Page 148 - Rapid Learning in Robotics

134 “Mixture-of-Expertise” or “Investment Learning”

must be re-adjusted to keep this fixation point visible in a constant im-
age position, serving at the same time the need of a fully visible region of
interest. These practical instructions achieve the reduction of free param-
eters per camera to its 2D lateral position, which can now be sufficiently
determined by a single extra observation of a chosen auxiliary world ref-
erence point ref . We denote the camera image coordinates of ref by u ref .
By reuse of the cameras as a “context” or “environment sensor”, u ref now
implicitly encodes the camera position.
For the present investigation, we chose from this set 9 different camera
positions, arranged in the shape of a grid (Fig. 9.6). For each of these

nine contexts, the associated mapping T T j , j
is learned
by a T-PSOM by visiting a rectangular grid set of end effector positions

i (here we visit a grid in x of size cm ) jointly with the loca-

tion in camera retina coordinates (2D) u i. This yields the tuples x i u i as
the training vectors w a for the construction of a weight set j (valid for
i
context j) for the T-PSOM in Fig. 9.3.
Each T j (the T-PSOM in Fig. 9.3, equipped with weight set j ) solves
the mapping task only for the camera position for which T j was learned.
Thus there is not yet any particular advantage to other, more specialized
methods for camera calibration (Fu, Gonzalez, and Lee 1987). However,
the important point is, that now we can employ the Meta-PSOM to rapidly
map a new camera position into the associated transform T by interpolating
in the space of the previously constructed basis mappings T j .

The constructed input-output tuples u ref j j , j g, serve f
as the training vectors for the construction of the Meta-PSOM in Fig. 9.3
such that each u ref observation that pertains to an intermediate camera
positioning becomes mapped into a weight vector that, when used in the
base T-PSOM, yields a suitably interpolated mapping in the space spanned
by the basis mappings T j .
This enables in the following one-shot adaptation for new, unknown cam-
, the Meta-PSOM
era places. On the basis of one single observation u ref new
provides the weight pattern new that, when used in the T-PSOM in Fig. 9.3,
provides the desired transformation T new for the chosen camera position.
Moreover (by using different projection matrices P), the T-PSOM can be
used for different mapping directions, formally:

x u F u x u u ref (9.1)
T P S O M