Page 151 - Rapid Learning in Robotics

9.3 Examples 137

In the investing pre-training phase, nine mappings T j are learned by
the T-PSOM, each camera visiting a grid, sharing the set of visited
robot positions i . As Fig. 9.3 suggests, normally the entire weight set
serves as part of the training vector to the Meta-PSOM. Here the prob-
lem factorizes since the left and right camera change tripod place inde-
pendently: the weight set of the T-PSOM is split, and the two parts can be
learned in separate Meta-PSOMs. Each training vector w a for the left cam-
j
era Meta-PSOM consists of the context observation u L and the T-PSOM
ref
L

for
weight set part L u u L (analogously the right camera Meta-

PSOM.)
Also here, only one single observation u ref is required to obtain the de-
sired transformation T. As visualized in Fig. 9.7, u ref serves as the input to
the second level Meta-PSOMs. Their outputs are interpolations between
previously learned weight sets, and they project directly into the weight
set of the basis level T-PSOM.
The resulting T-PSOM can map in various directions. This is achieved
by specifying a suitable distance function dist via the projection matrix
P, e.g.:

u x

x u F T P S u O L u L R u R (9.4)
ref
Mf
re
F T P S u O L u L R u R (9.5)
u

u
Mf
ref
re
x u

u x F T P S x O L u L R u R (9.6)
Mf
ref
re
u
L u L F M
P e t S a u L Of M L analog R u R (9.7)

ref
L
re
ref
Directly trained T-PSOM with
Mapping Direction T-PSOM Meta-PSOM
pixel u
x robot Cartesian error x 1.4 mm 0.008 4.4 mm 0.025
Cartesian x
u pixel error 1.2 pix 0.010 3.3 pix 0.025

pixel u
robot Cartesian error x 3.8 mm 0.023 5.4 mm 0.030
Table 9.3: Mean Euclidean deviation (mm or pixel) and normalized root mean
square error (NRMS) for 1000 points total in comparison of a directly trained T-
PSOM and the described hierarchical Meta-PSOM network, in the rapid learning
mode after one single observation.
Table 9.3 shows experimental results averaged over 100 random lo-
cations (from within the range of the training set) seen in 10 different