon in F-NTSMC. ESO-F-NTSMC can assure that the human gait trajectory tracking can converge to a bounded region smoothly and robustly. The phase identification-based human gait generation approach is also presented. The derivation process of the ESO-F-NTSMC is shown the and the Lyapunov-based stability analysis is conducted. To illustrate the proposed method’s effectiveness, experiments are performed on three human subjects walking on the floor at a natural speed. The results demonstrate that the exoskeleton can actively collaborate with the user under the proposed method.
... To enhance the robustness of the exoskeleton control system, SMC 14 and intelligent control NNAC 15 are mainly investigated. SMC has an advantage of parameter-insensitive, and NNAC is good at approximating uncertainties. ...
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Load-carrying exoskeletons need to cope with load variations, outside disturbances, and other uncertainties. This paper proposes an adaptive trajectory tracking control scheme for the load-carrying exoskeleton. The method is mainly composed of a computed torque controller and a fuzzy cerebellar model articulation controller. The fuzzy cerebellar model articulation controller is used to approximate model inaccuracies and load variations, and the computed torque controller deals with tracking errors. Simulations of an exoskeleton in squatting movements with model parameter changes and load variations are carried out, respectively. The results show a precise tracking response and high uncertainties toleration of the proposed method.
The exoskeleton has emerged as a promising technology to enhance humans’ strength and boost users’ efficiency. In order to provide congruent human–machine interaction for assisting the users, exoskeletons should have knowledge of human’s planned action and accordingly command the robot by the designed controller. It means the ubiquitous aspect of exoskeletons lies on motion intent understanding and active compliance control. In the last decade, extensive research has been conducted on the two topics. However, no major breakthrough has been made. Thus, a systematic review and analysis on this very subject is of great significance in developing exoskeletons. Within this context, this review first surveys the history of lower limb exoskeletons to summarize the various technologies for realizing transparent human exoskeleton coordination. Then, an overview about motion intent understanding and compliance control strategies are presented in detail. Furthermore, the future trend and research directions are also outlined.
This paper newly proposes a generalized control framework for exoskeletons. Motivated by the fact that the exoskeleton robot and its wearer physically interact by the force at each contact point and that this interaction depends on the controller used in the literature, the proposed method shows that the exoskeleton controllers can be generalized into a standard force feedback control system. To this end, the control system consists of the interaction force feedback control loop and the reference generation loop. The proposed method is advantageous in systematically implementing the conventional approaches and, moreover, extending it to other objectives. The proposed method is applied to a lower-limb exoskeleton, and verified by the experiments.
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Hydraulic exoskeleton with human-robot interaction becomes an important solution for those heavy load carrying applications. The good human motion intent inference and accurate human trajectory tracking are two challenging issues for the control of these systems, especially for hydraulically actuated exoskeleton where the nonlinear dynamics is quite complicated and various uncertainties are existing. However, robust performance to model uncertainties has been ignored in most of existing researches. To regulate these control problems, an adaptive robust cascade force control strategy is proposed for 1-DOF hydraulically actuated exoskeleton, which is namely grouped into two control levels. In the high-level, the integral of human-machine interaction force is minimized to generate the desired position (which can also be seen as the human motion intent). And in the low-level, the accurate motion tracking of the generated human motion intent is developed. The nonlinear high-order dynamics with unknown parameters and modeling uncertainties are built, and adaptive robust control (ARC) algorithms are designed in both control levels to deal with the complicated nonlinear dynamics and the effect of parametric and modeling uncertainties. Comparative simulation and experimental results indicate that the proposed approach can achieve smaller human-machine interaction force and good robust performance to various uncertainties.
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This paper presents a methodology of the dynamic analysis and control for a novel hybrid humanoid robot arm. The hybrid humanoid robot arm under consideration consists of a spherical parallel manipulator (SPM) connecting two revolute pairs in series form. The dynamic model of the hybrid humanoid robot arm has been set up based on the Lie group and Lie algebra combined with the principle of virtual work, which can avoid the processing of constraint reaction and the division of logic open chains, as well as a great quantity of differential operation. Aiming at the parameter uncertainties and disturbances, an adaptive backstepping sliding mode controller is developed. Compared with PD control in trajectory tracking simulation, the results show the advantage of the controller.
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With the increasing industrial requirements such as bigger size object, stable operation, and complex task, multilateral teleoperation systems extended from traditional bilateral teleoperation are widely developed. In this paper, the integrated control design is developed for multilateral teleoperation systems, where n master manipulators are operated by human to remotely control n slave manipulators cooperatively handling a target object. For the first time, the control objectives of multilateral teleoperation including stability, synchronization, transparency, and internal force distribution are clarified systematically. A novel communication architecture is proposed to cope with communication delays, where the estimated environmental parameters are transmitted from the slave side to the master, to replace the traditional environmental force measurement in the communication channel. A kind of nonlinear adaptive robust control technique is used to deal with nonlinearities, unknown parameters, and modeling uncertainties existing in the master, slave, and environmental dynamics, so that the excellent tracking performance is achieved in both master and slave sides. The coordinated motion/force control is designed in the slave side by the optimal internal force distribution among n slave manipulators, and the impedance control is designed in the master side to realize the target transparency behavior. In summary, the proposed control algorithm can achieve the guaranteed robust stability, the excellent synchronization and transparency performance, and the optimal internal force distribution simultaneously for multilateral teleoperation systems under arbitrary time delays and various modeling uncertainties. The simulation is carried out on a 2-master/2-slave teleoperation system, and the results show the effectiveness of the proposed control design. Copyright
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This article proposes a novel adaptive switching control of hypersonic aircraft based on type-2 Takagi-Sugeno-Kang fuzzy sliding mode control and focuses on the problem of stability and smoothness in the switching process. This method uses full-state feedback to linearize the nonlinear model of hypersonic aircraft. Combining the interval type-2 Takagi-Sugeno-Kang fuzzy approach with sliding mode control keeps the adaptive switching process stable and smooth. For rapid stabilization of the system, the adaptive laws use a direct constructive Lyapunov analysis together with an established type-2 Takagi-Sugeno-Kang fuzzy logic system. Simulation results indicate that the proposed control scheme can maintain the stability and smoothness of switching process for the hypersonic aircraft. © SAGE Publications Ltd, unless otherwise noted. Manuscript content on this site is licensed under Creative Commons Licenses.
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This study presents the development of a modular knee exoskeleton system that supports the knee joints of hemiplegic patients. The device is designed to realize the polycentric motion of real human knees using a four-bar linkage and to minimize its total weight. In order to determine the user's intention, force-sensitive resistors (FSRs) in the user's insole, a torque sensor on the robot knee joint, and an encoder in the motor are used. The control algorithm is based on a finite state machine (FSM), where the force control, position control and virtual damping control are applied in each state. The proposed hardware design and algorithm are verified by performing experiments on the standing, walking and sitting motion controls while wearing the knee exoskeleton.
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Existing control approaches for the precision motion control of linear motor driven systems are mostly based on rigid-body dynamics of the system. Since all drive systems are subjected to the effect of structural flexible modes of their mechanical parts, the neglected high-frequency dynamics resulting from these structural modes have become the main limiting factor when pushing for better tracking performance and higher closed-loop control bandwidth. In this paper, physical modeling and dynamic analysis that take into account the flexibility of the ball bearings between the stage and the linear guideways are presented with experimental verification. With the gained knowledge of these high-frequency dynamics, a novel μ-synthesis-based adaptive robust control strategy is subsequently developed. The proposed control algorithm uses adaptive model compensation having accurate online parameter estimation to effectively deal with various nonlinearity effects and to transform the difficult trajectory tracking control problem into a robust stabilization problem. The well-developed μ-synthesis-based linear robust control technique is then employed in the fast feedback control loop design to explicitly deal with the robust control issue associated with the high-frequency dynamics to achieve higher closed-loop bandwidth for better disturbance rejection. Comparative experiments have been performed and the results show the better tracking performance of the proposed algorithm over existing ones.
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In this article, two types of actuators are applied for a lower limb exoskeleton. They are DC motors with the harmonic drive and the pneumatic artificial muscles. This combination takes advantages of both the harmonic drive and the pneumatic artificial muscle. It provides both high accuracy position control and high ratio of strength and weight. The shortcomings of the two actuators are overcome by the hybrid actuation, for example, low control accuracy and modeling difficult of pneumatic artificial muscle, compactness, and structural flexibility of DC motors. The design and modeling processes are discussed to show the proposed exoskeleton can increase the strength of human lower limbs. Experiments and analysis of the exoskeleton are given to evaluate the effectiveness of the design and modeling.
Contouring control is an important issue in industrial applications. For better product quality and higher productivity, achieving higher contour tracking performance with feed rate as large as possible is essential. However, most existing research has focused on improving contour tracking accuracy only. The potential instability issue due to control input saturation under high feed-rate operations has been largely ignored. In this paper, the minimum time trajectory planning problem is formulated as a step toward solving this practically important problem. A novel back and forward check algorithm is developed to take into account physical constraints of the system when generating the desired trajectory to be followed. Compared with traditional numerical searching methods, the proposed algorithm is very computationally efficient because the optimal solution at each node can be obtained by several analytical equations directly. Moreover, the algorithm can incorporate some velocity-dependent constraints easily. Planning a Lissajous curve is used as the case study to verify the optimality and computational efficiency of the proposed algorithm. Experiments are conducted on an industrial biaxial gantry. Several implementation issues on tracking complicated contours are discussed. Experimental results indicate that the proposed trajectory planning approach enables simultaneous achievement of high contouring tracking accuracy and higher feed rate or shorter operation time.