Available via license: CC BY 4.0
Content may be subject to copyright.
https://doi.org/10.14311/AP.2023.63.0179
Acta Polytechnica 63(3):179–187, 2023 ©2023 The Author(s). Licensed under a CC-BY 4.0 licence
Published by the Czech Technical University in Prague
NEURAL NETWORK BASED PATIENT RECOVERY ESTIMATION
OF A PAM-BASED REHABILITATION ROBOT
Van-Vuong Dinh, Minh-Chien Trinh, Tien-Dat Bui, Minh-Duc Duong,
Quy-Thinh Dao∗
Hanoi University of Science and Technology, School of Electrical and Electronic Engineering, 11615 Hanoi,
Vietnam
∗corresponding author: thinh.daoquy@hust.edu.vn
Abstract. Rehabilitation robots have shown a promise in aiding patient recovery by supporting
them in repetitive, systematic training sessions. A critical factor in the success of such training is the
patient’s recovery progress, which can guide suitable treatment plans and reduce recovery time. In this
study, a neural network-based approach is proposed to estimate the patient’s recovery, which can aid in
the development of an assist-as-needed training strategy for the gait training system. Experimental
results show that the proposed method can accurately estimate the external torques generated by the
patient to determine their recovery. The estimated patient recovery is used for an impedance control
of a 2-DOF robotic orthosis powered by pneumatic artificial muscles, which improves the robot joint
compliance coefficients and makes the patient more comfortable and confident during rehabilitation
exercises.
Keywords: Pneumatic artificial muscle, rehabilitation robot, neural network, patient recovery.
1. Introduction
Nowadays, robots appear everywhere and play an
essential role in many fields, such as industry, mili-
tary, transportation and rescue service areas. With
the increasing number of older people and the lack
of physicians and nurses, robots are expected to as-
sist and replace humans in healthcare and daily life.
Healthcare and service robot systems have been the
subject of extensive research in recent years [
1
,
2
].
Currently, the majority of gait training systems com-
mercially available utilise electric motors as actuators.
However, these systems are associated with significant
concerns, such as high costs and a low power/weight
ratio of the motorised actuators. As an alternative,
the pneumatic artificial muscle (PAM) system has
been proposed due to its advantages, including a large
power/weight ratio, low cost, lightweight, and simi-
lar characteristics to human muscles, as reported in
recent studies [
3
–
8
]. For this reason, a many PAM-
based gait training systems have been developed in
the literature [
8
–
16
] that can assist the patient with
movement according to the exercises prescribed by
the physiotherapist.
Compared to other robot systems, the main differ-
ences of rehabilitation robots are the safety and the
capability to improve the patient’s recovery. Thus,
the interactive force/moment between the robot and
the human is required. To obtain force/moment in-
formation, one can usually use force/torque sensors,
mainly used in rehabilitation robot systems. However,
the external force/moment estimation without sensors
is considered due to the cost and complicated assem-
bly. Various studies have been conducted to estimate
the external force acting on industrial robots [
17
–
20
].
In [
17
], a task-oriented dynamics model learning and a
robust disturbance state observer are proposed. Force
estimation based on machine learning is developed
in [
18
,
20
]. In addition, Cartesian contact force estima-
tion for robotic manipulators using Kalman filter and
the generalised momentum is reported in [
19
]. These
methods are all for industrial robots and give good
external force estimation results. However, they re-
quire the robot’s dynamics and are pretty complicated,
resulting in a difficult implementation.
One better solution for the estimation of external
contact force is to use a neural network [
21
–
24
]. These
researches consider two estimation approaches. The
first approach is to estimate the contact force directly
from the robot’s motion information using a neural
network [
21
]. The second approach is to estimate the
robot’s inverse dynamic model [
22
–
24
]. Then, the con-
tact force is calculated by the difference between the
robot actuator’s torques for the case of contact force
and without contact force. The disadvantage of the
first approach is that the measurement of contact force
is required for offline training of Neural Network. In
contrast, the contact force measurement in the second
approach is not required since the inverse dynamic
model can be estimated in the free-motion condition.
For this reason, the second approach is promising to
estimate external force for rehabilitation robot. It
leads to the estimation of the patient recovery in a
training process.
In gait training robot systems, the estimation of
patient interaction forces can bring many benefits. At
first, this contact force can be used for the compliant
control, patient-cooperative control, assist-as-needed
179
V-V. Dinh, M-C. Trinh, T-D. Bui et al. Acta Polytechnica
(AAN) that is required in rehabilitation exercises [
8
],
together with trajectory tracking control. In addition,
the contact force information can help the physician
evaluate the patient’s recovery during the treatment.
The patient’s interaction force can be measured di-
rectly, using force/torque sensors [
8
], but the instal-
lation is complicated and may cause a physical dis-
comfort the patients. Another way to estimate the
interaction force is to use Electromyography (EMG)
signals of the patient’s muscles [
25
]. EMG signals can
be used to calculate the muscle force and supply the
valuable muscle health information for a diagnosis and
analysis of the patient’s recovery. Nevertheless, the
EMG measurement setup is complicated, and EMG
signals vary with the patient’s condition and time.
Thus, the use of EMG signal may not be appropriate
at present.
To overcome the limitation of contact force- and
EMG-based approaches and fully utilise the advan-
tages of the neural network based one, this research
develops a simple and online method for estimating the
external force of the PAM-based gait training robot.
Instead of the force sensor as most gait training robots,
this paper calculates the external force from forces
generated by PAM actuators and the robot inverse
dynamic. Since the rehabilitation robot has a complex
structure, the determination of robot parameters is
very complicated and inaccurate. This paper proposes
a method for estimating joint torques using a neural
network, which allows for an easy collection of train-
ing data in a robot free-motion mode. The estimated
joint torques are then used to obtain the external force
exerted by the patient, which is subsequently used for
the impedance control of a PAM-based gait training
system. In summery, the main contributions of the
paper are:
•
Using a neural network to estimate both the joint
torques required to guide the robot during gait train-
ing and the external force generated by the patient,
without the need for an external force measurement.
•
The estimated patient’s recovery is used for the
impedance control of the PAM-based gait training
system, improving the robot joint compliance coef-
ficients and making the patient more comfortable
and confident in their rehabilitation exercise.
•
The proposed method offers a simpler and more
practical approach to estimating the patient’s re-
covery as compared to previous methods.
•
The experimental results demonstrate the effective-
ness of the proposed method for estimating the
patient’s recovery and improving the gait training
robot system.
The rest of the paper is organised as follows. Sec-
tion 2 presents the structure of the 2-DOF prototype
exoskeletal robot for lower limb rehabilitation. The
force estimation is demonstrated in Section 3. Sec-
tion 4 presents the compliant control for the reha-
𝜃2
𝜃1
𝑙𝑐2
𝑙2
𝑙𝑐1
𝑙1
COM2
𝑦1
𝑦2
O1
O2
COM1
(a).
Hip PAMs
Knee PAMs
Hip Joint
Knee Joint
(b).
Figure 1. The proposed method’s experimental rig,
with a typical 2-DOF robot (A) and a BK-Gait PAM-
based lower limb orthosis (B) with COM representing
the centre of mass.
bilitation robot using the estimated patient’s force.
Conclusion and further studies are shown in Section 5.
2. Lower Limb Rehabilitation
Robot System
This paper considers a BK-Gait based lower limb
rehabilitation system for the experimental works. The
system’s main advantage is the suspension frame’s
direct attachment to the pre-shaped aluminum, which
fixes the robot and lifts the patient to the desired
height. The prototype robot is a 2-DOF robot, as
shown in Figure 1a, which drives the lower limb of
the subject with the help of two aluminum braces
attached to the thigh and shank parts. The length
of the robot’s links can be adjusted based on the
subjects’ body using the slider located between the
hip and knee joints. The hip and knee joints can
flex/extend to a maximum angle of
−
45
◦
/+45
◦
and
0
◦
/90
◦
, respectively. Overall, the system’s design
allows for a customisable and effective rehabilitation
experience for lower limb patients. The developed
robotic exoskeleton system is depicted in the actual
image shown in Figure 1b.
The robot system consists of two opposing muscles
and joints fixed on a flat surface to enable the move-
ment. The used PAM type is a McKibben artificial
muscle, 2.5 cm in diameter. This PAM also has a max-
imum contraction rate of 30% compared to muscle
length similar to human muscles. We used two pairs
of pressure regulators ITV-2030-212S-X26 by SMC in
the developed muscle system. A pressure difference
between the two control valves causes one muscle to
contract and the other to stretch. That creates a rota-
tion angle of the corresponding joint. A potentiometer
WDD35D8 that ranges up to 360
◦
is attached to each
robot joint to measure the joint’s position. Load cells
are attached to the muscle’s ends to measure the pull
force of muscles. The NI Myrio platform developed
by National Instrument was adopted to implement
180
vol. 63 no. 3/2023 Neural Network Based Patient Recovery Estimation
the control algorithm. NI Myrio also collects voltage
signals from load cells, potentiometers, and provides
control signals. The control algorithm is developed
and compiled in the Labview software environment
before being downloaded to NI Myrio for a real-time
control.
3. Human Torque Estimation
Let us consider the developed 2-DOF rehabilitation
robot which has a typical schematic diagram in Fig-
ure 1a. When a torque vector
M
is applied to the
robot system, the robot is moved with position vec-
tor
q
, and the dynamics of a robot system can be
expressed as [26]:
M=H(q)¨q+V(q, ˙q) + G(q),(1)
where
q
=
θ1
θ2
is the robot’s position vector with
θ1
being the hip joint’s angle and
θ2
the knee joint’s
angle.
H(q) = h11 h12
h21 h22 is the inertia matrix.
V(q, ˙q)
=
−m2l1lc2˙
θ2(2 ˙
θ1+˙
θ2) sin θ2
m2l1lc2sin θ2˙
θ2
1
is the
coriolis and centrifugal forces.
G(q)=(m1lc1+m2l1)gcos θ1+m2lc2cos(θ1+θ2)
m2glc2cos(θ1+θ2)
is the gravitational force vector.
h11 =m1l2
c1+m2(l2
1+l2
c2+ 2l1lc2cos θ2)
h12 =h21 =m2(l2
c2+l1lc2cos θ2)
h22
=
m2l2
c2
In the above equations,
li
and
mi
(
i
=
1
,
2) are the length and mass of the robot’s links;
lci
(
i
= 1
,
2) is the distances of the robot link’s centre of
mass from the respective joint rotation point. Table 1
shows the geometric parameters of the BK-Gait robot.
Parameters l1[m] m1[kg] l2[m] m2[kg]
Value 0.4 3.0 0.38 2.2
Table 1. Geometric parameters of the BK-Gait robot.
When the robot moves with an object (human), the
total torques
M
impact the robot’s joints, including
two components: the torque generated by PAMs and
the torque generated by the human.
M=MP AM +MHM ,(2)
where
MP AM
is the PAM torque vector generated by
PAMs and
MHM
is the human torque vector generated
by the human muscles. Then, the human torque
(MHM ) can be calculated as:
MHM =M−MP AM .(3)
The PAM torque (
MP AM
) can be calculated from
the force generated by the PAM, which is measured by
Oi
Ri
ai
ai
bi
ai
ai
Fi1
Fi2
𝐹𝑖1
𝑐
𝐹𝑖1
𝑞
𝜃𝑖
ri
A1
A2
P1
P2
𝛼𝑖
𝛾𝑖
𝜑𝑖
Li1
𝛽𝑖2
𝛽𝑖1
Figure 2. Geometric of the joint based on the antag-
onistic configuration of two PAMs.
the load cell mounted on each PAM. The joint torque
(
M
) can be calculated based on the robot’s inverse
dynamics from Equation
(1)
, theoretically. However,
in practice, the precise calculation of the robot’s joint
torques is complicated since the determination of coef-
ficients in
H
(
q
),
V
(
q, ˙q
), and
G
(
q
)is very complicated
and less precise. This research uses a neural network
to approximate the joint torque
M
to overcome this
difficulty. The estimation of the human torque
ˆ
MHM
can be computed from the approximated torques of
the neural networks MNN as:
ˆ
MHM =MN N −MP AM .(4)
3.1. Calculating the torque generated
by PAMs (MP AM )
Consider the geometric model of a robot joint in Fig-
ure 2. In this figure,
Fij
are the forces generated
by the anterior and posterior PAMs of joint
i
, and
j
= 1
,
2represents the anterior and posterior PAMs.
Ri
is the rotation radius of the joint.
Mi
is the mo-
ment of anterior and posterior PAMs effect on joint
i
.
Fq
ij
and
Fc
ij
are the rotation and centripetal elements
of
Fij
.
βij
is the angle between
Fij
and its centripetal
components. Based on the geometric of the joint, two
angles αi=const and γi=const we have:
φi=π−αi−γi−θi.(5)
Consider the triangle
OiA1A2
, we can calculate the
length of Li1as:
Li1=qR2
i+r2
i−2Riricos φi.(6)
In addition, we also have:
181
V-V. Dinh, M-C. Trinh, T-D. Bui et al. Acta Polytechnica
Input
Log-Sigmoid Layer
Liner Layer Output
q
q
q
M
Figure 3. Neural network model.
ri=qL2
i1+R2
i−2Li1Ricos βi1.(7)
Therefore:
βi1= arccos L2
i1+R2
i−r2
i
2Li1Ri
.(8)
As a result, the torque generated by the artificial
muscle at ith joint will be performed as follows:
MP AMi = (Fi1sin βi1−Fi2sin βi2)Ri.(9)
3.2.
Estimating the total torque applied
to robot joints (MNN )
The developed rehabilitation robot system contains
uncertainties in the system dynamic structure and
parameters. Thus, the model-based calculation of ap-
plied joint torques (inverse dynamics) such as in [
27
]
cannot improve the accuracy of torque estimations.
However, Neural Networks are proved to be an effi-
cient tool to approximate a wide variety of exciting
functions [
28
]. Thus, in this paper, Neural Networks
are used to estimate the total robot joint torques.
This research uses two independent neural networks
for each hip and knee joint. As shown in the robot
dynamic Equation
(1)
, the joint torque is the function
of joint acceleration, velocity, and position. Then,
each neural network to estimate joint torque includes
three inputs corresponding to the joint acceleration,
velocity, and position. Moreover, each neural network
has only one output corresponding to the estimated
joint torque. In addition, each neural network includes
two layers as follows:
-
Layer 1: The transfer function is the logsig function,
and the number of neurals is 4.
-
Layer 2: The transfer function is the purely linear
function, and the number of neurals is 1.
-
The objective function is chosen as the difference
between the actual and estimated output:
MSE =1
n
n
P
i=1
(yi−byi)2.
-
The learning method is the back-propagation
method Levenberg Marquardt.
0 2 4 6 8 10 12
-10
0
10
20
qHip (°)
0 2 4 6 8 10 12
-40
-20
0
20
40
0 2 4 6 8 10 12
-1000
-500
0
500
1000
0 2 4 6 8 10 12
Time(s)
-2
0
2
4
6
MHip (Nm)
Measured Torque Estimated Torque
Figure 4. Sample input and output of the neural
network for hip joint.
To obtain the training data of the neural network,
the developed robot system is controlled to track the
reference trajectory without a load (i.e. without re-
habilitation object). Then, the torques generated by
PAMs that affect robot joints are collected as output
data. The actual joint acceleration, velocity, and posi-
tion are collected as input data for the training. The
sample input and output are shown in Figure 4 and
Figure 5 for hip and knee joint, respectively.
Utilising the neural network toolbox in Matlab to
train the proposed neural networks, we obtain the
weight and bias coefficients for the two following net-
works. For the neural network that is used to estimate
hip joint’s torque:
wh1=
0.2501 −0.0160 0.0001
0.2824
0.7430
0.0337
0.0654
−0.0194
0.0039
−0.0004
0.0002
0.0000
,
bh1=
0.7303
3.1417
8.0478
−0.9932
,
wh2=3.4649 0.4422 2.7205 13.3358 ,
bh2=−6.5336 .
For the neural network that is used to estimate knee
joint’s torque:
182
vol. 63 no. 3/2023 Neural Network Based Patient Recovery Estimation
0 2 4 6 8 10 12
-30
-20
-10
0
qKnee (°)
0 2 4 6 8 10 12
-50
0
50
0 2 4 6 8 10 12
-1000
-500
0
500
1000
0 2 4 6 8 10 12
Time(s)
-3
-2
-1
0
1
MKnee (Nm)
Measured Torque Estimated Torque
Figure 5. Sample input and output of the neural
network for knee joint.
wk1=
−0.0814 −0.0026 −0.0000
−0.0463
−0.0786
−0.0540
−0.0455
−0.0027
0.0419
−0.0003
−0.0000
0.0000
,
bk1=
−1.3038
−0.1466
−1.2532
−0.1153
,
wk2=−1.3840 −1.1626 −1.3612 −1.0918 ,
bk2= 2.1821 ,
where
wij
and
bij
are the weight and bias of the neural
network, with
i
=
h
for hip, and
i
=
k
for knee joint,
j= 1,2represents the jth layer of neurons.
Both fourth sub-figures of Figure 4 and Figure 5
show the estimated torques using a neural network in
comparison to the actual torques. It can be seen that
a precise approximation is obtained. The root mean
square error (RMSE) is under 0.2 Nm for both joints.
Hence, we can conclude that the estimation has a
high accuracy. To verify the estimation’s accuracy,
the robot is operated in the trajectory tracking mode
with a lower frequency (0.3Hz). Both torques, includ-
ing the estimation from NNs (
MNN
) and inverse one
(
MIN V
) computed from inverse dynamic Equation
(1)
are obtained for an analysis. As shown in Figure 6,
in comparison to estimation using inverse dynamics
0 2 4 6 8 10 12 14 16 18 20
-2
0
2
4
6
Momen Hip (Nm)
MINV MNN MPAMs
0 2 4 6 8 10 12 14 16 18 20
Time(s)
-3
-2
-1
0
Momen Knee (Nm)
Figure 6. Comparison of the torque estimation re-
sults for neural network and inverse dynamic when
tracking a 0.3 Hz gait patterns.
calculation, the estimation using a neural network
achieves a much better precision. The high deviation
in inverse dynamics calculation can be attributed to
the fact that it cannot estimate the unknown com-
ponent forces, such as friction, external disturbance,
and other unmodelled dynamics.
3.3.
Estimation of the patient’s recovery
After determining the total applied torque
MNN
and computing the torque generated by the PAMs
(
MP AM
), the external torques generated by the human
can be calculated using Equation
(4)
. This method
allows for the easy estimation of the patient’s recovery
over time from the torques generated by the human.
To verify the accuracy of this proposed method for
estimating the torque generated by the patients, an
experiment was conducted to estimate the torque gen-
erated by a load. In this experiment, a dumbbell was
attached at the centre of mass of the robot’s hip joint,
and the robot was controlled to follow the reference
gait trajectory at a frequency of 0.5 Hz. The moment
of the dumbbell can be quickly obtained through the
joint angle and distance from its position to the ro-
tation point. This information can then be used to
calculate the external torque generated by the load
and to validate the accuracy of the proposed method
for estimating the torque generated by a patient dur-
ing rehabilitation.
Figure 7 show that the estimation of the torque gen-
erated by the dumbbell is highly accurate, with RMSE
is under 0.26 Nm. Although the error is still there, it
is inevitable when we depend on the theoretical model
for the estimation and verification. Positive dumb-
bell estimation results make it possible to estimate
the patient’s rehabilitation (also known as the torque
estimate of the human muscle). The following section
will use the patient’s recovery estimate to control the
gait training robot.
183
V-V. Dinh, M-C. Trinh, T-D. Bui et al. Acta Polytechnica
0 2 4 6 8 10 12
-0.2
0
0.2
0.4
0.6
Momen (Nm)
MEstimated MLoad
Figure 7. Estimation verification with the external
load is a 5 kg-dumbbell.
3.4. Robot impedance control
One of the essential criteria of a rehabilitation robot
is its stiffness, or impedance. The nominal pressure
supply to the antagonistic actuator’s two PAMs deter-
mines its stiffness property. This study employs the
stiffness-nominal pressure relationship presented by
Choi et al. [
29
]. The compliance
γi
of an antagonistic
actuator driven by PAMs is calculated as follows:
γi=θi
2r2K0iθi+K1i(r2πP0ei −Pef ixei r) + K1ir2∆Pi
,(10)
where
γi
is the compliance of joint
i
,∆
Pi
represents
the pressure values that can be controlled in the pneu-
matic artificial muscles (PAMs), which are considered
as arbitrary functions of time. The symbol
r
is used
to denote the radius of the disks for the hip and knee
joints in the robotic gait training orthosis;
K0i
and
K1i
are parameters of the PAM numerical model (see
Table 2),
xei
as the PAM length is expressed in
θi
, and
P0ei
and
Pefi
are the nominal pressures for extension
PAM and the difference in nominal pressures for the
PAMs powering hip and knee sagittal plane joints,
respectively.
Actuators K0i [N] K1i [N
100kPa ]
Hip PAMs 0.691 1.096
Knee PAMs 0.572 0.835
Table 2. The spring parameters of the used PAMs.
Figure 8 depicts the robotic orthosis’ impedance
control design. The external force effect to the robot
Fex
can be used to control the robot’s impedance.
The notion of robotic orthosis impedance control is
to set the robot impedance high (low compliance)
if the external force opposes the rotating movement
(prevents movement). In the opposite situation, if the
external torque supports the robot’s movement, the
robot’s impedance is reduced. The following equation
represents the impedance controller’s control signal.
Figure 8. The neural network-based impedance con-
trol diagram of gait training robot.
∆P0i,t =(KuiMestimated ,if Mestimated >0
0,otherwise ,(11)
where
Kui
is the positive gain that is tuned based
on the initial pressure
P0i
and the estimation torque
Mestimated
. Since the impedance controller only in-
creases joint compliance, the initial state of the robot
is set with the maximum impedance that strictly
guides the patient to designate trajectories. For the
safety requirement, the initial pressure of PAMs is the
upper limit of the impedance controller’s control sig-
nal. In addition, an adaptive sliding mode control is
inherent from previous research in [
30
] for a trajectory
tracking purpose.
4. Experiments and results
4.1. Experiment Setup
To evaluate the effectiveness of the controller when
adding an estimate of the patient’s recovery, we used
two bicycle tubes attached to the hip and knee joints
for creating cycling forces. The test process to eval-
uate the control quality in this research is based on
the set trajectory. The signals for the robot joints
are taken according to the sample trajectory of the
human foot with maximum elasticity:
−
12
◦
/
−
17
◦
for
the hip joint and
−
29
◦
/
−
0
◦
for the knee joint. The
controller’s sampling time is 5 ms. The actual image
of the experimental setup is given in Figure 9. The
robot is set to trajectory tracking mode in the experi-
ment’s first phase. In the second step, the impedance
control is turned on to regulate the robot joint compli-
ance after the system is stable. During experiments,
data on each joint’s desired, measured trajectories and
compliance are gathered for evaluation.
4.2. Experimental results
The mean of all observed trajectories is derived first
to evaluate the system’s performance in trajectory
tracking mode. The maximum tracking error (MTE)
and root mean square tracking error (RMSTE) be-
tween the measured and intended trajectories are then
determined and presented in Table 3. Figure 10 de-
picts the tracking performances of the BK-Gait robot
184
vol. 63 no. 3/2023 Neural Network Based Patient Recovery Estimation
Figure 9. Experimental platform.
0 2 4 6 8 10 12
-30
-20
-10
0
10
Knee Angle (°)
Desired MeasuredTrack MeasuredImp
0 2 4 6 8 10 12
Time(s)
-10
0
10
20
Hip Angle (°)
Desired MeasuredTrack MeasuredImp
Figure 10. Tracking performance of the BK-Gait
robot when operating in trajectory tracking and
impedance control mode. The blue line is the de-
sired trajectory. The black dash line and dash-dot red
line represent the measured trajectories in trajectory
tracking and impedance control mode, respectively.
in both trajectory tracking and impedance control
modes. We can see that the robot always tracks the
desired trajectory in both operating modes. In de-
tail, the MTE and RMSTE are below 3.35
◦
for both
hip and knee joints in trajectory tracking mode. The
tracking performance is somewhat decreased in the
impedance control mode, with MTE = 5.91
◦
and
RMSTE = 2.89
◦
. It commonly happens in rehabilita-
0 2 4 6 8 10 12
0
0.5
1
1.5
2
2.5
3
3.5
Hip compliance (rad/Nm)
Trajectory tracking mode Impedance control mode
0 2 4 6 8 10 12
Time(s)
0
1
2
3
4
Knee compliance (rad/Nm)
Trajectory tracking mode Impedance control mode
Figure 11. Joint compliance of the robot in trajectory
tracking and impedance control mode.
Trajectory Impedance
Parameter tracking control control
Hip Knee Hip Knee
MTE [◦] 2.2 3.4 3.6 5.9
RMSTE [◦] 1.2 1.8 1.8 2.9
Max compli-
ance
[Rad·Nm−1] 0.9 1.8 2.7 3.0
Table 3. Experimental evaluation.
tion robots, allowing patients to be more confident in
impedance control mode. In comparison to the simi-
lar configuration PAM-based robot orthosis in [
8
,
27
],
the BK-Gait robot achieves an equivalent trajectory
tracking performance in the impedance control mode.
For example, the MTE of the Airgait in [
8
] is about
6.81
◦
and the 7-DOF robot’s MTE [
8
] is less than 15
◦
.
Figure 11 shows the robot joints’ compliances
in both scenarios of the experiment. When the
robot is set for trajectory tracking purposes with
a high impedance, the joints’ compliances reach
0.92 rad
·
Nm
−1
for the hip joint and 1.83 rad
·
Nm
−1
for the knee joint. When the impedance control
mode is enabled, the robot compliance increases to
2.69 rad
·
Nm
−1
and 3.01 rad
·
Nm
−1
for the hip and knee
joints, respectively, in response to the external force
from the tubes. While the tracking controller remains
steady, the impedance controller may modify its joint
compliance to the patient recovery represented by the
external force. The impedance controller performs
effectively when adapting the joints’ compliances to
the external force representing the human effort. We
can observe that the joints’ compliance changes are
185
V-V. Dinh, M-C. Trinh, T-D. Bui et al. Acta Polytechnica
similar to the two counter systems reported in [
8
,
27
].
5. Conclusion
In this paper, a neural network-based method was
proposed to estimate the patient’s recovery, an impor-
tant factor for a gait training robot system powered
pneumatic artificial muscles. Since the robot system
operates at a slow velocity range, the neural network
structure can be kept simple, and the training data can
be collected without the need for measuring external
forces, making it easy to implement in practice with
highly accurate estimation. The estimated patient
recovery is then used for the impedance control of the
gait training robot system, leading to improved joint
compliance coefficients, which make patients more
comfortable and confident in performing rehabilita-
tion exercises. In the future, the developed system
will be tested with real human subjects to evaluate
its effectiveness in practice. Overall, this study offers
a promising approach for enhancing the rehabilitation
process and improving the quality of life for patients.
Acknowledgements
This research is funded by Hanoi University of Science
and Technology (HUST) under project number T2022 –
PC – 002.
References
[1] M. Kyrarini, F. Lygerakis, A. Rajavenkatanarayanan,
et al. A survey of robots in healthcare. Technologies
9(1):8, 2021.
https://doi.org/10.3390/technologies9010008
[2] G. Morone, S. Paolucci, A. Cherubini, et al. Robot
assisted gait training for stroke patients: Current state
of the art and perspectives of robotics. Neuropsychiatric
disease and treatment 13(1):1303–1311, 2017.
https://doi.org/10.2147/NDT.S114102
[3] D. B. Reynolds, D. W. Repperger, C. A. Phillips,
G. Bandry. Modeling the dynamic characteristics of
pneumatic muscle. Annals of Biomedical Engineering
31(3):317–319, 2003.
https://doi.org/10.1114/1.1554921
[4] C.-P. Chou, B. Hannaford. Measurement and modeling
of McKibben pneumatic artificial muscles. IEEE
Transactions on Robotics and Automation 12(1):90–102,
1996. https://doi.org/10.1109/70.481753
[5] T.-Y. Choi, J.-J. Lee. Control of manipulator using
pneumatic muscles for enhanced safety. IEEE
Transactions on Industrial Electronics 57(8):2815–2825,
2010. https://doi.org/10.1109/TIE.2009.2036632
[6] X. Cheng, Y. Zhou, C. Zuo, X. Fan. Design of an
upper limb rehabilitation robot based on medical theory.
Procedia Engineering 15:688–692, 2011.
https://doi.org/10.1016/j.proeng.2011.08.128
[7] L. Zhao, H. Cheng, Y. Xia, B. Liu. Angle tracking
adaptive backstepping control for a mechanism of
pneumatic muscle actuators via an AESO. IEEE
Transactions on Industrial Electronics 66(6):4566–4576,
2019. https://doi.org/10.1109/TIE.2018.2860527
[8] Q.-T. Dao, S.-i. Yamamoto. Assist-as-needed control
of a robotic orthosis actuated by pneumatic artificial
muscle for gait rehabilitation. Applied Sciences
8(4):499, 2018.
https://doi.org/10.3390/app8040499
[9] M.-C. Trinh, T.-H. Do, Q.-T. Dao. Development of a
rehabilitation robot: Modeling and trajectory tracking
control. ASEAN Engineering Journal 12(4):121–129,
2022. https://doi.org/10.11113/aej.v12.17196
[10] P. Beyl, M. Van Damme, R. Van Ham, et al. Pleated
pneumatic artificial muscle-based actuator system as a
torque source for compliant lower limb exoskeletons.
IEEE/ASME Transactions on Mechatronics
19(3):1046–1056, 2014.
https://doi.org/10.1109/TMECH.2013.2268942
[11] C.-T. Chen, W.-Y. Lien, C.-T. Chen, et al. Dynamic
modeling and motion control of a cable-driven robotic
exoskeleton with pneumatic artificial muscle actuators.
IEEE Access 8:149796–149807, 2020.
https://doi.org/10.1109/ACCESS.2020.3016726
[12] Z. Q. Tang, H. L. Heung, X. Q. Shi, et al. Probabilistic
model-based learning control of a soft pneumatic glove
for hand rehabilitation. IEEE Transactions on
Biomedical Engineering 69(2):1016–1028, 2022.
https://doi.org/10.1109/TBME.2021.3111891
[13] C. M. Thalman, M. Debeurre, H. Lee. Entrainment
during human locomotion using a soft wearable ankle
robot. IEEE Robotics and Automation Letters
6(3):4265–4272, 2021.
https://doi.org/10.1109/LRA.2021.3066961
[14] Q.-T. Dao, V.-V. Dinh, M.-C. Trinh, et al. Nonlinear
extended observer-based ADRC for a lower-limb
PAM-based exoskeleton. Actuators 11(12):369, 2022.
https://doi.org/10.3390/act11120369
[15] Y. Wang, Q. Xu. Design and testing of a soft parallel
robot based on pneumatic artificial muscles for wrist
rehabilitation. Scientific Reports 11:1273, 2021.
https://doi.org/10.1038/s41598-020-80411-0
[16] P. Ohta, L. Valle, J. King, et al. Design of a
lightweight soft robotic arm using pneumatic artificial
muscles and inflatable sleeves. Soft Robotics 5(2):204–
215, 2018. https://doi.org/10.1089/soro.2017.0044
[17] A. Colomé, D. Pardo, G. Alenyà, C. Torras. External
force estimation during compliant robot manipulation.
In 2013 IEEE International Conference on Robotics and
Automation, pp. 3535–3540. 2013.
https://doi.org/10.1109/ICRA.2013.6631072
[18] E. Berger, S. Grehl, D. Vogt, et al. Experience-based
torque estimation for an industrial robot. In 2016 IEEE
International Conference on Robotics and Automation
(ICRA), pp. 144–149. 2016.
https://doi.org/10.1109/ICRA.2016.7487127
[19] A. Wahrburg, E. Morara, G. Cesari, et al. Cartesian
contact force estimation for robotic manipulators using
Kalman filters and the generalized momentum. In 2015
IEEE International Conference on Automation Science
and Engineering (CASE), pp. 1230–1235. 2015.
https://doi.org/10.1109/CoASE.2015.7294266
[20] Y. Lu, Y. Shen, C. Zhuang. External force
estimation for industrial robots using configuration
optimization. Automatika 64(2):365–388, 2023.
https://doi.org/10.1080/00051144.2023.2166451
186
vol. 63 no. 3/2023 Neural Network Based Patient Recovery Estimation
[21] A. C. Smith, F. Mobasser, K. Hashtrudi-Zaad.
Neural-network-based contact force observers for haptic
applications. IEEE Transactions on Robotics
22(6):1163–1175, 2006.
https://doi.org/10.1109/TRO.2006.882923
[22] N. Yilmaz, J. Y. Wu, P. Kazanzides, U. Tumerdem.
Neural network based inverse dynamics identification
and external force estimation on the da Vinci research
kit. In 2020 IEEE International Conference on Robotics
and Automation (ICRA), pp. 1387–1393. 2020.
https://doi.org/10.1109/ICRA40945.2020.9197445
[23] Z. Chua, A. M. Okamura. Characterization of
real-time haptic feedback from multimodal neural
network-based force estimates during teleoperation. In
2022 IEEE/RSJ International Conference on Intelligent
Robots and Systems (IROS), pp. 1471–1478. 2022.
https://doi.org/10.1109/IROS47612.2022.9981662
[24] J. Y. Wu, N. Yilmaz, U. Tumerdem, P. Kazanzides.
Robot force estimation with learned intraoperative
correction. In 2021 International Symposium on
Medical Robotics (ISMR), pp. 1–7. 2021.
https://doi.org/10.1109/ISMR48346.2021.9661568
[25] M. Chiako, B. Mahdi, A. Vahid. Muscle force
estimation from lower limb EMG signals using novel
optimised machine learning techniques. Medical and
Biological Engineering and Computing 60(3):683–699,
2022.
https://doi.org/10.1007/s11517-021-02466-z
[26] B. Siciliano, L. Sciavicco, L. Villani, G. Oriolo.
Robotics: Modelling, Planning and Control. Springer
London, London, 1st edn., 2009.
[27] S. Hussain, S. Q. Xie, P. K. Jamwal. Adaptive
impedance control of a robotic orthosis for gait
rehabilitation. IEEE Transactions on Cybernetics
43(3):1025–1034, 2013.
https://doi.org/10.1109/TSMCB.2012.2222374
[28] R. Uhrig. Introduction to artificial neural networks.
In Proceedings of IECON ’95 – 21st Annual Conference
on IEEE Industrial Electronics, vol. 1, pp. 33–37. 1995.
https://doi.org/10.1109/IECON.1995.483329
[29] T.-Y. Choi, J.-J. Lee. Control of manipulator using
pneumatic muscles for enhanced safety. IEEE
Transactions on Industrial Electronics 57(8):2815–2825,
2010. https://doi.org/10.1109/TIE.2009.2036632
[30] Q.-T. Dao, V. V. Dinh, C. T. Vu, et al. An adaptive
sliding mode controller for a PAM-based actuator.
Engineering, Technology and Applied Science Research
13(1):10086–10092, 2023.
https://doi.org/10.48084/etasr.5539
187
