Information Technology Reference
In-Depth Information
B
: elevator, pitch angle of the lower rotor.
A
: aileron, roll angle of the lower rotor.
T
: throttle, resultant force of the two rotor thrusts.
Q
: rudder, difference of the two torques generated by the two rotors.
The corresponding control signals are denoted by
u
1
,
u
2
,
u
3
and
u
4
. Note that
x
,
y
,
z
and
φ
are controlled by applying
u
1
,
u
2
,
u
3
and
u
4
, respectively.
19.4
Image Jacobian Matrices
This section defines some image Jacobian matrices to explain our visual servoing
technique in subsequent sections.
We have sixteen image features, since there exist four cameras in the flight field
and the positions of the four black balls attached to the helicopter are used as image
features. We set
=
...
ξ
16
ξ
1
ξ
2
ξ
(19.4)
2
ξ
4(
i
−
1)+
j
∈
R
where recall that
denote the position of ball
j
in the image plane of
camera
i
. In addition, we define
ξ
I
=
σ
1
ξ
σ
2
σ
|
I
|
ξ
...
ξ
(19.5)
where
I
⊂{
1
,
2
...,
16
}
,
|
I
|
is the size of the set
I
,
σ
j
∈
I
(
j
= 1
,
2
,...,|
I
|
) and
σ
1
<
σ
2
< ... <
σ
|
I
|
.
(19.6)
I
As we shall see later,
implies a set of correctly extracted image features. The
ξ
I
ξ
i
∈
I
vector
is used to generate a control input, when
with
i
can be extracted
ξ
i
with
i
∈
I
correctly and when
can not be extracted due to occlusion. Details will
be discussed in Section 19.6.
Using a nonlinear function
α
i
of
q
, we can write
ξ
i
= α
i
(
q
)
(19.7)
when occlusion does not occur (see for instance [8]). We define
(
q
)=
α
1
(
q
)
...
α
16
(
q
)
α
2
(
q
)
α
(19.8)
and we have
ξ
α
(
q
)
=
.
(19.9)
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