Now we have to derive more plausible "online" tool
to find C. And due to this learning it will be one way defined for
a given arm.
How we could estimate the noise reduction?
Our posterior probability is
(22a)
Where q waved is q desired and we call E a covariance matrix
of angles' construction errors.
(23a)
The total mistake could be estimated on logarithmic scale
as
(24a)
Lets take derivates of this total mistake by elements of
matrix C.
(25a)
Taking advantage of
(26a)
and of (where delta is Kroneker simbol)
(27a)
We would derive at the end
(28a)
Thus we prove relations between the angles driving's error
and stiffness matrix.
So we could simpy seak for the desired stiffness matrix
using our experience, as we know E matrix. Deviations of angles
q from the desired values could be estimated roughly as
(29a)
In such a way this theory could imply neural networks implications.
Lets consider a neural network that is mapping from the space of our configurations
to the space of matrices C. Every matrix C could be learned
in a batch process over the set of our mistakes at this particular configuration.
