Page 126 - Rapid Learning in Robotics

112 Application Examples in the Robotics Domain

z
160
150
140
130
120
110
100
90

40
30 20
x 10 0 -10
-20 -30 10 20 30
-40
r -40 -30 -20 -10 0 y θ

Figure 8.4: The 27 training data vectors for the Back-propagation networks: (left)

in the input space r and (right) the corresponding target output values .

gets the same data-pairs as training vectors — but additionally, it obtains
the assignment to the node location a in the 3 3 3 node grid illustrated
in Fig. 8.5.
As explained before in Sec. 5, specifying a A introduces topological
order between the training vectors w a. This allows the PSOM to advanta-
geously draw extra curvature information from the data set — information,
that is not available with other techniques, such as the MLP or the RBF
network approach. The visual comparison of the two viewgraphs demon-
strates the essential value of the added structural information.

8.2 A Higher Dimensional Mapping:

The 6-DOF Inverse Puma Kinematics

To demonstrate the capabilities of the PSOM approach in a higher dimen-
sional mapping domain, we apply the PSOM to construct an approxima-
tion to the kinematics of the Puma 560 robot arm with six degrees of free-
dom. As embedding space X we first use the 15-dimensional space X
spanned by the variables

x x y z r rr x y a z a a x y n z
n n