IEEE Systems, Man and Cybernetics Magazine - July 2022 - 65

rt ke tk ed
eL r
cp ii i
t
.
^^ ^hh h#
L
=+ xx
=Each
operator is designed using the proposed model.
(19)
About Learning-Based Models
The actuator to be studied has nonlinear characteristics in
the input-output relationship due to elasticity and pneumatic
drive. Some of these characteristics can be expressed in
mathematical formulas, but they are complex. Complex mathematical
models make the control system design difficult.
Therefore, assistance of models with uncertainty is considered.
Several procedures have been proposed to supplement
control system design [14]. In this research, it is suggested
to use input-output models obtained by machine learning.
The machine learning method used is called SVR, which
is the regression analysis application of a support vector
machine. A standard SVR equation,
The x is the input vector, and +aa
ii
f
,x^h is shown in (20).
,, (, ),K xx and b are
i
called the dual variables, kernel function, and bias term,
respectively. Kernel functions allow the SVR to represent
nonlinear input-output relationships.
n
fK (, ).bxxxii
i
^ =- +
=1
h |^aa
+-h
i
(20)
However, a conventional SVR cannot handle multioutput
problems. Therefore, it is difficult to apply them to 3-DOF
soft actuators, which have three-input and three-output
systems. Therefore, a method called M-SVR, which has
been extended to solve multioutput problems, is used in
this study. The loss function used in M-SVR is shown in
Lu = 222
()
(
uu
where u ee eT
,
-+
1
ff $
u
u
f
f
(21)
,
== e is the residuals, and f is the
insensitivity parameter. A standard SVR uses a loss function
based on the L1 norm, which requires treating each dimension
separately and complicates the solution. On the other
hand, the loss function expressed in (21) is based on the L2
norm and, thus, all dimensions can be treated as a single
one. Because of these features, M-SVR can represent mutual
relationships in multiple-input, multiple-output systems. In
addition, it has the advantage that the parameters can be
easily adjusted because it is treated as a single system [18].
Figures 7 and 8 show examples of input-output relationships
for models based on learning. These are compared
to the actual input-output relationship in the
actuator. However, in this case, the input to the two artificial
muscles is equivalent, and there is no movement in the
x-coordinate. These figures, which present a comparison
to the actuator's behavior, show that the model can
describe these relationships well.
Designing Operators
The control system is designed based on operator theory.
This theory allows for the design of control systems using
models that include nonlinear characteristics [15], [16].
5
-5
-10
-15
-20
-25
-30
-35
-40
0.5
1
1.5
P1, P3 [Pa]
Figure 7. The input-output results by M-SVR
(y-coordinate).
5
-5
-10
-15
-20
-25
-30
-35
-40
0.5
1
1.5
P1, P3 [Pa]
Figure 8. The input-output results by M-SVR
(z-coordinate).
July 2022 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 65
2
2.5
× 105
2
2.5
× 105
Experimental Result
Result by Learning
From these input-output relationships, transform (8), (9),
and (18), respectively, into simultaneous equations (22)-
(24). However, Kr is an alternative correction formula for
Kt, which is calculated from f based on (9).
rP rP rP s
rr
rs
11 1122 13 31
11
++ =
=13=+
^
^
21
1222 23 32
21
++ =
== =
22
23
1
2 =- k
r =+ -expa
sEI^ci
:1
3 =
h .
ir ia () @
3sP D
"
h6 12
2 - th
max
k
3Pmaxmax
log` -+j
f
f 13 th
P
2
2 ^
h ,
(24)
(23)
sincos tan
sincos tan
rP rP rP s
rr r
s
rP rP rP s
rK Ll CC Cl
Kk P
31 1322 33 33
30
++ =
=- -^cf
ciba i
-1
aa c
aa c
h
h
,
,
12 =-1
1 = 0
(22)
Experimental Result
Result by Learning
y (mm)
y (mm)
IEEE Systems, Man and Cybernetics Magazine - July 2022

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