Information Technology Reference
In-Depth Information
1) as
q
o
ξ
(
k
).Weuse
q
(
k
of all the image features at time
k
is written by
−
at time
o
at time
k
, which satisfies (19.14). The arguments
of image Jacobian matrices and Moore-Penrose inverse of them are
q
(
k
α
(
q
(
k
−
ξ
k
. We thus use
1)) as
−
1),but
the arguments are omitted to simplify notation.
The implemented algorithm consists of image feature extraction, image feature
selection, update of the state, control input calculation and image feature estimation
as illustrated in Figure 19.4, where the initial state
q
(0) is given. Let us now show
details of the implemented algorithm:
1.
image feature extraction
: image features at time
k
are extracted by using an
estimate of image features at time
k
−
1. The center of a search area to extract
ˆ
ξ
i
(
k
) is set at
ξ
i
(
k
−
1). The image feature
ξ
i
(
k
) is given by the center of gravity
in the corresponding search area;
2.
image feature selection
: let the minimum size of
I
,say
m
s
, and a tolerance
ε
(
0) be given. The following algorithm determines the set of visible image
features
>
I
:
I
=
{
1
,
2
,...,
m
}
for
i
= 1
,
2
,...,
m
−
1
for
j
=
i
+ 1
m
if
the search areas of
i
and
j
are overlapped
I
←
I
−{
,
2
,...,
i
,
j
}
end
end
end
until
|
I
|≥
m
s
˜
(
k
)=
J
I
J
+
ξ
I
I
{
ξ
I
(
k
)
−
α
I
(
q
(
k
−
1))
}
+
α
I
(
q
(
k
−
1))
˜
if
max
i
∈
I
ξ
i
(
k
)
>
ε
= arg max
i
∈
I
ξ
i
(
k
)
−
−
ξ
i
(
k
)
˜
ξ
i
(
k
)
I
←
I
−{}
else
break
end
end
3.
update of the state
:thestate
q
(
k
) is given by
q
(
k
)=
J
+
I
{
ξ
I
(
k
)
−
α
I
(
q
(
k
−
1))
}
+
q
(
k
−
1);
(19.27)
4.
control input calculation
: a control input signal
u
(
k
) is determined by a set of
proportional integral derivative (PID) controllers. Details are shown in the next
section, since special reference signals are required for take-off and landing
control;
5.
image feature estimation
: using (19.19), image features are estimated by
ˆ
(
k
)=
JJ
+
ξ
I
{
ξ
I
(
k
)
−
α
(
q
(
k
−
1))
}
+
α
(
q
(
k
−
1))
.
(19.28)
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