Page 128 - Rapid Learning in Robotics

114 Application Examples in the Robotics Domain

θ

θ

θ

o Figure 8.6:
θ n The 15 com-
ponents of the training data
r a vectors for the PSOM net-
θ works: The six Puma axes
l and the position r and orien-
z
tation vectors n, o, and a of
θ
the tool frame.

components, using the forward kinematics transform equations (Paul 1981)

( [-135 ,-45 ], [-180 ,-100 ], [-35 ,55 ], [-45 ,45 ], [-90 ,0 ],

[45 ,135 ], and tool length l z ={0,200} mm in z direction of the T frame,
see Fig. 8.6.
Similar to the previous example, we then test the PSOM based on the
points in the inverse mapping direction. To this end, we specify Cartesian
a
goal positions and orientation values n at 200 randomly chosen inter-
r

mediate test points and use the PSOM to obtain the missing joint angles .
Thus, nine dimensions of the embedding space X are selected as in-
r
put sub-space. The three components fr x y z rg are given in length units
([mm] or [m]) and span intervals of range {1.5, 1.2, 1.6} meters for the given
training set, in contrast to the other six dimensionless orientation compo-
nents, which vary in the interval [-1,+1]. Here the question arises what to
do with these incommensurable components of different unit and magni-
tude? The answer is to account for this in the distance metric dist . The
best solution is to weight each component k in Eq. 4.7 reciprocally to the
measurement variance
p k var w k (8.2)

If the number of measurements is small, as it is usual for small data sets,