Information Technology Reference
In-Depth Information
•
L
s
=
L
(
s
(
t
)
,
Z
(
t
))
, noted
L
c
: the interaction matrix is updated at each iteration;
•
L
s
=
L
(
s
(
t
)
,
Z
∗
)
, noted
L
p
: the depth computed or measured at the reference position
noted
Z
∗
is used. The interaction matrix varies only through the current measure
of the visual features;
•
L
s
=
L
(
s
∗
,
Z
∗
)
, noted
L
d
: the interaction matrix is constant and corresponds to its
value at the reference position; and
•
L
s
=
2
(
L
(
s
∗
,
Z
∗
)
+
L
(
s
(
t
)
,
Z
(
t
))
), noted
L
m
: the interaction matrix is the mean of the
constant and current interaction matrices.
In order to compare the VPC approach with the classical IBVS, no constraint on
the control input is considered in the first part. Then, mechanical and visibility con-
straints will be taken in consideration with the VPC approach. In all cases, the con-
trol inputs are normalized if needed. The bounds are 0.25 m/s for the translation
speed and 0.25 rad/s for the rotation speed.
20.4.1
Case 1: Pure Rotation around the Optical Axis
In case 1, the required camera motion is a pure rotation of
2
radians around the
optical axis. Due to the lack of space and since it is a classical case, all simulation
results are not presented here but all are discussed.
Image plane
Image errors
0.3
0.4
ε
u
1
ε
u
2
ε
u
3
ε
u
4
0.2
0.2
0
−0.2
0.1
−0.4
1
2
3
4
5
6
7
8
9
10
Seconds
0
0.4
ε
v
1
ε
v
2
ε
v
3
ε
v
4
−0.1
0.2
0
−0.2
−0.2
−0.4
−0.3
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
1
2
3
4
5
6
7
8
9
10
u
Seconds
Camera pose errors
Control
0.2
0.25
Tx (m/s)
Ty (m/s)
Tz (m/s)
Wx (rad/s)
Wy (rad/s)
Wz (rad/s)
0
0.2
−0.2
0.15
0.1
−0.4
ε
T
x
(m)
ε
T
y
(m)
ε
T
z
(m)
ε
W
x
(rad)
ε
W
y
(rad)
ε
W
z
(rad)
0.05
−0.6
0
−0.8
−0.05
−0.1
−1
−0.15
−1.2
−0.2
−1.4
−0.25
−1.6
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
Seconds
Seconds
Fig. 20.5
Case 1: Classical IBVS with
L
p
Search WWH ::
Custom Search