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52 CHAPTER 5. RESULTS
• laser_tilt_frame → laser_frame:
translation: o lf = [ 0.2 0 0.1 ] T
position uncertainty: σ 2 p,lf = 0
The values chosen for the uncertainties are higher than they would normally be in reality to make the
results more obvious. With these values it is possible to run the simulation. Nevertheless an additional
frame for the laser point named laser_point_frame should be introduced. This artificial frame
allows to calculate the uncertainty with the provided methods. It is assumed that the point is captured
without uncertainty which of course does not hold in reality. However for the question that should be
answered this assumption is feasible. Thus the transformation can be defined as:
• laser_frame → laser_point_frame:
translation: o lpf = [ 2 0 0 ] T
position uncertainty: σ 2 p,lpf = 0
5.2 Discussion of the Results
To actually compare the results of the different runs, the average of the position uncertainty for one
thousand transformations is used. This is an easy and sufficient enough approach to see how the tuning
of parameters is influencing the quality. Figure 5.3 gives an impression where the frames are located
in 3D space and how good the position quality for the laser_point_frame is at a specific point
in time.
laser_frame
laser_tilt_frame
torso_frame
laser_point_frame
base_frame
Figure 5.3: Frames in 3D space with 3σ uncertainty ellipsoid for the laser_point_frame.
The results for the different simulations which were performed to answer the questions are listed
in Table 5.1. There, only the values in millimeter of the standard deviation in x and z-direction are
shown. The variance in y-direction is zero and the cross-covariances can hardly be interpreted.