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44 CHAPTER 4. METHOD
In the example the default rotation (see Section 3.1) is considered to be zero for all frames. The
vector of the default translation o, as well as the values for the state vector x and the covariance matrix
P are listed below for each frame. The default translation is just called Translation and describes the
translation between the Parent and Child frame when the joint is in the default position. The state
vector consists of the current position s and velocity v. In the case of a revolute joint the position is
the angle in rad and in the case of a prismatic joint, it is the distance in cm from the default position.
The state vector and covariance matrix, thus are defined as
x =
P =
[ s
v]
[ ] σ
2
s 0
0 σ 2 v
The point in time where the different TF Data is captured and the point in time, at which the transformation
wants to be known, is shown in Figure 4.26.
slide_frame
tilt_frame
pan_frame
100 180 235 300
time (ms)
tf data
sensor data
Figure 4.26: Time where TF Data was captured.
The default translation, the state vector at time t 0 and the covariance matrix at time t 0 for the different
frames of the tf tree are:
• slide_frame:
• pan_frame:
• tilt_frame:
⎡ ⎤
5
o a = ⎣2⎦ , x a,0 =
8
⎡ ⎤
9
o b = ⎣0⎦ , x b,0 =
3
⎡ ⎤
1
o c = ⎣0⎦ , x c,0 =
2
[ ] [ ]
0
0.1
2
0
, P
100 a,0 =
0 10 2
[ 0
π
2
[ 0
π
3
] [ ]
0.01
2
0
, P b,0 =
0 ( π 4 )2
] [ ]
0.01
2
0
, P c,0 =
0 ( π 4 )2