TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

IDENTIFICATION OF MIMO DYNAMIC SYSTEM USING INVERSE MIMO

NEURAL NARX MODEL

Ho Pham Huy Anh(1), Nguyen Thanh Nam(2)

(1) Ho Chi Minh City University of Technology, VNU-HCM

(2) DCSELAB, University of Technology, VNU-HCM

(Manuscript Received on April 5th, 2012, Manuscript Revised May 15th, 2013)

ABSTRACT: This paper investigates the application of proposed neural MIMO NARX model to

a nonlinear 2-axes pneumatic artificial muscle (PAM) robot arm as to improve its performance in

modeling and identification. The contact force variations and nonlinear coupling effects of both joints of

the 2-axes PAM robot arm are modeled thoroughly through the novel dynamic inverse neural MIMO

NARX model exploiting experimental input-output training data. For the first time, the dynamic neural

inverse MIMO NARX Model of the 2-axes PAM robot arm has been investigated. The results show that

this proposed dynamic intelligent model trained by Back Propagation learning algorithm yields both of

good performance and accuracy. The novel dynamic neural MIMO NARX model proves efficient for

modeling and identification not only the 2-axes PAM robot arm but also other nonlinear dynamic

systems.

Keywords: dynamic modeling, pneumatic artificial muscle (PAM), 2-axes PAM robot arm,

inverse identification, neural MIMO NARX model, back propagation (BP) algorithm

1. INTRODUCTION

Rehabilitation robots up to now begin to be

applied for treatment of patients suffering from

et al. [3] added different constant external

loads, by a robot in torque control mode.

Pneumatic

Artificial

Muscle

(PAM)

trauma or stroke. Since the number of patients

actuators are now used in the various fields of

is large and the treatment is time consuming, it

medical robots. The modern robotics toward

is a big advantage if rehabilitation robots can

applications

assist in performing treatment. Noritsugu et al.

between robot actuator and human operator.

[1] designed an arm-like robot for treating

PAM actuator has achieved increasing belief to

patients with trauma, and developed four

the ability of providing advantages such as high

modes of linear motion with impedance control

power/weight ratio, full of hygiene, easiness in

to control the force during the movement.

preservation and especially the capacity of

Krebs et al. [2] designed a planar robot with

human compliance which is the most important

impedance control for guiding patients to make

requirement in medical and human welfare

movements along the specified trajectories. Ju

field. Therefore PAM has been regarded during

requires

greater

friendliness

Trang 13

Science & Technology Development, Vol 16, No.K2- 2013

the recent decades as an interesting alternative

approaches combining conventional methods

to

actuators.

with new learning techniques are required (Lin

Consequently, PAM-based applications have

and Lee, 1991)[13]. Thanks to their universal

been published increasingly. Caldwell et al.

approximation capabilities, neural networks

(2003) in [4] have developed and controlled of

provide the implementation tool for modeling

a PAM-based Soft-Actuated Exoskeleton for

the complex input-output relations of the

use in physiotherapy and training. Kobayashi et

multiple n DOF PAM manipulator which is

al. (2003) in [5] have applied PAM as to

able to solve dynamic problems like variable-

develop a Muscle suit for Upper Body.

coupling complexity and state-dependency.

Noritsugu et al. (2005) in [6] have used PAM

During the last decade several neural network

for developing an Active Support Splint among

models and learning schemes have been

them.

applied to offline learning of manipulator

hydraulic

and

electric

principal

dynamics (Karakasoglu et al., 1993)[14],

difficulty inherent in PAM actuators is the

(Katic et al., 1995)[15], (Lewis et al.,

problem of modeling and controlling them

1999)[16], (Boerlage et al., 2003)[17]. In

efficiently and precisely. This is because they

(Pham et al., 2005)[18], authors applied neuro-

are highly nonlinear and time varying. Since

fuzzy

the rubber tube and plastic sheath are

manipulators for trajectory tracking. Ahn and

continually in contact with each other and the

Anh in [19] have optimized successfully a

PAM shape is continually changing, the PAM

pseudo-linear ARX model of the PAM

temperature varies with use, changing the

manipulator using genetic algorithm. These

properties

time.

authors in (Anh et al., 2007)[20] have

Approaches to PAM modeling and control

identified the highly nonlinear 2-axes PAM

have included PID control, adaptive control

manipulator

(Lilly, 2003)[7], nonlinear optimal predictive

networks. Nevertheless, the drawback of all

control [8], variable structure control [9], and

these

various soft computing approaches including

manipulator as n independent decoupling

intelligent model + phase plane switching

joints. Consequently, all intrinsic coupling

control (Ahn et al., 2006)[10], neuro-fuzzy

features of the n-DOF manipulator have not

model and genetic control in (Carbonell et al.,

represented in its NN model respectively.

Unfortunately,

of

the

up

to

now

actuator

over

2001)[11], (Lilly and Chang, 2003)[12] and so

on.

modeling

results

based

is

and

on

control

of

robot

recurrent

considered

the

neural

n-DOF

To overcome this disadvantage, in this

paper, a new approach of neural networks,

Among such advanced modeling and

proposed dynamic inverse neural MIMO

control schemes, as to guarantee a good

NARX model, firstly utilized in simultaneous

tracking performance, robust adaptive control

modeling and identification of the nonlinear 2-

Trang 14

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

axes PAM robot arm system. The experiment

(also called nodes or neurons), and m

results have demonstrated the feasibility and

outputs units is shown in Fig. 1.

good performance of the proposed intelligent

inverse model which overcomes successfully

external and internal disturbances such as

contact force variations and highly nonlinear

coupling effects of both joints of the 2-axes

PAM robot arm.

The outline of this paper composes of the

Figure 1. Structure of feed-forward MLPNN

section 1 for introducing related works in PAM

robot arm modeling and identification. The

section 2 presents identification procedure of

In Fig.1, w10,.., wq0 and W10,..,Wm0 are

weighting values of Bias neurons of Input

Layer and Hidden Layer respectively.

an inverse neural MIMO NARX model using

Consider an ARX model with noisy input,

back propagation learning algorithm. The

section 3 proves and analyses experimental

studies and results considering the contact

which can be described as

A(q 1 ) y(t ) B(q 1 )u (t T ) C (q 1 )e(t )

(1)

force variations and highly nonlinear coupling

A(q1) 1 a1q1 a2q2

effects of both joints of the nonlinear dynamic

with

system. Finally, the conclusion belongs to the

B(q 1 ) b1 b2 q 1

section 4.

2. IDENTIFICATION USING DYNAMIC

INVERSE

NEURAL

MIMO

C(q1) c1 c2q1 c3q2

where e(t) is the white noise sequence with

NARX

zero mean and unit variance; u(t) and y(t) are

MODEL

2.1. Dynamic Neural MIMO NARX Model

Inverse Neural MIMO NARX model used

input and output of system respectively; q is

the shift operator and T is the time delay.

From equation (1), not consider noise

in this paper is a combination between the

Multi-Layer

Perceptron

Neural

Networks

(MLPNN) structure and the ARX model. Due

to this combination, Inverse MIMO NARX

model possesses both of powerful universal

approximating feature from MLPNN structure

component e(t), we have the general form of

the discrete ARX model in domain z (with the

time delay T=nk=1)

b1 z 1 b2 z 2 ... bnb z nb

y( z 1 )

u ( z 1 ) 1 a1 z 1 a 2 z 2 ... a na z na

and strong predictive feature from nonlinear

ARX model.

(2)

in which na and nb are the order of output

-1

y(z ) and input u(z-1) respectively.

A fully connected 3-layer feed-forward

MLP-network with n inputs, q hidden units

Trang 15

Science & Technology Development, Vol 16, No.K2- 2013

This paper investigates the potentiality of

having only one hidden layer and using

various simple MIMO NARX models in order

sigmoid activation functions. From Fig.1,

to exploit them in modeling, identification and

predictive output value yˆ (t ) is calculated as

control as well. Thus, by embedding a 3-layer

follows:

MLPNN (with number of neurons of hidden

q

yˆi (w,W) Fi WijOj (w) Wi0

j 1

layer = 5) in a 2nd order ARX model with its

characteristic equation derived from (2) as

follows:

y1 (k ) b11u1 (k ) b12u2 (k ) a11 y1 (k 1) a12 y2 (k 1) (3)

y2 (k ) b21u1 (k ) b22u2 (k ) a21 y1 (k 1) a22 y2 (k 1)

We will design the proposed inverse

MIMO Neural NARX11 model (na = 1, nb = 1,

nk =1) with 6 inputs (including u11 (t) and u12(t)

identical to input value u1(t), u21(t) and u22(t)

identical to input value u2 (t), and recurrent

(4)

q

n

Fi Wij. f j wjl zl wj0 Wi0

l 1

j 1

The weights are the adjustable parameters

of the network, and they are determined from a

set of examples through the process called

training. The examples, or the training data as

they are usually called, are a set of inputs, u(t),

and corresponding desired outputs, y(t).

delayed values y1(t-1), y2(t-1)), 2 output values

Specify the training set by:

(y1hat(t), y2hat(t)). Its structure is shown in Fig. 2.

Z N u (t ), y(t ) t 1,..., N (5)

The objective of training is then to

determine a mapping from the set of training

ˆ

data to the set of possible weights: Z

N

so

produce

that

the

network

will

predictions yˆ (t ) , which in some sense are

Figure 2. Structure of MIMO Neural NARX11

model

“closest” to the true joint angle outputs y(t) of

PAM robot arm.

By this way, the parameters a11, a12, b11,

The prediction error approach, which is the

b12 of linear ARX model now become

strategy applied here, is based on the

nonlinear and will be determined from the

introduction of a measure of closeness in terms

weighting values Wij and wjl of the nonlinear

of a mean sum of square error (MSSE)

MIMO Neural NARX model. This feature

criterion:

makes MIMO Neural NARX model very

powerful in modeling, identification and in

model-based advanced control as well.

The class of MLPNN-networks considered

in this paper is furthermore confined to those

Trang 16

EN ,Z N

1

N

y(t) yˆ (t ) y(t) yˆ (t )

2N

t 1

T

(6)

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

Based on the conventional error Back-

Error to be minimized:

Propagation (BP) training algorithms, the

W ( k 1) W ( k )

E (W k )

W k

1 m

y i y i 2

2 i 1

E

weighting value is calculated as follows:

(7)

with k is kth iterative step of calculation and

is learning rate which is often chosen as a

(10)

Using chain rule method, we have:

E

E y i S i

W ij

y i S i W ij

(11)

From equation (10), the following equation

small constant value.

Concretely, the weights Wij and wjl of

is derived.

neural NARX structure are then updated as:

E

y i yi

y i

W ij k 1 W ij k W ij k 1

W ij k 1 . i .O

(12)

(8)

j

q

i y i 1 y i y i y i

S i W ij .O j bias i as

with

sum

j 1

with

i is search direction value of ith

neuron of output layer (i=[1 m]); Oj is the

th

output value of j

neuron of hidden layer

(j=[1 q]); yi and y i are truly real output

and predicted output of i

th

neuron of output

calculation at ith node of output layer

and y i

1

, it gives

1 e Si

yi e Si 1 1

1

1

1

2

Si

S

i

Si 1 e

1 e 1 e Si

layer (i=[1 m]), and

(13)

yi 1 yi

w jl k 1 w jl k w jl k 1

w jl k 1 . j .u l

(9)

m

j O j 1 O j iW ij

S i

Oj

Wij

(14)

i 1

in which

j is search direction value of jth

Replace (12), (13), (14) to (11) and then

put all to (7), the following equation is derived.

neuron of hidden layer (j=[1 q]); Oj is the

W ij k 1 W ij k W ij k 1

output value of jth neuron of hidden layer

W ij k 1 . i .O

th

(j=[1 q]); ul is input of l neuron of input

layer (l=[1 n]).

These results of equations (8) and (9) are

demonstrated as follow in case of sigmoid

being activate function of hidden and output

(15)

j

i y i 1 y i y i y i

Equation (8) has been demonstrated.

The same way for updating the weights of

hidden layer, using the chain rule method, we

have:

layer. Consider in case of output layer:

Trang 17

Science & Technology Development, Vol 16, No.K2- 2013

2.2. Experiment Set Up

E

E O j S j

w jl O j S j w jl

(16)

Then

m

E

E S i

[

]

O j i 1 S i O j

E q

W

O

bias

ij j

i

i 1

S i O j j 1

m

m

i 1

m

Wij iWij

i

i 1

E

S

(17)

Figure 3. Block diagram for working principle of

n

S j w jl .u l bias j

with

as sum

the 2-axes PAM robot arm.

l 1

calculation at jth node of hidden layer and

Oj

1

S

1 e j

O j

e

S j

S j

2-axes PAM robot arm shown through the

, it gives

schematic diagram of the 2-axes PAM robot

arm and the photograph of the experimental

11

1

1 e 1 e

S j 2

S j

1

1

S

1 e j

O j 1 O j

S j

w jl

A general configuration of the investigated

(18)

apparatus are shown in Fig.3 and Fig.4,

respectively. Both of joints of the 2-axes PAM

robot

arm

are

simultaneously

ul

(19)

modeled

through

and

identified

proposed

neural

MIMO NARX model.

The hardware includes an IBM compatible

Replace (17), (18), (19) to (16) and then

put all to (7), the following equation is derived.

w jl k 1 w jl k w jl k 1

w jl k 1 . j .u l

m

j O j 1 O j iWij

i 1

Equation (9) has been demonstrated.

PC (Pentium 1.7 GHz) which sends the voltage

signals u1(t) and u2(t) to control the two

proportional valves (FESTO, MPYE-5-1/8HF-

(20)

710B), through a D/A board (ADVANTECH,

PCI 1720 card) which changes digital signals

from PC to analog voltage u1(t) and u2(t)

respectively. The rotating torque is generated

by the pneumatic pressure difference supplied

from air-compressor between the antagonistic

artificial muscles. Consequently, the both of

Trang 18

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

joints of the 2-axes PAM robot arm will be

Table 1. The lists of experimental hardware

rotated to follow the desired joint angle

references (YREF1 (k) and YREF2(k)) respectively.

The joint angles, 1[deg] and 2 [deg], are

detected by two rotary encoders (METRONIX,

H40-8-3600ZO) and fed back to the computer

through a 32-bit counter board (COMPUTING

MEASUREMENT, PCI QUAD-4 card) which

changes digital pulse signals to joint angle

values y1 (t) and y2(t). Simultaneously, through

an A/D board (ADVANTECH, PCI 1710 card)

which will send to PC the external force value

3. IDENTIFICATION USING DYNAMIC

INVERSE

NEURAL

MIMO

NARX

MODEL

which is detected by a force sensor CBFS-10.

The pneumatic line is conducted under the

pressure of 5[bar] and the software control

algorithm of the closed-loop system is coded in

C-mex program code run in Real-Time

In general, the procedure which must be

executed when attempting to identify a

dynamical system consists of four basic steps

(see Fig.5)

Windows Target of MATLAB-SIMULINK

STEP 1 (Getting Training Data)

environment.

the

STEP 2 (Select Model Structure)

configuration of the hardware set-up installed

STEP 3 (Estimate Model)

STEP 4 (Validate Model:

Table

1

presents

from Fig.3, and Fig.4.

Force

Sensor

Figure 4. Photograph of the experimental 2-axes

Figure 5. Neural MIMO NARX Model

PAM robot arm.

Identification procedure

Trang 19

Science & Technology Development, Vol 16, No.K2- 2013

To realize Step 1, Fig.6 presents the PRBS

the

hardware

using

the tested 2-axes PAM robot arm and the

angle of both of PAM antagonistic pair. The

responding end-effector external force and joint

experiment results of 2-axes PAM robot arm

angle outputs collected from force sensor and

force/position control prove that experimental

rotary encoders. This experimental PRBS

control voltages u1 (t) and u2(t) applied to both

input-output data is used for training and

of PAM antagonistic pairs of the 2-axes PAM

validating the Inverse neural MIMO NARX

robot arm is to function well in these ranges.

model of the whole dynamic two-joint structure

Likewise, the chosen frequency of PRBS-1(2)

of the 2-axes PAM robot arm as illustrated in

signals is also chosen carefully based on the

Fig.7.

working frequency of the 2-axes PAM robot

arm will be used as an elbow and wrist 2-axes

JOINT 2 - PRBS TRAINING DATA

[V ]

PRBS input

5.5

PRBS input

PAM-based rehabilitation robot in the range of

5

4.5

0

10

20

30

40

50

60

70

80 0

60

10

20

30

40

50

60

70

80

(0.025 – 0.2) [Hz].

JOINT ANGLE output

JOINT ANGLE output

JOINT 1 - INVERSE PRBS TRAINING DATA

40

20

JOINT 2 - INVERSE PRBS TRAINING DATA

40

60

JOINT ANGLE 2 input

JOINT ANGLE 1 input

20

40

20

0

[d e g ]

0

-20

-20

20

0

0

-20

-40

0

10

20

30

40

50

F O R C E [N ]

60

40

-40

60

70

80 0

External FORCE 60

Filtered FORCE

40

-20

10

20

30

40

50

60

70

80

External FORCE

Filtered FORCE

-40

300

10

20

30

40

50

60

70

-40

80 300

20

20

0

10

20

30

40

50

60

70

0

80 0

10

20

30

40

50

60

experiment

PRBS-1(2) inputs and Force/Joint Angle

outputs during (40–80)[s] will be used for

while

PRBS-1(2)

70

20

30

40

50

10

20

30

40

50

0

inputs

and

0

10

20

30

40

50

5.5

60

70

PRBS1 output

0

5.5

5

5

4.5

4.5

0

10

20

30

40

50

t [sec]

60

70

0

80 0

10

20

30

40

50

t [sec]

Figure 7. Inverse Neural MIMO NARX Model

Training data obtained by experiment

structure. A nonlinear neural NARX model

The range (4.4 – 5.6) [V] and the shape of

structure is attempted. The full connected

st

60

70

80

PRBS2 output

(0–40)[s] will be used for validation purpose.

PRBS-1 voltage input applied to the 1 joint as

Multi-Layer Perceptron (MLPNN) network

well as the range (4.5 – 5.5) [V] and the shape

architecture composes of 3 layers with 5

of PRBS-2 voltage input applied to rotate the

neurons in hidden layer is selected (results

joint of the 2-axes PAM robot arm is

derived from Ahn et al., 2007 [24]). The final

chosen carefully from practical experience

structure of proposed Inverse neural MIMO

Trang 20

80

FORCE INPUT

80

The 2nd step relates to select model

2

70

10

Force/Joint Angle outputs in the lapse of time

nd

60

20

FORCE INPUT

80

[V ]

Figure 6. Input-Output training data obtained by

training,

10

[N ]

20

10

0

set-up

proportional valve to control rotating joint

5.5

5

4.5

[d e g ]

on

input applied simultaneously to the 2 joints of

JOINT 1 - PRBS TRAINING DATA

40

based

60

70

80

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

NARX11 used in proposed neural MIMO

voltage values u1(k-1), u2(k-1) respectively of

NARX FNN-PID hybrid force/position control

experimental modeling block diagram depicted

scheme is shown in Fig.8.

in Fig.9.

The proposed neural MIMO NARX11

model structure is defined as a nonlinear neural

MLPNN integrated a 1st order ARX model

(with nA=1; nB=1 and nK=1) possessed 5

neurons in hidden layer. The activating

function applied in neurons of hidden Layer

and of output layer is hyperbolic tangent

function and linear function respectively. Fig.9

represents the experiment block diagram for

modeling and identifying the Inverse neural

MIMO NARX11 model of the 2-axes PAM

Figure 9. Block diagram for modeling of Inverse

robot arm.

Neural MIMO NARX model of the 2-Axes PAM

2-AXES PAM ROBOT ARM - NEURAL MIMO INVERSE NARX MODEL

robot arm

u23(t)

ESTIMATION of NEURAL INVERSE MIMO NARX

-1

10

FITNESS CONVERGENCE

u22(t)

u21(t)

yhat2(t)

y2(t-1)

u12(t)

yhat1(t)

FITNESS

u13(t)

-2

10

u11(t)

y1(t-1)

Figure 8. Structure of proposed Inverse neural

-3

10

MIMO NARX11 models of 2-axes PAM robot arm

In Fig.8, input values u11(t)/ u21(t), u12(t)/

u22(t), u13(t)/ u23(t) and recurrent delayed input

0

10

20

30

40

50

Iteration

60

70

80

90

Figure 10. The fitness convergence of proposed

Neural Inverse MIMO NARX11 Model

values y1(t-1), y2(t-1) in neural structure of

The 3rd step estimates trained Inverse

proposed neural Inverse MIMO NARX11

neural MIMO NARX11 model. A good

model will be identical to input values Joint-1

minimized convergence is shown in Fig.10

Angle y1 (k), Joint-2 Angle y2(k), Force value

with the minimized Mean Sum of Scaled Error

yF(k) and desired recurrent delayed control

(MSSE) value is equal to 0.002659 after

Trang 21

100

Science & Technology Development, Vol 16, No.K2- 2013

number of training 100 iterations with the

proposed Inverse neural MIMO NARX11. An

nonlinear

excellent estimating result, which proves the

models. Applying the same experimental

perfect performance of resulted Inverse Neural

diagram in Fig.6, an excellent validating result,

MIMO NARX model, is also shown in Fig.11.

which proves the performance of resulted

JOINT ANGLE 2 input

JOINT ANGLE 1 input

[de g]

MIMO

NARX

20

0

minimized

0

-20

-20

-40

0

5

10

15

20

25

35

-40

40 0

FORCE input

28

30

28

26

24

24

[N ]

26

6.5 0

5

10

15

20

[V ]

5.5

5

errors

demonstrate

the

good

performance of the Inverse neural MIMO

5

10

15

20

25

30

35

40

NARX11 Model (the excellent error < 0.01[V]

FORCE input

for both of Uh1/Uh2 control voltage values

30

35

406.5 0

PRBS1 reference

6

Uh1 output

5.5

25

6

5

10

15

20

25

30

35

40

PRBS2 reference

Uh2 output

respectively applied to 2 joints of the 2-axes

PAM robot arm).

5

4.5

4.5

0

5

10

15

20

25

30

1

35

40 0

ERROR1

5

10

15

20

25

30

1

0

35

40

ERROR2

0

5

10

15

20

t [sec]

25

30

35

Finally, Table 2 tabulates the resulting

weighting values of proposed Inverse neural

0

-1

MIMO NARX model which can be used not

-1

40 0

5

10

15

20

t [sec]

25

30

35

40

only in modeling identification and simulation

Figure 11. Estimation of 2-axes PAM robot arm

offline but also can be applied effectively

Inverse neural MIMO NARX11 Model

online

VALIDATION of INVERSE NEURAL MIMO NARX - JOINT 1

40

JOINT ANGLE 1 input

20

[d e g ]

Inverse

in Fig.12. The experimental results of the

40

20

neural

Inverse Neural MIMO NARX model, is shown

ESTIMATION of INVERSE NEURAL MIMO NARX - JOINT 2

ESTIMATION of INVERSE NEURAL MIMO NARX - JOINT 1

40

[V ]

The last step relates to validate resulting

VALIDATION of INVERSE NEURAL MIMO NARX - JOINT 2

advanced

control

algorithms (Ahn and Anh, 2011)[21]. The final

JOINT ANGLE 2 input

designed structure of proposed Inverse MIMO

0

-20

model-based

40

20

0

in

NARX11 model is shown in Fig.8.

-20

-40

300

5

10

15

20

25

30

35

40 0

30

5

10

15

20

25

30

FORCE input

40

6. CONCLUSIONS

In this study, a new approach of recurrent

25

[N ]

25

35

FORCE input

neural networks, proposed neural Inverse

20

6.50

5

10

15

20

25

6

20

30

35

40 0

6.5

PRBS1 reference

6

Uh1 output

5.5

5

5

[V ]

5.5

4.5

10

15

20

25

30

35

40

PRBS2 reference

Uh2 output

5

10

15

20

25

30

1

35

Error1

0

40 0

nonlinear 2-axes pneumatic artificial muscle

5

10

15

20

25

30

1

35

40

(PAM) system, has successfully overcome the

Error 1

0

-1

0

5

10

15

20

t [sec]

25

30

35

-1

40 0

MIMO NARX model firstly utilized in

modeling and identification of the highly

4.5

0

[V ]

5

contact force variations, coupled effect and

5

10

15

20

t [sec]

25

30

35

40

nonlinear characteristic of the 2-axes PAM

Figure 12. Validation of 2-axes PAM robot arm

robot arm system. The 2-axes PAM robot

Inverse neural MIMO NARX11 Model

arm’s coupled dynamics was taken into

account. Results of training and testing on the

complex dynamic systems such as 2-axes PAM

Trang 22

TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 16, SỐ K2- 2013

robot arm show that the newly proposed neural

Acknowledgment

Inverse MIMO NARX model presented in this

This research was partially supported by

study is quite suitable to be applied for the

the NAFOSTED and the DCSELAB of Viet

modeling and identification not only the 2-axes

Nam.

PAM robot arm but also other nonlinear

dynamic systems.

Table 2. Resulted weights of Inverse neural MIMO NARX11 – Total Number of weighting values = 57

NHẬN DẠNG HỆ ĐỘNG HỌC MIMO

SỬ DỤNG MƠ HÌNH MIMO NEURAL NARX NGƯỢC

Hồ Phạm Huy Ánh(1), Nguyễn Thanh Nam(2)

(1) Trường Đại học Bách Khoa, ĐHQG-HCM

(2) ĐHQG-HCM

TĨM TẮT: Bài báo khảo sát ứng dụng mơ hình neural MIMO NARX để cải thiện chất lượng

nhận dạng hệ tay máy phi tuyến 2 bậc dùng bắp thịt khí nén nhân tạo (PAM). Các yếu tố như biến động

của lực tiếp xúc hay các ảnh hưởng ghép cặp phi tuyến của 2 khớp nối của tay máy sẽ được nhận dạng

đầy đủ bởi mơ hình neural MIMO NARX ngược thơng qua bộ dữ liệu huấn luyện thực nghiệm đầu vào –

đầu ra. Lần đầu tiên, mơ hình động học nơ rơn MIMO NARX ngược của tay máy 2 bậc dùng bắp thịt khí

nén nhân tạo (PAM) được khảo sát hồn chỉnh. Các kết quả cho thấy mơ hình động học thơng minh

được đề xuất, được huấn luyện bằng thuật tốn Lan Truyền Ngược (BP learning algorithm) cho chất

lượng tốt với độ chính xác khi nhận dạng rất cao. Mơ hình động học nơ rơn MIMO NARX ngược cho

Trang 23

Science & Technology Development, Vol 16, No.K2- 2013

thấy chúng có thể dùng hiệu quả trong nhận dạng không chỉ hệ tay máy PAM 2-bậc mà cho cả các hệ

cơ động học phi tuyến đa biến khác.

Keywords: mô hình động học, bắp thịt khí nén nhân tạo (PAM), tay máy PAM 2 bậc, nhận dạng

mô hình ngược, mô hình nơ rôn MIMO NARX ngược, thuật toán lan truyền ngược (BP).

[7].

REFERENCES

Lilly,

J.

H.,

Adaptive

tracking

for

pneumatic muscle actuators in bicep and

[1].

Noritsugu, T., Tanaka, T., Application of

tricep configurations, IEEE Trans. Neural

rubber artificial muscle manipulator as a

Syst. Rehabil. Eng., , 11, 3, 333–339

rehabilitation robot, IEEE/ASME Trans.

(2003).

Mechatronics, 2, 4, 259–267 (1997).

[8].

[2].

Krebs, H. I., Hogan, N., Aisen, M. L.,

Volpe,

B.

T.,

Robot-aided

Nagaoka, T., Konishi, Y., Ishigaki, H.,

Nonlinear optimal predictive control of

neuro-

rubber artificial muscle, Proc. SPIE- Int.

rehabilitation, IEEE Trans. Rehab. Eng., 6,

Soc. Opt. Eng., 2595, 54–61 (1995).

1, 75–87 (1998).

[9].

[3].

Ju, M.S., Lin, C.C. K., Chen, J.R., Cheng,

H.S., Lin, C.W., Performance of elbow

tracking under constant torque disturbance

in stroke patients and normal subjects,

Clinical Biomech., 17, 640–649 (2002).

[4].

Development and Control of a SoftExoskeleton

Physiotherapy

and

for

Use

in

J.

of

Training,

C. A., VSC position tracking system

involving a large scale pneumatic muscle

actuator, Proc. IEEE Conf. Decision

Control, Tampa, FL, 4302–4307 (1998).

[10]. Ahn, K. K., Thanh, T. D. C., Intelligent

Caldwell, D. G., Tsagarakis, G. N.,

Actuated

Repperger, D. W., Johnson, K. R., Phillips,

phase

plane

switching

control

of

pneumatic artificial muscle manipulators

with

magneto-rheological

brake,

Mechatronics, 16, 2, 85-95 (2006).

Autonomous Robots, 15,1, 21-33 (2003).

[11]. Carbonell, P., Jiang, Z. P., Repperger, D.

[5].

Kobayashi, H., Uchimura, A., Shiiba, T.,

Development of Muscle suit for Upper

Body, Proceedings Intelligent Robots and

Systems

(IROS

2003-IEEE

Int.

W., A fuzzy backstepping controller for a

pneumatic muscle actuator system, Proc.

IEEE Int. Symposium Intelligent Control,

Mexico City, 353–358 (2001).

Conference), 4, 3624-3629 (2003).

[12]. Lilly, J. H. and Chang, X. Tracking control

[6].

Noritsugu, T., Sasaki, D., Takaiwa, M.,

Rehabilitation Robotics: Development of

Active Support Splint driven by Pneumatic

Soft Actuator (ASSIST), Proceedings of

2005 IEEE Int. Con. On Robotics and

Automation, Barcelona, Spain, (2005).

Trang 24

of a pneumatic muscle by an evolutionary

fuzzy controller. IEEE Intell. Automat.

Soft Comput., Sep.2003, vol. 9, no. 3, pp.

227–244.

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

[13]. Lin, C.T., Lee, C.S.G., Neural NetworkBased Fuzzy Logic Control and Decision

[18]. Pham, D.T., Fahmy, A.A., Neuro-fuzzy

System, IEEE Transactions on Computers,

Modeling

40, 12, 1320-1336 (1991).

Manipulators for Trajectory Tracking, 16th

[14]. Karakasoglu,

A.,

Sudharsanan,

S.I.,

Sundareshan, M.K., Identification and

decentralized

dynamical

adaptive

neural

control

using

networks

with

and

Control

of

Robot

IFAC WORLD CONGRESS, Prague, 4-8

(2005).

[19]. Ahn,

K.

K.,

Anh,

H.P.H.,

System

modeling and identification of the two-link

application to robotic manipulators, IEEE

pneumatic

Trans. on neural networks, 4, 6, 919-930

manipulator

(1993).

algorithm, Proceedings 2006 IEEE-ICASE

[15]. Katic, D.M., Vukobratovic, M. K., Highly

efficient robot dynamics learning by

decomposed

connectionist

feed-Inverse

artificial

optimized

muscle

(PAM)

with

genetic

Int. Conf., Busan, Korea, 4744-4749,

(2006).

[20]. Ahn K.K., Anh H.P.H., A new approach of

control structure, lEEE Trans. on syst. man

modeling

and cybern., 25, 1, 145-158 (1995).

pneumatic

and

identification

artificial

muscle

of

the

(PAM)

[16]. Lewis, F. L., Jagannathan, S., Yesildirek,

manipulator based on recurrent neural

A., Neural network control of robot

network, Proceedings IMechE, Part I:

manipulators

Journal

and

nonlinear

systems,

Taylor & Francis (1999).

van

FeedForward

de

Wal,

for

Systems

and

Control

Engineering, 221(I8), 1101-1122 (2007).

[17]. Boerlage, M., Steinbuch, M., Lambrechts,

P.,

of

ModelBased

Motion

Systems,

[21]. Ahn K.K., Anh H.P.H. Compliance ForcePosition Control of the 2-Axes PAM-based

Rehabilitation

Robot

Using

Neural

Proceedings of IEEE Conference on

Networks, Journal of ISA Transactions,

Control Applications, 1, 1158 1163

(2011).

(2003).

Trang 25

IDENTIFICATION OF MIMO DYNAMIC SYSTEM USING INVERSE MIMO

NEURAL NARX MODEL

Ho Pham Huy Anh(1), Nguyen Thanh Nam(2)

(1) Ho Chi Minh City University of Technology, VNU-HCM

(2) DCSELAB, University of Technology, VNU-HCM

(Manuscript Received on April 5th, 2012, Manuscript Revised May 15th, 2013)

ABSTRACT: This paper investigates the application of proposed neural MIMO NARX model to

a nonlinear 2-axes pneumatic artificial muscle (PAM) robot arm as to improve its performance in

modeling and identification. The contact force variations and nonlinear coupling effects of both joints of

the 2-axes PAM robot arm are modeled thoroughly through the novel dynamic inverse neural MIMO

NARX model exploiting experimental input-output training data. For the first time, the dynamic neural

inverse MIMO NARX Model of the 2-axes PAM robot arm has been investigated. The results show that

this proposed dynamic intelligent model trained by Back Propagation learning algorithm yields both of

good performance and accuracy. The novel dynamic neural MIMO NARX model proves efficient for

modeling and identification not only the 2-axes PAM robot arm but also other nonlinear dynamic

systems.

Keywords: dynamic modeling, pneumatic artificial muscle (PAM), 2-axes PAM robot arm,

inverse identification, neural MIMO NARX model, back propagation (BP) algorithm

1. INTRODUCTION

Rehabilitation robots up to now begin to be

applied for treatment of patients suffering from

et al. [3] added different constant external

loads, by a robot in torque control mode.

Pneumatic

Artificial

Muscle

(PAM)

trauma or stroke. Since the number of patients

actuators are now used in the various fields of

is large and the treatment is time consuming, it

medical robots. The modern robotics toward

is a big advantage if rehabilitation robots can

applications

assist in performing treatment. Noritsugu et al.

between robot actuator and human operator.

[1] designed an arm-like robot for treating

PAM actuator has achieved increasing belief to

patients with trauma, and developed four

the ability of providing advantages such as high

modes of linear motion with impedance control

power/weight ratio, full of hygiene, easiness in

to control the force during the movement.

preservation and especially the capacity of

Krebs et al. [2] designed a planar robot with

human compliance which is the most important

impedance control for guiding patients to make

requirement in medical and human welfare

movements along the specified trajectories. Ju

field. Therefore PAM has been regarded during

requires

greater

friendliness

Trang 13

Science & Technology Development, Vol 16, No.K2- 2013

the recent decades as an interesting alternative

approaches combining conventional methods

to

actuators.

with new learning techniques are required (Lin

Consequently, PAM-based applications have

and Lee, 1991)[13]. Thanks to their universal

been published increasingly. Caldwell et al.

approximation capabilities, neural networks

(2003) in [4] have developed and controlled of

provide the implementation tool for modeling

a PAM-based Soft-Actuated Exoskeleton for

the complex input-output relations of the

use in physiotherapy and training. Kobayashi et

multiple n DOF PAM manipulator which is

al. (2003) in [5] have applied PAM as to

able to solve dynamic problems like variable-

develop a Muscle suit for Upper Body.

coupling complexity and state-dependency.

Noritsugu et al. (2005) in [6] have used PAM

During the last decade several neural network

for developing an Active Support Splint among

models and learning schemes have been

them.

applied to offline learning of manipulator

hydraulic

and

electric

principal

dynamics (Karakasoglu et al., 1993)[14],

difficulty inherent in PAM actuators is the

(Katic et al., 1995)[15], (Lewis et al.,

problem of modeling and controlling them

1999)[16], (Boerlage et al., 2003)[17]. In

efficiently and precisely. This is because they

(Pham et al., 2005)[18], authors applied neuro-

are highly nonlinear and time varying. Since

fuzzy

the rubber tube and plastic sheath are

manipulators for trajectory tracking. Ahn and

continually in contact with each other and the

Anh in [19] have optimized successfully a

PAM shape is continually changing, the PAM

pseudo-linear ARX model of the PAM

temperature varies with use, changing the

manipulator using genetic algorithm. These

properties

time.

authors in (Anh et al., 2007)[20] have

Approaches to PAM modeling and control

identified the highly nonlinear 2-axes PAM

have included PID control, adaptive control

manipulator

(Lilly, 2003)[7], nonlinear optimal predictive

networks. Nevertheless, the drawback of all

control [8], variable structure control [9], and

these

various soft computing approaches including

manipulator as n independent decoupling

intelligent model + phase plane switching

joints. Consequently, all intrinsic coupling

control (Ahn et al., 2006)[10], neuro-fuzzy

features of the n-DOF manipulator have not

model and genetic control in (Carbonell et al.,

represented in its NN model respectively.

Unfortunately,

of

the

up

to

now

actuator

over

2001)[11], (Lilly and Chang, 2003)[12] and so

on.

modeling

results

based

is

and

on

control

of

robot

recurrent

considered

the

neural

n-DOF

To overcome this disadvantage, in this

paper, a new approach of neural networks,

Among such advanced modeling and

proposed dynamic inverse neural MIMO

control schemes, as to guarantee a good

NARX model, firstly utilized in simultaneous

tracking performance, robust adaptive control

modeling and identification of the nonlinear 2-

Trang 14

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

axes PAM robot arm system. The experiment

(also called nodes or neurons), and m

results have demonstrated the feasibility and

outputs units is shown in Fig. 1.

good performance of the proposed intelligent

inverse model which overcomes successfully

external and internal disturbances such as

contact force variations and highly nonlinear

coupling effects of both joints of the 2-axes

PAM robot arm.

The outline of this paper composes of the

Figure 1. Structure of feed-forward MLPNN

section 1 for introducing related works in PAM

robot arm modeling and identification. The

section 2 presents identification procedure of

In Fig.1, w10,.., wq0 and W10,..,Wm0 are

weighting values of Bias neurons of Input

Layer and Hidden Layer respectively.

an inverse neural MIMO NARX model using

Consider an ARX model with noisy input,

back propagation learning algorithm. The

section 3 proves and analyses experimental

studies and results considering the contact

which can be described as

A(q 1 ) y(t ) B(q 1 )u (t T ) C (q 1 )e(t )

(1)

force variations and highly nonlinear coupling

A(q1) 1 a1q1 a2q2

effects of both joints of the nonlinear dynamic

with

system. Finally, the conclusion belongs to the

B(q 1 ) b1 b2 q 1

section 4.

2. IDENTIFICATION USING DYNAMIC

INVERSE

NEURAL

MIMO

C(q1) c1 c2q1 c3q2

where e(t) is the white noise sequence with

NARX

zero mean and unit variance; u(t) and y(t) are

MODEL

2.1. Dynamic Neural MIMO NARX Model

Inverse Neural MIMO NARX model used

input and output of system respectively; q is

the shift operator and T is the time delay.

From equation (1), not consider noise

in this paper is a combination between the

Multi-Layer

Perceptron

Neural

Networks

(MLPNN) structure and the ARX model. Due

to this combination, Inverse MIMO NARX

model possesses both of powerful universal

approximating feature from MLPNN structure

component e(t), we have the general form of

the discrete ARX model in domain z (with the

time delay T=nk=1)

b1 z 1 b2 z 2 ... bnb z nb

y( z 1 )

u ( z 1 ) 1 a1 z 1 a 2 z 2 ... a na z na

and strong predictive feature from nonlinear

ARX model.

(2)

in which na and nb are the order of output

-1

y(z ) and input u(z-1) respectively.

A fully connected 3-layer feed-forward

MLP-network with n inputs, q hidden units

Trang 15

Science & Technology Development, Vol 16, No.K2- 2013

This paper investigates the potentiality of

having only one hidden layer and using

various simple MIMO NARX models in order

sigmoid activation functions. From Fig.1,

to exploit them in modeling, identification and

predictive output value yˆ (t ) is calculated as

control as well. Thus, by embedding a 3-layer

follows:

MLPNN (with number of neurons of hidden

q

yˆi (w,W) Fi WijOj (w) Wi0

j 1

layer = 5) in a 2nd order ARX model with its

characteristic equation derived from (2) as

follows:

y1 (k ) b11u1 (k ) b12u2 (k ) a11 y1 (k 1) a12 y2 (k 1) (3)

y2 (k ) b21u1 (k ) b22u2 (k ) a21 y1 (k 1) a22 y2 (k 1)

We will design the proposed inverse

MIMO Neural NARX11 model (na = 1, nb = 1,

nk =1) with 6 inputs (including u11 (t) and u12(t)

identical to input value u1(t), u21(t) and u22(t)

identical to input value u2 (t), and recurrent

(4)

q

n

Fi Wij. f j wjl zl wj0 Wi0

l 1

j 1

The weights are the adjustable parameters

of the network, and they are determined from a

set of examples through the process called

training. The examples, or the training data as

they are usually called, are a set of inputs, u(t),

and corresponding desired outputs, y(t).

delayed values y1(t-1), y2(t-1)), 2 output values

Specify the training set by:

(y1hat(t), y2hat(t)). Its structure is shown in Fig. 2.

Z N u (t ), y(t ) t 1,..., N (5)

The objective of training is then to

determine a mapping from the set of training

ˆ

data to the set of possible weights: Z

N

so

produce

that

the

network

will

predictions yˆ (t ) , which in some sense are

Figure 2. Structure of MIMO Neural NARX11

model

“closest” to the true joint angle outputs y(t) of

PAM robot arm.

By this way, the parameters a11, a12, b11,

The prediction error approach, which is the

b12 of linear ARX model now become

strategy applied here, is based on the

nonlinear and will be determined from the

introduction of a measure of closeness in terms

weighting values Wij and wjl of the nonlinear

of a mean sum of square error (MSSE)

MIMO Neural NARX model. This feature

criterion:

makes MIMO Neural NARX model very

powerful in modeling, identification and in

model-based advanced control as well.

The class of MLPNN-networks considered

in this paper is furthermore confined to those

Trang 16

EN ,Z N

1

N

y(t) yˆ (t ) y(t) yˆ (t )

2N

t 1

T

(6)

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

Based on the conventional error Back-

Error to be minimized:

Propagation (BP) training algorithms, the

W ( k 1) W ( k )

E (W k )

W k

1 m

y i y i 2

2 i 1

E

weighting value is calculated as follows:

(7)

with k is kth iterative step of calculation and

is learning rate which is often chosen as a

(10)

Using chain rule method, we have:

E

E y i S i

W ij

y i S i W ij

(11)

From equation (10), the following equation

small constant value.

Concretely, the weights Wij and wjl of

is derived.

neural NARX structure are then updated as:

E

y i yi

y i

W ij k 1 W ij k W ij k 1

W ij k 1 . i .O

(12)

(8)

j

q

i y i 1 y i y i y i

S i W ij .O j bias i as

with

sum

j 1

with

i is search direction value of ith

neuron of output layer (i=[1 m]); Oj is the

th

output value of j

neuron of hidden layer

(j=[1 q]); yi and y i are truly real output

and predicted output of i

th

neuron of output

calculation at ith node of output layer

and y i

1

, it gives

1 e Si

yi e Si 1 1

1

1

1

2

Si

S

i

Si 1 e

1 e 1 e Si

layer (i=[1 m]), and

(13)

yi 1 yi

w jl k 1 w jl k w jl k 1

w jl k 1 . j .u l

(9)

m

j O j 1 O j iW ij

S i

Oj

Wij

(14)

i 1

in which

j is search direction value of jth

Replace (12), (13), (14) to (11) and then

put all to (7), the following equation is derived.

neuron of hidden layer (j=[1 q]); Oj is the

W ij k 1 W ij k W ij k 1

output value of jth neuron of hidden layer

W ij k 1 . i .O

th

(j=[1 q]); ul is input of l neuron of input

layer (l=[1 n]).

These results of equations (8) and (9) are

demonstrated as follow in case of sigmoid

being activate function of hidden and output

(15)

j

i y i 1 y i y i y i

Equation (8) has been demonstrated.

The same way for updating the weights of

hidden layer, using the chain rule method, we

have:

layer. Consider in case of output layer:

Trang 17

Science & Technology Development, Vol 16, No.K2- 2013

2.2. Experiment Set Up

E

E O j S j

w jl O j S j w jl

(16)

Then

m

E

E S i

[

]

O j i 1 S i O j

E q

W

O

bias

ij j

i

i 1

S i O j j 1

m

m

i 1

m

Wij iWij

i

i 1

E

S

(17)

Figure 3. Block diagram for working principle of

n

S j w jl .u l bias j

with

as sum

the 2-axes PAM robot arm.

l 1

calculation at jth node of hidden layer and

Oj

1

S

1 e j

O j

e

S j

S j

2-axes PAM robot arm shown through the

, it gives

schematic diagram of the 2-axes PAM robot

arm and the photograph of the experimental

11

1

1 e 1 e

S j 2

S j

1

1

S

1 e j

O j 1 O j

S j

w jl

A general configuration of the investigated

(18)

apparatus are shown in Fig.3 and Fig.4,

respectively. Both of joints of the 2-axes PAM

robot

arm

are

simultaneously

ul

(19)

modeled

through

and

identified

proposed

neural

MIMO NARX model.

The hardware includes an IBM compatible

Replace (17), (18), (19) to (16) and then

put all to (7), the following equation is derived.

w jl k 1 w jl k w jl k 1

w jl k 1 . j .u l

m

j O j 1 O j iWij

i 1

Equation (9) has been demonstrated.

PC (Pentium 1.7 GHz) which sends the voltage

signals u1(t) and u2(t) to control the two

proportional valves (FESTO, MPYE-5-1/8HF-

(20)

710B), through a D/A board (ADVANTECH,

PCI 1720 card) which changes digital signals

from PC to analog voltage u1(t) and u2(t)

respectively. The rotating torque is generated

by the pneumatic pressure difference supplied

from air-compressor between the antagonistic

artificial muscles. Consequently, the both of

Trang 18

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

joints of the 2-axes PAM robot arm will be

Table 1. The lists of experimental hardware

rotated to follow the desired joint angle

references (YREF1 (k) and YREF2(k)) respectively.

The joint angles, 1[deg] and 2 [deg], are

detected by two rotary encoders (METRONIX,

H40-8-3600ZO) and fed back to the computer

through a 32-bit counter board (COMPUTING

MEASUREMENT, PCI QUAD-4 card) which

changes digital pulse signals to joint angle

values y1 (t) and y2(t). Simultaneously, through

an A/D board (ADVANTECH, PCI 1710 card)

which will send to PC the external force value

3. IDENTIFICATION USING DYNAMIC

INVERSE

NEURAL

MIMO

NARX

MODEL

which is detected by a force sensor CBFS-10.

The pneumatic line is conducted under the

pressure of 5[bar] and the software control

algorithm of the closed-loop system is coded in

C-mex program code run in Real-Time

In general, the procedure which must be

executed when attempting to identify a

dynamical system consists of four basic steps

(see Fig.5)

Windows Target of MATLAB-SIMULINK

STEP 1 (Getting Training Data)

environment.

the

STEP 2 (Select Model Structure)

configuration of the hardware set-up installed

STEP 3 (Estimate Model)

STEP 4 (Validate Model:

Table

1

presents

from Fig.3, and Fig.4.

Force

Sensor

Figure 4. Photograph of the experimental 2-axes

Figure 5. Neural MIMO NARX Model

PAM robot arm.

Identification procedure

Trang 19

Science & Technology Development, Vol 16, No.K2- 2013

To realize Step 1, Fig.6 presents the PRBS

the

hardware

using

the tested 2-axes PAM robot arm and the

angle of both of PAM antagonistic pair. The

responding end-effector external force and joint

experiment results of 2-axes PAM robot arm

angle outputs collected from force sensor and

force/position control prove that experimental

rotary encoders. This experimental PRBS

control voltages u1 (t) and u2(t) applied to both

input-output data is used for training and

of PAM antagonistic pairs of the 2-axes PAM

validating the Inverse neural MIMO NARX

robot arm is to function well in these ranges.

model of the whole dynamic two-joint structure

Likewise, the chosen frequency of PRBS-1(2)

of the 2-axes PAM robot arm as illustrated in

signals is also chosen carefully based on the

Fig.7.

working frequency of the 2-axes PAM robot

arm will be used as an elbow and wrist 2-axes

JOINT 2 - PRBS TRAINING DATA

[V ]

PRBS input

5.5

PRBS input

PAM-based rehabilitation robot in the range of

5

4.5

0

10

20

30

40

50

60

70

80 0

60

10

20

30

40

50

60

70

80

(0.025 – 0.2) [Hz].

JOINT ANGLE output

JOINT ANGLE output

JOINT 1 - INVERSE PRBS TRAINING DATA

40

20

JOINT 2 - INVERSE PRBS TRAINING DATA

40

60

JOINT ANGLE 2 input

JOINT ANGLE 1 input

20

40

20

0

[d e g ]

0

-20

-20

20

0

0

-20

-40

0

10

20

30

40

50

F O R C E [N ]

60

40

-40

60

70

80 0

External FORCE 60

Filtered FORCE

40

-20

10

20

30

40

50

60

70

80

External FORCE

Filtered FORCE

-40

300

10

20

30

40

50

60

70

-40

80 300

20

20

0

10

20

30

40

50

60

70

0

80 0

10

20

30

40

50

60

experiment

PRBS-1(2) inputs and Force/Joint Angle

outputs during (40–80)[s] will be used for

while

PRBS-1(2)

70

20

30

40

50

10

20

30

40

50

0

inputs

and

0

10

20

30

40

50

5.5

60

70

PRBS1 output

0

5.5

5

5

4.5

4.5

0

10

20

30

40

50

t [sec]

60

70

0

80 0

10

20

30

40

50

t [sec]

Figure 7. Inverse Neural MIMO NARX Model

Training data obtained by experiment

structure. A nonlinear neural NARX model

The range (4.4 – 5.6) [V] and the shape of

structure is attempted. The full connected

st

60

70

80

PRBS2 output

(0–40)[s] will be used for validation purpose.

PRBS-1 voltage input applied to the 1 joint as

Multi-Layer Perceptron (MLPNN) network

well as the range (4.5 – 5.5) [V] and the shape

architecture composes of 3 layers with 5

of PRBS-2 voltage input applied to rotate the

neurons in hidden layer is selected (results

joint of the 2-axes PAM robot arm is

derived from Ahn et al., 2007 [24]). The final

chosen carefully from practical experience

structure of proposed Inverse neural MIMO

Trang 20

80

FORCE INPUT

80

The 2nd step relates to select model

2

70

10

Force/Joint Angle outputs in the lapse of time

nd

60

20

FORCE INPUT

80

[V ]

Figure 6. Input-Output training data obtained by

training,

10

[N ]

20

10

0

set-up

proportional valve to control rotating joint

5.5

5

4.5

[d e g ]

on

input applied simultaneously to the 2 joints of

JOINT 1 - PRBS TRAINING DATA

40

based

60

70

80

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

NARX11 used in proposed neural MIMO

voltage values u1(k-1), u2(k-1) respectively of

NARX FNN-PID hybrid force/position control

experimental modeling block diagram depicted

scheme is shown in Fig.8.

in Fig.9.

The proposed neural MIMO NARX11

model structure is defined as a nonlinear neural

MLPNN integrated a 1st order ARX model

(with nA=1; nB=1 and nK=1) possessed 5

neurons in hidden layer. The activating

function applied in neurons of hidden Layer

and of output layer is hyperbolic tangent

function and linear function respectively. Fig.9

represents the experiment block diagram for

modeling and identifying the Inverse neural

MIMO NARX11 model of the 2-axes PAM

Figure 9. Block diagram for modeling of Inverse

robot arm.

Neural MIMO NARX model of the 2-Axes PAM

2-AXES PAM ROBOT ARM - NEURAL MIMO INVERSE NARX MODEL

robot arm

u23(t)

ESTIMATION of NEURAL INVERSE MIMO NARX

-1

10

FITNESS CONVERGENCE

u22(t)

u21(t)

yhat2(t)

y2(t-1)

u12(t)

yhat1(t)

FITNESS

u13(t)

-2

10

u11(t)

y1(t-1)

Figure 8. Structure of proposed Inverse neural

-3

10

MIMO NARX11 models of 2-axes PAM robot arm

In Fig.8, input values u11(t)/ u21(t), u12(t)/

u22(t), u13(t)/ u23(t) and recurrent delayed input

0

10

20

30

40

50

Iteration

60

70

80

90

Figure 10. The fitness convergence of proposed

Neural Inverse MIMO NARX11 Model

values y1(t-1), y2(t-1) in neural structure of

The 3rd step estimates trained Inverse

proposed neural Inverse MIMO NARX11

neural MIMO NARX11 model. A good

model will be identical to input values Joint-1

minimized convergence is shown in Fig.10

Angle y1 (k), Joint-2 Angle y2(k), Force value

with the minimized Mean Sum of Scaled Error

yF(k) and desired recurrent delayed control

(MSSE) value is equal to 0.002659 after

Trang 21

100

Science & Technology Development, Vol 16, No.K2- 2013

number of training 100 iterations with the

proposed Inverse neural MIMO NARX11. An

nonlinear

excellent estimating result, which proves the

models. Applying the same experimental

perfect performance of resulted Inverse Neural

diagram in Fig.6, an excellent validating result,

MIMO NARX model, is also shown in Fig.11.

which proves the performance of resulted

JOINT ANGLE 2 input

JOINT ANGLE 1 input

[de g]

MIMO

NARX

20

0

minimized

0

-20

-20

-40

0

5

10

15

20

25

35

-40

40 0

FORCE input

28

30

28

26

24

24

[N ]

26

6.5 0

5

10

15

20

[V ]

5.5

5

errors

demonstrate

the

good

performance of the Inverse neural MIMO

5

10

15

20

25

30

35

40

NARX11 Model (the excellent error < 0.01[V]

FORCE input

for both of Uh1/Uh2 control voltage values

30

35

406.5 0

PRBS1 reference

6

Uh1 output

5.5

25

6

5

10

15

20

25

30

35

40

PRBS2 reference

Uh2 output

respectively applied to 2 joints of the 2-axes

PAM robot arm).

5

4.5

4.5

0

5

10

15

20

25

30

1

35

40 0

ERROR1

5

10

15

20

25

30

1

0

35

40

ERROR2

0

5

10

15

20

t [sec]

25

30

35

Finally, Table 2 tabulates the resulting

weighting values of proposed Inverse neural

0

-1

MIMO NARX model which can be used not

-1

40 0

5

10

15

20

t [sec]

25

30

35

40

only in modeling identification and simulation

Figure 11. Estimation of 2-axes PAM robot arm

offline but also can be applied effectively

Inverse neural MIMO NARX11 Model

online

VALIDATION of INVERSE NEURAL MIMO NARX - JOINT 1

40

JOINT ANGLE 1 input

20

[d e g ]

Inverse

in Fig.12. The experimental results of the

40

20

neural

Inverse Neural MIMO NARX model, is shown

ESTIMATION of INVERSE NEURAL MIMO NARX - JOINT 2

ESTIMATION of INVERSE NEURAL MIMO NARX - JOINT 1

40

[V ]

The last step relates to validate resulting

VALIDATION of INVERSE NEURAL MIMO NARX - JOINT 2

advanced

control

algorithms (Ahn and Anh, 2011)[21]. The final

JOINT ANGLE 2 input

designed structure of proposed Inverse MIMO

0

-20

model-based

40

20

0

in

NARX11 model is shown in Fig.8.

-20

-40

300

5

10

15

20

25

30

35

40 0

30

5

10

15

20

25

30

FORCE input

40

6. CONCLUSIONS

In this study, a new approach of recurrent

25

[N ]

25

35

FORCE input

neural networks, proposed neural Inverse

20

6.50

5

10

15

20

25

6

20

30

35

40 0

6.5

PRBS1 reference

6

Uh1 output

5.5

5

5

[V ]

5.5

4.5

10

15

20

25

30

35

40

PRBS2 reference

Uh2 output

5

10

15

20

25

30

1

35

Error1

0

40 0

nonlinear 2-axes pneumatic artificial muscle

5

10

15

20

25

30

1

35

40

(PAM) system, has successfully overcome the

Error 1

0

-1

0

5

10

15

20

t [sec]

25

30

35

-1

40 0

MIMO NARX model firstly utilized in

modeling and identification of the highly

4.5

0

[V ]

5

contact force variations, coupled effect and

5

10

15

20

t [sec]

25

30

35

40

nonlinear characteristic of the 2-axes PAM

Figure 12. Validation of 2-axes PAM robot arm

robot arm system. The 2-axes PAM robot

Inverse neural MIMO NARX11 Model

arm’s coupled dynamics was taken into

account. Results of training and testing on the

complex dynamic systems such as 2-axes PAM

Trang 22

TẠP CHÍ PHÁT TRIỂN KH&CN, TẬP 16, SỐ K2- 2013

robot arm show that the newly proposed neural

Acknowledgment

Inverse MIMO NARX model presented in this

This research was partially supported by

study is quite suitable to be applied for the

the NAFOSTED and the DCSELAB of Viet

modeling and identification not only the 2-axes

Nam.

PAM robot arm but also other nonlinear

dynamic systems.

Table 2. Resulted weights of Inverse neural MIMO NARX11 – Total Number of weighting values = 57

NHẬN DẠNG HỆ ĐỘNG HỌC MIMO

SỬ DỤNG MƠ HÌNH MIMO NEURAL NARX NGƯỢC

Hồ Phạm Huy Ánh(1), Nguyễn Thanh Nam(2)

(1) Trường Đại học Bách Khoa, ĐHQG-HCM

(2) ĐHQG-HCM

TĨM TẮT: Bài báo khảo sát ứng dụng mơ hình neural MIMO NARX để cải thiện chất lượng

nhận dạng hệ tay máy phi tuyến 2 bậc dùng bắp thịt khí nén nhân tạo (PAM). Các yếu tố như biến động

của lực tiếp xúc hay các ảnh hưởng ghép cặp phi tuyến của 2 khớp nối của tay máy sẽ được nhận dạng

đầy đủ bởi mơ hình neural MIMO NARX ngược thơng qua bộ dữ liệu huấn luyện thực nghiệm đầu vào –

đầu ra. Lần đầu tiên, mơ hình động học nơ rơn MIMO NARX ngược của tay máy 2 bậc dùng bắp thịt khí

nén nhân tạo (PAM) được khảo sát hồn chỉnh. Các kết quả cho thấy mơ hình động học thơng minh

được đề xuất, được huấn luyện bằng thuật tốn Lan Truyền Ngược (BP learning algorithm) cho chất

lượng tốt với độ chính xác khi nhận dạng rất cao. Mơ hình động học nơ rơn MIMO NARX ngược cho

Trang 23

Science & Technology Development, Vol 16, No.K2- 2013

thấy chúng có thể dùng hiệu quả trong nhận dạng không chỉ hệ tay máy PAM 2-bậc mà cho cả các hệ

cơ động học phi tuyến đa biến khác.

Keywords: mô hình động học, bắp thịt khí nén nhân tạo (PAM), tay máy PAM 2 bậc, nhận dạng

mô hình ngược, mô hình nơ rôn MIMO NARX ngược, thuật toán lan truyền ngược (BP).

[7].

REFERENCES

Lilly,

J.

H.,

Adaptive

tracking

for

pneumatic muscle actuators in bicep and

[1].

Noritsugu, T., Tanaka, T., Application of

tricep configurations, IEEE Trans. Neural

rubber artificial muscle manipulator as a

Syst. Rehabil. Eng., , 11, 3, 333–339

rehabilitation robot, IEEE/ASME Trans.

(2003).

Mechatronics, 2, 4, 259–267 (1997).

[8].

[2].

Krebs, H. I., Hogan, N., Aisen, M. L.,

Volpe,

B.

T.,

Robot-aided

Nagaoka, T., Konishi, Y., Ishigaki, H.,

Nonlinear optimal predictive control of

neuro-

rubber artificial muscle, Proc. SPIE- Int.

rehabilitation, IEEE Trans. Rehab. Eng., 6,

Soc. Opt. Eng., 2595, 54–61 (1995).

1, 75–87 (1998).

[9].

[3].

Ju, M.S., Lin, C.C. K., Chen, J.R., Cheng,

H.S., Lin, C.W., Performance of elbow

tracking under constant torque disturbance

in stroke patients and normal subjects,

Clinical Biomech., 17, 640–649 (2002).

[4].

Development and Control of a SoftExoskeleton

Physiotherapy

and

for

Use

in

J.

of

Training,

C. A., VSC position tracking system

involving a large scale pneumatic muscle

actuator, Proc. IEEE Conf. Decision

Control, Tampa, FL, 4302–4307 (1998).

[10]. Ahn, K. K., Thanh, T. D. C., Intelligent

Caldwell, D. G., Tsagarakis, G. N.,

Actuated

Repperger, D. W., Johnson, K. R., Phillips,

phase

plane

switching

control

of

pneumatic artificial muscle manipulators

with

magneto-rheological

brake,

Mechatronics, 16, 2, 85-95 (2006).

Autonomous Robots, 15,1, 21-33 (2003).

[11]. Carbonell, P., Jiang, Z. P., Repperger, D.

[5].

Kobayashi, H., Uchimura, A., Shiiba, T.,

Development of Muscle suit for Upper

Body, Proceedings Intelligent Robots and

Systems

(IROS

2003-IEEE

Int.

W., A fuzzy backstepping controller for a

pneumatic muscle actuator system, Proc.

IEEE Int. Symposium Intelligent Control,

Mexico City, 353–358 (2001).

Conference), 4, 3624-3629 (2003).

[12]. Lilly, J. H. and Chang, X. Tracking control

[6].

Noritsugu, T., Sasaki, D., Takaiwa, M.,

Rehabilitation Robotics: Development of

Active Support Splint driven by Pneumatic

Soft Actuator (ASSIST), Proceedings of

2005 IEEE Int. Con. On Robotics and

Automation, Barcelona, Spain, (2005).

Trang 24

of a pneumatic muscle by an evolutionary

fuzzy controller. IEEE Intell. Automat.

Soft Comput., Sep.2003, vol. 9, no. 3, pp.

227–244.

TAẽP CH PHAT TRIEN KH&CN, TAP 16, SO K2- 2013

[13]. Lin, C.T., Lee, C.S.G., Neural NetworkBased Fuzzy Logic Control and Decision

[18]. Pham, D.T., Fahmy, A.A., Neuro-fuzzy

System, IEEE Transactions on Computers,

Modeling

40, 12, 1320-1336 (1991).

Manipulators for Trajectory Tracking, 16th

[14]. Karakasoglu,

A.,

Sudharsanan,

S.I.,

Sundareshan, M.K., Identification and

decentralized

dynamical

adaptive

neural

control

using

networks

with

and

Control

of

Robot

IFAC WORLD CONGRESS, Prague, 4-8

(2005).

[19]. Ahn,

K.

K.,

Anh,

H.P.H.,

System

modeling and identification of the two-link

application to robotic manipulators, IEEE

pneumatic

Trans. on neural networks, 4, 6, 919-930

manipulator

(1993).

algorithm, Proceedings 2006 IEEE-ICASE

[15]. Katic, D.M., Vukobratovic, M. K., Highly

efficient robot dynamics learning by

decomposed

connectionist

feed-Inverse

artificial

optimized

muscle

(PAM)

with

genetic

Int. Conf., Busan, Korea, 4744-4749,

(2006).

[20]. Ahn K.K., Anh H.P.H., A new approach of

control structure, lEEE Trans. on syst. man

modeling

and cybern., 25, 1, 145-158 (1995).

pneumatic

and

identification

artificial

muscle

of

the

(PAM)

[16]. Lewis, F. L., Jagannathan, S., Yesildirek,

manipulator based on recurrent neural

A., Neural network control of robot

network, Proceedings IMechE, Part I:

manipulators

Journal

and

nonlinear

systems,

Taylor & Francis (1999).

van

FeedForward

de

Wal,

for

Systems

and

Control

Engineering, 221(I8), 1101-1122 (2007).

[17]. Boerlage, M., Steinbuch, M., Lambrechts,

P.,

of

ModelBased

Motion

Systems,

[21]. Ahn K.K., Anh H.P.H. Compliance ForcePosition Control of the 2-Axes PAM-based

Rehabilitation

Robot

Using

Neural

Proceedings of IEEE Conference on

Networks, Journal of ISA Transactions,

Control Applications, 1, 1158 1163

(2011).

(2003).

Trang 25

## Tài liệu Combatting Heavy Equipment Theft - An Officer’s Guide to the Proper Identification of Construction Equipment docx

## Báo cáo " Development of a spectrometry system Using lock-in amplification technique " doc

## AN IMPLEMENTATION OF INTRUSION DETECTION SYSTEM USING GENETIC ALGORITHM pptx

## SYSTEMATIC METHOD FOR ANALYSIS OF PERFORMANCE LOSS WHEN USING SIMPLIFIED MPC FORMULATIONS pptx

## landscape image of regional tourism classification using neural network

## high efficient library for online handwriting recognition system using unipen database

## báo cáo hóa học:" Identification of a biomarker panel using a multiplex proximity ligation assay improves accuracy of pancreatic cancer diagnosis" doc

## Scientific report: "The potential energy recovery from landfills and evaluate the environmental benefits of the generation system using gas from landfills in Nam Son landfill, Vietnam" docx

## Scientific report: "The potential energy recovery from landfills and evaluate the environmental benefits of the generation system using gas from landfills in Nam Son landfill, Vietnam" pps

## Báo cáo y học: "Identification of novel genetic susceptibility loci for Behçet''''s disease using a genome-wide association study" pps

Tài liệu liên quan