Information Technology Reference
In-Depth Information
20.4.1.1
Classical IBVS
For the classical IBVS, the following results are obtained:
•
with
L
c
, the trajectories in the image plane are pure straight lines as expected [5].
The camera motion is then a combination of a backward translation and a rotation
with respect to the camera optical axis (retreat problem). Due to this undesired
retreat, the camera might reach the limit of the workspace;
•
with
L
p
, the results are approximatively the results obtained in the first case (re-
treat problem), see Figure 20.5. The visual feature trajectories tend to straight
lines;
•
with
L
d
, the camera moves toward the target and simultaneously rotates around
the optical axis (advance problem) [5]. Due to this undesired forward motion,
some features can go out the camera field of view during the camera motion; and
•
with
L
m
, the camera motion is a pure rotation [18]. No additional motion is in-
duced along the optical axis and the visual feature trajectories are circular.
20.4.1.2
VPC with a Local Model
(
VPC
LM
)
The following simulations are obtained with the VPC strategy using a local model
based on the interaction matrix
L
p
. The comparison with the classical IBVS is done
for different
N
p
values (
N
p
= 1
20) and different weighted matrices (
Q
(
j
)=
I
or
Q
TV
).For
N
p
= 1, the results are similar to the classical IBVS with
L
p
since
the model used to predict the next image is exactly the same (see Figure 20.6). The
only difference is the behavior of the control law, decreasing exponentially with
IBVS. For
N
p
= 10 (see Figure 20.7) or
N
p
= 20 (see Figure 20.8), the trajectories
in the image plane become circular. Indeed, the only constant control over
N
p
which
minimizes the cost function is a pure rotation. Thus the translation motion along the
optical axis decreases with the increase of
N
p
value.
The time-varying matrix
Q
TV
accentuates the decoupling control by giving im-
portance at the end of
N
p
which corresponds to the final objective (see Figure 20.9).
It seems to be equivalent to the behavior obtained with
L
m
which takes into account
the desired position. For a
,
10
,
rotation around the optical axis, the classical IBVS with
L
c
,
L
p
or
L
d
fails as well as VPC
LM
with
Q
(
j
)=
I
and whatever
N
p
. On the other
hand, VPC
LM
achieves the satisfying motion with
Q
TV
and
N
p
≥
π
20 (see Figure
20.10).
To illustrate the capability of visibility constraint handling, the visual features are
constrained to stay in a window defined by the inequalities
u
min=
u
max
= 0
−
.
.
0
22
22
≤
≤
.
s
m
(
j
)
(20.22)
v
min=
−
0
.
22
v
max
= 0
.
22
In that case, VPC
LM
satisfies both visibility constraint and control task (see Figure
20.11). A translation along the optical axis is then induced to ensure that the visual
features do not get out the camera field of view.
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