Page 154 - Rapid Learning in Robotics

140 Summary

cially available sensor sub-systems. As a consequence, we started to en-
large the robot's sensory equipment in the direction of force, torque, and
haptic sensing. We developed a multi-layer tactile sensor for detailed in-
formation on the current contact state with respect to forces, locations and
dynamic events. In particular, the detection of incipient slip and timely
changes of contact forces are important to improve stable fine control on
multi-contact grasp and release operations of the articulated robot hand.

Returning to the more narrow sense of rapid learning, what is important?
To be practical, learning algorithms must provide solutions that can
compete with solutions hand-crafted by a human who has analyzed the
system. The criteria for success can vary, but usually the costs of gather-
ing data and of teaching the system are a major factor on the side of the
learning system, while the effort to analyze the problem and to design an
algorithm is on the side of the hand crafted solution.
Here we suggest the “Parameterized Self-Organizing Map” as a versa-
tile module for the rapid learning of high-dimensional, non-linear, smooth
relations. As shown in a row of application examples, the PSOM learning
mechanism offers excellent generalization capabilities based on a remark-
ably small number of training examples.
Internally, the PSOM builds an m-dimensional continuous mapping
manifold, which is embedded in a higher d-dimensional task space (d
m). This manifold is supported by a set of reference vectors in conjunc-
tion with a set of basis functions. One favorable choice of basis functions
is the class of (m-fold) products of Lagrange approximation polynomials.
Then, the (m-dimensional) grid of reference vectors parameterizes a topo-
logically structured data model.
This topologically ordered model provides curvature information —
information which is not available within other learning techniques. If
this assumed model is a good approximation, it significantly contributes
to achieve the presented generalization accuracy. The difference of infor-
mation contents — with and without such a topological order — was em-
phasized in the context of the robot finger kinematics example.
On the one hand, the PSOM is the continuous analog of the standard
discrete “Self-Organizing Map” and inherits the well-known SOM's un-
supervised learning capabilities (Kohonen 1995). One the other hand, the
PSOM offers a most rapid form of “learning”, i.e. the form of immediate