Page 156 - Rapid Learning in Robotics

142 Summary

Generally, in robotics the availability of precise mappings from and to
different variable spaces, including sensor, actuator, and reference coordi-
nate spaces, plays a crucial role. The applicability of the PSOM is demon-
strated in the robot finger application, where it solves the classical forward
and inverse kinematics problem in Cartesian, as well as in the actuator pis-
ton coordinates — within the same PSOM. Here, a set of only 27 training
data points turns out sufficient to approximate the 3 D inverse kinemat-
ics relation with a mean positioning deviation of about 1 % of the entire
workspace range.
The ability to augment the PSOM embedding space allows to easily
add a “virtual sensor” space to the usual sensorimotor map. In conjunc-
tion with the ability of rapid learning this opens the interesting possibil-
ity to demonstrate desired robot task performance. After this learning by
demonstration phase, robot tasks can also be specified as perceptual ex-
pectations in this newly learned space.
The coefficients p k can weight the components relative to each other,
which is useful when input components are differently confident, impor-
tant, or of uneven scale. This choice can be changed on demand and can
even be modulated during the iterative completion process.
Internally, the PSOM associative completion process performs an it-
erative search for the best-matching parameter location in the mapping
manifold. This minimization procedure can be viewed as a recurrent net-
work dynamics with an continuous attractor manifold instead of just attrac-
tor points like in conventional recurrent associative memories. The re-
quired iteration effort is the price for rapid learning. Fortunately, it can
be kept small by applying a suitable, adaptive second order minimization
procedure (Sect. 4.5). In conjunction with an algorithmic formulation op-
timized for efficient computation also for high-dimensional problems, the
completion procedure converges already in a couple of iterations.

For special purposes, the search path in this procedure can be directed.
By modulating the cost function during the best-match iteration the PSOM
algorithm offers to partly comply to an additional, second-rank goal func-
tion, possibly contradicting the primary target function. By this means, a
mechanism is available to flexibly optimize a mix of extra constraints on
demand. For example, the six-dimensional inverse Puma kinematics can
be handled by one PSOM in the given workspace. For under-specified po-
sitioning tasks the same PSOM can implement several options to flexibly