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Fig. 6.2
The two-wheel differential robot example
⎧
⎨
K
i
0
K
i
D
K
j
for
T
D
for
T
D
≤
τ<
τ<
K
i
=
T
I
(6.22)
⎩
i
I
(
F
j
(τ ))
for
τ
≥
T
I
where:
•
K
i
0
is inferred by the premise variables
ϑ(τ)
and designed to be robust against
model uncertainties;
•
K
i
D
is inferred by the premise variables
and designed to be robust against
model uncertainties and all the possible faults in
ϑ(τ)
F
, considered as if they were
uncertain parameters;
N
sets of subsystem controllers
K
i
I
(
K
i
I
(
•
F
1
(τ)),...,
F
N
(τ ))
are such that the
j
th
controller
K
i
I
(
F
j
(τ ))
is inferred by the premise variables and the
j
th fault estima-
tion, used as an additional premise variable
F
i
(τ )
, and is designed to be robust
against model uncertainties.
6.4 Application Example
The application example used in this chapter is a two-wheel differential robot in
simulation. The robot has a circular shape with a diameter
d
=
2
r
=
0
.
34 m and a
mass
m
92 kg. The vehicle is driven by two differential drive wheels that can
reach the maximum speed of
=
2
.
z
max
=
˙
.
5 m/s. By altering the speed of the individual
wheels, the direction of the robot movements can be changed.
A mathematical model of the robot (Fig.
6.2
) can be obtained through a balance
of the forces and the moments acting on the system:
0
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