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Fig. 6.14
in vivo
heart-tool synchronization: on the top, the recorded disturbance and on the
bottom the tracking error
6.5.2.1
Robotic System Description and Modeling
The Cardiolock active cardiac stabilizer described in Section 6.2 is used. Figure 6.15
shows a block diagram of the visual loop. The computed control signal
u
is con-
verted into an analog voltage with a digital to analog conversion modeled by a ZOH.
This voltage corresponds to the reference of the piezo position servo loop
α
∗
.Due
α
∗
=
to the high dynamics of this loop, we assume that
. The output
y
is measured
using the position of a visual marker
v
in the image given by a high speed camera
with a sampling period
T
s
= 3 ms. The dynamic effects of the camera can be mod-
eled as an averaging filter representing the exposure time effect. The camera model
C
m
can be written [36] as C
m
(
z
)=
1+
z
−
1
α
2
.
A time delay of one period is required for the acquisition and the processing of the
current image. The whole open loop model of the visual servoing can be written as
G
(
s
)
s
}
z
−
1
)
Z{
C
m
(
z
)
z
−
1
H(
z
)=(1
−
.
(6.23)
This model is identified using standard identification techniques. P representing the
transfer between the heart force applied on the stabilizer and the stabilizer tip posi-
tion can be easily obtained from H(
z
).
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