Information Technology Reference
In-Depth Information
Table 19.2
PID gains
i
i
P
i
I
i
D
i
12
.
15
−
3
.
80
−
0
.
10
−
2
.
0
22
.
67
3
.
80
0
.
10
2
.
0
31
.
85
3
.
40
1
.
00
1
.
8
42
.
39
1
.
50
0
.
80
0
.
1
k
τ=0
q
i
(τ)+
D
i
(
q
i
(
k
)
−
q
i
(
k
−
1))
,
u
i
(
k
)=
b
i
+
P
i
q
i
(
k
)+
I
i
(19.33)
where
b
i
,
P
i
,
I
i
and
D
i
are constants for
i
= 1
4. The PID gains are heuristically
tuned to the values in Table 19.2. The signs of the gains depend on the property
of the transmitter. If the reference vector
q
ref
,...,
is fixed over a period of time, then
hovering motion is generated.
For take-off control, the following proportional derivative (PD) controllers are
used:
u
i
(
k
)=
b
i
+
P
i
q
i
(
k
)+
D
i
(
q
i
(
k
)
−
q
i
(
k
−
1))
,
(19.34)
where
b
i
,
P
i
and
D
i
are set to the values in Table 19.2. In order to ensure a smooth
take-off in ground effect, the reference
z
ref
(
k
) should be set underground at first. In
our experiments,
z
ref
(
k
) varies from 0
.
1mto
−
1 m smoothly, since the rotors stop
when
z
ref
(
k
)=0
.
1 and ground effect vanishes at an altitude of
−
1 m. Recall that
z
ref
(
k
)
0 means that the reference is underground (see Figure 19.3).
For landing control, the PD controllers (19.34) are also used. The reference
z
ref
(
k
)
increases until
z
(
k
) is larger than a given threshold. In our experiments,
z
ref
(
k
) is set
to 0
>
02 m. Recall that the rotors stop when
z
ref
(
k
)=0
.
1m,when
z
(
k
)
>−
0
.
.
1.
19.8 Experimental Result
The reference of the generalized coordinates for hovering is set at
00
10
with
−
w
. The cameras are located as shown in Table
19.3 (The cameras are set as follows. Camera
i
is first set at the origin of
respect to the world reference frame
Σ
w
.The
Σ
Table 19.3
Camera configuration
camera index
x
y
z
φ
θ
1
−
1
.
42
0
.
00
−
0
.
97
0
−
7π
/
36
2
0
.
00
−
1
.
42
−
0
.
97
−
π
/
2
−
7π
/
36
3
−
1
.
43
0
.
00
−
0
.
12
0
π
/
9
4
0
.
00
−
1
.
43
−
0
.
12
−
π
/
2
π
/
6
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