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9.3 Examples 131

be efficient in particular with respect to the number of required training
points.
The PSOM network appears as a very attractive solution, but not the
only possible one. Therefore, the first example will compare three ways
to apply the mixture-of-expertise architecture to a four DOF problem con-
cerned about coordinate transformation. Two further examples demon-
strate a visuo-motor coordination tasks for mono- and binocular camera
sight.

9.3.1 Coordinate Transformation with and without Hierar-
chical PSOMs

This first task is related to the visual object orientation finder example pre-
sented before in Sec. 7.2 (see also Walter and Ritter 1996a). Here, an inter-
esting skill for a robot could be the correct coordinate transformation from
a camera reference frame (world or tool; yielding coordinate values x )to
the object centered frame (yielding coordinate values x ). This mapping
would have to be represented by the T-BOX. The “context” would be the
current orientation of the object relative to the camera.
Fig. 9.5 shows three ways how the investment learning scheme can be
implemented in that situation. All three share the same PSOM network
type as the META-BOX building block. As already pointed out, the “Meta-
PSOM” bears the advantage that the architecture can easily cope with sit-
uations where various (redundant) sensory values are or are not available
(dynamic sensor fusion problem).

Context Image Completion Context Image Completion Context Image Completion
Meta-PSOM Meta-PSOM Meta-PSOM
ω=(φ,θ,ψ,z) ω ω
4..8 points Parameter 4..8 points Coefficients 4..8 points Weights
Roll-Pitch Matrix
X 1 Yaw-Shift X 2 X 1 Multiplier X 2 X 1 T-PSOM X 2
(i) (ii) (iii)
Figure 9.5: Three different ways to solve the context dependent, or investment
learning task.

The first solution i uses the Meta-PSOM for the reconstruction of ob-
ject pose in roll-pitch-yaw-depth values from Sec. 7.2. The T-BOX is given
by the four successive homogeneous transformations (e.g. Fu et al. 1987)
on the basis of the z values obtained from the Meta-PSOM.