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4.6. CONSTRUCTING TF SYSTEMS 43
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
−0.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Figure 4.24: Mean and covariance for t 0 and t 1 .
4.6.3 Calculating the Quality of a Transformation Chain
In the last example, the quality of a single transformation was considered. This section will show how
the single qualities of each element in a chain can be incorporated to get the quality of the whole transformation
chain. As an example, the tf tree shown in Figure 4.25(a) will be used. This tree consists of
sensor_frame
tilt_frame
pan_frame
z
slide_frame
y
(a) Tf tree of the transformation
chain.
x
base_frame
(b) Tf frames with axis of movement.
Figure 4.25: Tf tree and frames for a transformation chain.
a frame called base_frame which is the root element of the tf tree. The slide_frame is linked
with the base_frame by a prismatic joint. This prismatic joint can move in the direction of the
x-axis of the slide_frame. The pan_frame is linked with the slide_frame through a revolute
joint, that rotates around the z-axis. Further the tilt_frame is linked with the pan_frame
through a revolute joint, which rotates around the y-axis. Finally the sensor_frame is linked with
the tilt_frame through a fixed joint. These frames and their direction of movement are shown in
Figure 4.25(b). To actually calculate the quality of the transformation chain, assumptions for different
values have to be made.