Keywords 
Rehabilitation robotic system; Humanrobot cooperative;
Variable impedance control; Electromyogram; Root mean square of
the EMG signals 
Introduction 
Recently with rapid aging of population and declining birthrate
in many countries, public health burden associated with strokerelated
disability in lower limbs has been increasing year by year
[1,2]. The stroke could lead to lifelong dependency on caregivers
and a tremendous decrease of the quality of life (QOL). These factors
are driving research work for more costeffective methods for poststroke
rehabilitation, including robotic devices that provide movement
therapies. As an effective tool for therapists, rehabilitation medicine
and technology have been playing a more and more important role in
dealing with those social issues. Moreover, a number of rehabilitation
robotic systems have been developed for the purpose of improving
motor function after stroke over the past few years [3,4]. Their
therapeutic effects have been proved by numbers of studies: they could
not only improve stroke patients’ Range Of Motion (ROM), strengthen
muscle, but also rebuild patients’ life confidence and help them restore
their impaired motor functions to improve their QOL [5]. 
Rehabilitation robotic systems could be divided into 3 categories
according to the type of motion support [6,7]: 1) continuous passive
motion [8,9], 2) activeresisted movement [10], 3) activeassisted
movement [11,12]. Among these, activeassisted movement has
been proved to be the more effective system for motor functional
improvement than other two methods on both the upper limbs
and lower limbs [6,11,12]. However, this motion support requires rehabilitation robotic systems to support active movement in
cooperation with human subjects. 
Impedance control has been employed recently for this type of
robotic systems to cooperate with human subjects’ motion, reacting to
their voluntary intention detected from EMG or torque sensors [13,14].
The MitManus has been implemented based on impedance control to
ensure a compliant trajectory [15] and the assistance output torque was
produced from the angular error between the desired position and the
patient’s position, with the aim to reach the desired position accurately.
The HAL1 proposed an assistance feedback control scheme that could
generate an angular displacement and provide a ramp torque in the
movement in response to a patient’s torque by using impedance control
based on the output of torque sensors [13]. These devices can reach
the desired position precisely and rapidly with lower power. However,
a torque sensor was used to decide the parameter of control system with an invariable relationship, which was determined by experiences
and, in that case, the same control parameter was adopted, both the
extension task and flexion task, the control system was unstable if force
output of the two target muscle varied greatly. Moreover, if a subject
has a limited ROM by some reasons, and the torque output could not
be measured, these systems would provide passive movement rather
than cooperative movement. 
EMG, as a biosignal source, could be used to detect muscle
activity, reflected characteristics of muscle activities in the realtime.
Some researchers have applied EMG signals to estimate the changing
impedance of knee joint in rehabilitation robotic system. Artificial
neural networks have mainly been used to verify the relationship
between the EMG signals and the parameter of impedance control [16].
It could be used to estimate the parameters of impedance control by
using EMG signals. However such approaches have limited ability to
adapt to changing physiological conditions, and being of a blackbox
structure, do not permit stability and performance analysis [11]. 
There were also some other methods to clarify the relationship
between EMG signals and changing impedance in a joint. Kusumoto
et al. [17] studied the impedance parameters of human thumb muscle
by using EMG signals based on isometric contraction at a fixed angle
[18]. The impedance of thumb muscle was well calculated by increasing
the power of contraction. However, this method could not reflect
the dynamic characteristics of muscle because of the experimental
condition of isometric contraction. Nichols and Houk [19] followed
the methods that applied electrical stimulation to isolated muscle,
to estimate the impedance parameter [20]. An accurate model was
proposed at different conditions, such as different length of muscle, and
stimulus intensities. However, this invasive method used animals as
subjects, which was not clear how this could be transferred to humans. 
Furthermore, power assist control for a walking aid system based
on EMG signals and impedance control have been proposed by some
researchers [21,22]. In this case, a virtual torque derived from the EMG
signals was adopted as a basic control method, thus the system can help
the operator to achieve the intended motion. However, in those studies
the relationship between control parameters, i.e., impedance, and
EMG was assumed as invariable not only for different moment in one
motion, but also for different motions, such as extension and flexion.
Few studies employed changing impedance, but limited to linear
[23] and motionindependent [14,24] impedance values, determined
through subjective opinion of engineers, therapists or even subjects. 
However, if a fixed parameter of impedance control does not match
with operator’s joint stiffness in one certain or different direction
of motions, the cooperative system would become unstable, even
vibrating, and it would be difficult for the system to reach a target
trajectory, that is, the position error would be quite big [23]. Therefore,
a variable impedance controller with motiondependent and nonlinear
impedance control model should be designed considering target
muscles dynamic characteristics to make the robotic system more useroriented
in humanrobot cooperative tasks. 
The aim of this study was to investigate the possibility of impedance
estimation from EMG signals recorded during extension task and
flexion task, and the effectiveness of the variable impedance control
based on the estimated impedance for a lower limb rehabilitation
robotic system. For this purpose, two experiments were conducted in
this study. The primary objective of the first experiment (Experiment1)
was to study the relationship between EMG and changing impedance
in knee joint extension task and flexion task. In this experiment, EMG
signals were measured, and normalized RMS_EMG was paired with increasing changing designated impedance, and anon linear model was
proposed to fit the recorded data to express the relationship between
them. The second experiment (Experiment2) was to confirm the
effectiveness of variable impedance control with the models acquired
from the Experiment1. The discrepancy between desired and reached
angular trajectories, and sum of RMS_EMG of target muscles were used
to evaluate the validity of our proposed nonlinear variable impedance
control method. 
Methods 
An Overview of the Lowerlimb rehabilitation system 
The lower limb rehabilitation robotic system is composed of 3
parts: 
An interface: It contains a monitor for visual information, such
as experiment instruction, angular position for feedback, raw recorded
signals. The display of the visual information and measurement of the
signals were implemented in LabVIEW9.0 (A/D: USB6225, National
Instruments, and USA). 
A controller: It realizes impedance estimation with EMG signals
and variable impedance control, which is described in detail in
subsection B. The controller is implemented using a PC (CFB10,
Panasonic, Japan). 
Hardware of the robotic system: It consists of a swing arm (lower
limb holder), a torque sensor, a reduction gear box, a servo motor
(SGMAH02AAA21, Yasukawa Electric, Japan), which was driven by a
motor driver (SGDM02BDA Yasukawa Electric, Japan). 
The configuration of the rehabilitation robotic system is shown in
(Figure 1). The angle of swing arm was calculated from the readings
of a potentiometer (5K ohm, Nidec Servo, Japan), and input (voltage
value) to the motor was calculated from variable impedance controller. 
For safety reasons, 4 safety measures were taken to protect subjects
during all the following experiments. First, an emergency stop button
could be pressed by a subject to stop the servomotor immediately if
needed. Second, the output torque was limited to arrange of 0 N×m to
50N×m by the software program, and the operation would be stopped if the motor exceeded this range. Third, the maximum speed of lower
limb holder was limited to 2rad/s by the servomotor driver. Fourth,
two mechanical stops were used to limit the rotation range of the swing
arm. 
Variable impedance control 
The model of the swing arm and knee joint could be described as
below [25]: 
(1) 
where, I_{o} is an inertia moment, θ is the angle of the swing arm, B_{o} is
a viscous coefficient, k_{o} is an elastic modulus, MgL is an item for
gravitational effects, f_{r} is an item for friction effects, τ_{e} is an external
torque, τ is a torque command vector. 
Assume that the desired impedance control model was given by: 
(2) 
In this equation, I_{d} is a desired inertia moment, B_{d} is a desired
viscous coefficient; Kd is a desired elastic modulus, θ_{d} is a desired angle
position, τ_{e} is the external torque. Integrating Equation (1) and (2), the
torque command output for the impedance control could be derived
as Equation (3). 
(3) 
In order to implement a variable impedance control, K_{d} and
B_{d} should be determined or estimated. Firstly, the static synthetic
impedance of knee joint and swing arm was identified using least
squares method, and the influence of those was compensated to
accurately estimate K_{d} and B_{d}. Then, assuming these two variable
parameters could be approximated by Equation (4). 
(4) 
EMGsignal processing 
The EMG signals were sampled with surface EMGsensors (TYE
100, Tsukasa Kiko Engineering, Japan), placed on the Rectus Femor is
muscle and Semi membranous muscle of lower limb of subject. EMG
signals were amplified with a gain of 1000 and processed by a bandpass
filter (10 to 1000Hz). The sampling rate is 3000Hz. The EMG signals was
then fullwave rectified and smooth educing a moving average filter
with a window size of 6. Then, Root mean square of EMG (RMS_EMG)
was calculated as Equation (5). 
(5) 
Where T is a time span, t is a variable of integration, and a sampling
space was settled as 0.1s in this study. The processed EMG signals
were then normalized to the range 01 by the value MVC (Maximum
Voluntary Contraction) for % EMG as in the following Equation (6)
[26]. 
(6) 
Where, (RMS_EMG)_{t} is the RMS_EMG of the target muscle, (RMS_
EMG)_{t_MVC} is the maximal value of target muscle during its maximal
voluntary contractions by 3 times measurement and (RMS_EMG)_{t_rest} is
the average RMS_EMG value of target muscle during the resting state. 
Moreover, the differential values of EMG of target muscles between
the agonist and antagonist as MVC% was used in this study as Equation
(7). 
(7) 
Where, % EMG_{agonist} is the RMS_EMG of agonist muscle
(Rectus Femoris during extension, or Semi membranous during
flexion), %EMG_{antagonist} is the RMS_EMG of antagonist muscle (Semi
membranous during extension, or Rectus Femor is during flexion).
An example of EMGsignal processing procedures when doing
experimental extension task is shown as in Figure 2. 
Modeling and caculating K_{d} 
In the following experiments, EMG of the Rectus Femor in muscle
and Semi membranous muscle were measured, and the differential
values of normalized RMS_EMG between the two muscles were
calculated, and used to quantify the relationship between the EMG and
changing impedance in knee joint. However, to verify the changing
impedance in knee joint, the static synthetic impedance of knee joint
and swing arm has been identified using least squares method, and
the influence of it was compensated in the all following experiments.
Therefore, in this the changing impedance is defined as the active
mechanical impedance (viscous coefficient and elastic modulus) [27]
of target lower limber knee joint. 
As shown in Equations (3) and (4), viscous coefficient and elastic modulus are the two determinant factors of variable impedance control. 
Regarding viscous coefficient B_{d}, as reported by some researchers,
viscous coefficient of muscle was almost unchanging, and with a small
value compared with elastic modulus [17,19]. To make sure of that, a
preliminary experiment was carried out by one subject, in which, the
%MVC (percentage of RMS_EMG) amplitude during extension task
and flexion task was measured when increasing the velocity by a step
of 0.1 rad/s incrementally from 0.05 rad/s to 1 rad/s, the range was
frequently applied in rehabilitation device [27]. For each step, 3 sets
were done. Then, the average RMS_EMG of 3 sets for each step was
calculated. The results show that % MVC was increasing monotonically
with a small gradient for both extension (<0.03) and flexion (<0.02),
and the value of % MVC is also small (0.02 to 0.08), as shown in Figure
3. In other words, it is reasonable to set a fixed value for the viscous
coefficient, and focus on the relationship between EMG and desired
elastic modulus (K_{d}) during extension task and flexion task in knee
joint. To quantify the relationship between EMG and desired elastic
modulus (K_{d}), the static synthetic impedance of knee joint and swing
arm was identified firstly using least squares method (subsection B of
this section), and the influence of static impedance of swing arm and
lower limb, friction effects, and viscous coefficient were compensated
as Equation (3). Then, a set of different values were set for K_{d}. For
each K_{d} value, knee extension and flexion experiment (Experiment1,
as described by the next subsection) was done, and EMG signals for
a pair of antagonist muscle were recorded and calculated as denoted
by subsection C. Thus, a set of KdEMG data could be collected, and
through curve fitting (Equation (8)), a continuous function could be
acquired. 
(8) 
In the experiment for confirming the effectiveness of the variable
impedance control (Experiment2, as described in the following subsection),
The value of desired elastic modulus K_{d} could be calculated
by reverse looking up the function acquired through curve fitting
(Equation (8) in the last step, Experiment1), using the EMG measured. 
(9) 
Experiment procedure 
Experiment1: The purpose of this experiment was to investigate
the relationship between EMG and parameters of changing impedance
during knee joint extension task and flexion task. The experiment setup could be illustrated in Figure 4. Nine subjects (three women and
six men, aged from 24 to 32, Weight 5075 Kg, and with no apparent
sensory or motor impairment on lower limbs) participated in this
experiment. A full explanation was made about the contents and
purpose of experiment to all nine subjects, then an informed consent
was signed by all subjects. During each intervention session, a sufficient
rest was arranged. In this study, extension task was defined as a move
from an initial angle (vertical to the ground) to an end angle (1 rad
in relation to the ground), and flexion task was vice versa with the
extension task. 
To quantify the relationship between EMG and desired elastic
modulus (K_{d}), the static synthetic impedance of knee joint and swing
arm was identified firstly using least squares method (subsection B of
METHOLD), and the influence of static impedance of swing arm and
lower limb, friction effects, and viscous coefficient were compensated
as equation 3. Then, the value of desired elastic modulus (K_{d}) was
incrementally increasing by a step of 10 N×m/rad from 0 N×m/rad as
a negative torque. The EMG of target muscles was measured in each
step. For each step, 3 sets were done. Then, the average of 3 sets for
each step was calculated. All the subjects were required to track with a
specified rhythm (0.1 Hz) in a sitting position as shown Figure 4. The
lower limb angle and designated tracking angle were fed back to the
subject through a monitor, as shown in Figure 5. θ_{d} was settled from
reached angle as 0.1 radius in this study. 
Experiment2: The second experiment (Experiment2) was to
confirm the effectiveness of the variable impedance control with the
motiondependent models acquired in Experiment1, and to verify
whether the motiondependent variable impedance control method
could achieve a stable and robust assist movement. To confirm the
effectiveness of the impedance estimation with EMG signals and the
variable impedance control based on the estimation, and find a suitable
control parameter considering target muscles’ dynamic characteristics
to make the robotic system more useroriented in humanrobot
cooperative tasks. Four different control policies were tested, i.e.,
NA: No Assist; FO: using EMGimpedance model from the Flexion
Task; EO: using EMGimpedance graph from the Extension Task;
FE: using two EMGimpedance models from Flexion and Extension
task correspondently.The same nine subjects as in the Experiment1
participated in this experiment. The subjects were required to do the
movement of extension and flexion reciprocally to track the desired
tracking angle in the range of 01 radius in sitting position as shown
in (Figures 4 and 5). The discrepancy between a desired and reached
angle, and sum of RMS_EMG (one set) of target muscles were used to
evaluate the validity of our methods. For each test, 10 sets were done.
And there, the time rang of each set was 10 s (0.1 Hz). Then, the average
of 10 sets for each subject was calculated. 
Results 
Results of experiment1 
Figure 6 shows the RMS_EMG of one subject during extension
task and flexion task when increasing the desired elastic modulus
incrementally. It indicates that the RMS_EMG of target muscle
increases as the elastic modulus increases. The RMS_EMG of flexion
task reached 80% when the value of desired elastic modulus was set
to 205N×m /rad. However, contrary to the RMS_EMG of flexion task,
the RMS_EMG of extension task reached about 80% when the value of
desired elastic modulus was almost 405N×m /rad. That is to say, the
EMGimpedance properties of the two different types of movement are
asymmetric. To express this in a model, a mathematical formula could
be suggested as Equation (8) in subsection D of method section. Table
1 show that the fitting parameters of all nine subjects by equation 8
during extension task and flexion task. Figure 7 shows the RMS_EMG
of two different subjects. It indicates that the RMS_EMG of the two
subjects both extension task and flexion task increases as the elastic
modulus increases. However, results also indicate that the value of
desired elastic modulus is different for the two subjects when reaching
about 80% MVC of target muscle both extension task and flexion task.
Table 2 shows the value of desired elastic modulus of all nine subjects
both extension task and flexion task when reaching 80% MVC. It also
shows that the desired elastic modulus of extension task is bigger
(p<0.01, ttest) than flexion task when reaching 80% MVC. However,
the proposed model is able to approximate the relationship between the EMG and the desired elastic modulus by adjusting the fitting
parameters a and b, as described in Equation (8). 
Figure 8 shows the fitting curve by linear model and the fitting
curve by proposed nonlinear model. Table 3 shows mean residual
(the differential values between the real value and estimated value)
of desired elastic modulus value between linear model and proposed
model. Results show the mean residual of proposed model express a
smaller value (p<0.01, ttest) than linear model. 
Although the nonlinear model fits the recorded data better than the linear model, it is still possible to simplify the model by connecting
several special points with the proposed model. In this way, the
proposed model could be identified easily, quickly, and reasonably by
some special points, i.e., the inflection points, as a medical evaluation
method for paralyzed people for whom it is difficult to attend the
experiments. For the inflection point of the proposed model, the first
and second derivatives were expressed as follows. 
(10) 
(11) 
Therefore, from the property of the second derivatives, to calculate
the infection point of proposed model, Equation 12 could is formed as: 
(12) 
From Equation 12, the inflection point could be calculated as
bellow: 
(13) 
(14) 
Table 4 shows an inflection point of proposed model. EMGelastic
modulus relationship could be described by an inflection point and the
other two points i.e., the maximum K_{d} and minimum value K_{d}, because
the proposed model has the property of bilateral symmetry. That is, the
changes of EMGdesired elastic modulus relationship could be easily
represented by only three points. 
Results of experiment2 
The purpose of the second experiment (Experiment2) was to
confirm the effectiveness of the variable impedance control with
the motiondependent models acquired in Experiment1. To verify
effectiveness of different control methods, four different tests were done,
i.e., NA: No Assist; FO: using EMGimpedance model from the Flexion
Task; EO: using EMGimpedance graph from the Extension Task; FE:
using two EMGimpedance models from Flexion and Extension task
correspondently. In the FO, EO and FE, the value of desired elastic
modulus was calculated from RMS_EMG as an assist torque output
expressed in Equation 9. The actuator provides torque assistance in the
FO, and EO, FE tests to assist the subject to track the designed tracking
angle using impedance control policy. Figure 9 shows an example of
two cycles of the desired angle and torque output from actuator (servo
motor) by proposed variable impedance controller (FE). It indicated that actuator could provide torque assistance to track desired angle in
the cooperative system. 
In this experiment, the accuracy of position control, i.e., the angular
error, and muscle effort needed, i.e., the sum of RMS_EMG of target
muscles was used to evaluate the effectiveness of motiondependent
impedance control by comparing with the invariable impedance
control method. Figures 10 and 11 shows an example of trajectories
of the two angles (desired and reached angle) and RMS_EMG data of
proposed impedance model by comparing with other control policies.
Figures 12 and 13 shows the sum of RMS_EMG and angular error
comparison of the different control policies (NA, FO, EO, FE, see the
description of Experiment1 in METHODS section), respectively. 
Results indicate that there is a significant difference (p<0.01, ttest)
in angular error between the FE case (i.e., the case of using motiondependent
impedance models), the EO (i.e., the case of using only
impedance model of extension task) and NA (i.e., no assist case). A significant difference with (p<0.01, ttest) is observed in sum of RMS_
EMG between using FE and NA, and a significant difference with
(P<0.01) is also observed in sum of value of RMS_EMG between FE
and FO. Results also indicate proposed nonlinear variable impedance
control method (using nonlinear control parameter) could achieve
a smaller discrepancy (P<0.05, ttest) than using linear variable
impedance control as shown in Figure 14. However, there are no
significant differences noted in sum of value of RMS_EMG between
using the nonlinear variable impedance control method and using
linear variable impedance control as shown in Figure 15. 
Discussion 
As discussed before, a number of rehabilitation robotic systems
based on EMGdriven impedance control, capable of reacting to the
patient’s voluntary muscle activations, have been developed for the
purpose of improving motor function after stroke over the past few
years. However, to develop a stable and robust active assistive, it is
crucial to clarify the relationship between EMG signals and changing
impedance during different tasks i.e., extension task and flexion task. 
Experiment1 investigated the possibility of impedance estimation
from EMG signals recorded during extension and flexion in knee
joint. The results showed that RMS_EMG of target muscles increases
as specified elastic modulus increases, but there is a difference in
property between the extension task and flexion task. However, as an
experiment condition during each intervention session a sufficient rest was arranged to all subjects in this experiment. In addition, the
relationship between EMG signals and changing impedance during
fatigued condition was studied. Here fatigued condition was definite
as those subjects were required to repeat the movement of extension
and flexion reciprocally in the range of 01 radius in sitting position as
shown in Figure 4, where a 35% of maximum resisted movement of 2~3
minutes to lower limb [27]. Figure 16 shows the relationship between
% MVC and desired elastic modulus during normal and fatigued
condition both extension task and flexion task when increasing desired
elastic modulus incrementally. Result indicates that the % MVC shows
a different feature between normal and fatigued condition when increasing the value of elastic modulus to same values. The width of %
MVC became narrower at a fatigued condition compared with taking
a sufficient rest for both the tasks. The changing range of flexion task
is bigger than extension task. However, our proposed model could also
fit that by adjusting the parameters of model as Equation (8). Figure 17
shows the % MVC and fitting curve during extension task of one subject
when increasing (5~400 N×m/rad) and decreasing (400~5 N×m/rad)
the desired elastic modulus gradually. Result indicates that % MVC
by the condition of decreasing the desired elastic modulus gradually
is bigger than the condition of increasing the desired elastic modulus
gradually when reached about 80% MVC. However, the % MVC of
two conditions is similar when the value of desired elastic modulus
is below 200 N×m/rad, and the % MVC when increasing the desired
elastic modulus is bigger than decreasing the desired elastic modulus
when the value of desired elastic modulus over 200 N×m/rad. Figure
18 shows the relationship between EMG and changing elastic modulus
using different move velocity from 0.1 rad/s to 0.6 rad/s. It shows that
the RMS_EMG of target muscle increases as the velocity increases, but
the increasing rate is different with different velocity. Therefore, the
effect of velocity should be considered in a high speed rehabilitation
system. Figures 1618 shows the relationship between EMG and the
changing elastic modulus in three different conditions, i.e., fatigued
condition, different path of the changing elastic modulus (increasing
or decreasing), and different velocity of the motion. Results show that
the EMGimpedance model varies with different conditions. As shown
by Experiment2, if the parameters of impedance control models did
not match users’ joint stiffness, the angular error was bigger and more
muscle effort was required, since the cooperative system would become
unstable and difficult to control. To accurately describe the relationship
between EMG and the changing impedance, it is necessary to establish
conditiondependent model, by adjusting the parameters of Equation (8). The method described in subsection D of Methods section and
could be used. Nevertheless, in the next stage, the effectiveness of the
conditiondependent models should be verified by further experiments. 
Figure 19 shows the relationship between EMG and elastic modulus
by using different initial position. It shows that the RMS_EMG of target
muscle increases as the elastic modulus increases, but the increasing
rate is different with different initial positions. It shows that the elastic
modulus could be different in different initial angle of lower limb. This
result could be predicted by neurophysiologic property of muscle.
However this would not be an obstacle of applying the impedance
estimation to variable controller, since a fixed initial and final position
could be chosen. The purpose of the second experiment was to verify
the effectiveness of the impedance estimation and variable impedance
control based on the EMG signals. There is a significant difference
(p<0.01, ttest) in angular error between the case of estimating
impedance using two separated properties, and the case of using
only the property of extension task and no assist case. A difference
with (p<0.01, ttest) is observed in sum value of RMS_EMG between
using the separated properties and no assist case, and a difference with
(P<0.05, ttest) is also observed in sum of value of RMS_EMG between
using the separated properties and using EMGimpedance graph
from the extension task. It indicates that the proposed impedance
control method could offer a durable and required less muscle effort
compared with other methods. On the other hand, the cooperative
system is unstable when improper control parameters were adopted.
Therefore, in order to use EMG signals to control rehabilitation robotic
system more userfriendly, the calculated method of RMS_EMG, for
example the integration interval and sample frequency have or not
affect the result of control system should to investigate. Therefore, in
the next stage, we should focus on how the RMS_EMG of integration
interval and sample frequency influences the control system by using
more subjects. Moreover, to subjects of the hemiplegic, how to use
the relationship between EMG signals and changing impedance of
healthy side to control the paralysis, that the effectiveness should be
investigated in next stage. 
Conclusion 
In this study, two experiments were performed to investigate the
variable impedance control based on a model of impedance estimation
with EMG signals for a lower limb rehabilitation robotic system. The
first experiment was to study the relationship between EMG signals
and value of desired elastic modulus. Based on the experiment results,
a nonlinear and motiondependent model was proposed. The second
experiment was to verify the effectiveness of the variable impedance
control with the impedance estimation model acquired in Experiment1.
The achievements obtained in this study are summarized below: 
1) A nonlinear and motiondependent model could represent the
relationship between EMG and changing impedance, resulting in a
smaller mean residual (the differential values between the real value
and estimated value) than the linear model. 
2) The proposed variable impedance control method (using
nonlinear control parameter) could achieve a smaller angular error and
require less muscle effort in knee joint extension and flexion tasks than
the invariable impedance control, and it also could achieve a smaller
angular error than the motiondependent linear variable impedance
control. 
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