Page 41 - Human Inspired Dexterity in Robotic Manipulation

Sensorimotor Learning of Dexterous Manipulation 37

To generate motor output in trial n, the sensorimotor system had to first
generate a plan based on visual context cues:
T
x c nðÞ ¼ x nðÞ c nðÞ (3.4)
T
T
where c(n) is a selection vector that takes the value of [1,0] or [0,1] for
context A and B. The final motor output, however, is biased due to a non-
linear interaction between two internal states x c and u:

ynðÞ ¼ x c nðÞ + bias nðÞ (3.5)
bias nðÞ ¼ D•unðÞ= 1 + exp sign unðÞ•E•x c nðÞððð ÞÞÞ (3.6)
where sign(u) is 1 and 1if u is positive and negative, respectively. Although
Eq. (3.6) seems to be arbitrary, it effectively captures the nonlinear combi-
nation of two sensorimotor processes with only two parameters (D and E).
Note that two parameters are necessary to account for such a context-
dependent combination of the two processes. In fact, Eq. (3.6) is essentially
a sigmoid function whose shape (both magnitude and direction) is modu-
lated by u. A positive u generates a small- and large-positive bias to a positive
and negative x c , respectively, whereas a negative u generates a small- and
large-negative bias to negative and positive x c , respectively.
Finally, to model the effect of the break duration, we again assume that
subjects can well retain the context-dependent memory component, and
that the context-independent and use-dependent memory decays exponen-
tially, such that the half-life of the decay is F•ln(2)

un + tÞ ¼ unðÞ•e t=F (3.7)
ð
We used a nonlinear optimization procedure in Matlab (“fmincon”) to
estimate the six parameters (A, B, C, D, E, F) of our DPNI model. This
procedure minimizes a mean-squared error between the output of the
model and experimental data (T com ) from selected trials in multiple groups
(Rndm, Ctrl, and IF). The mean T com averaged within each of these trials
was used because the data from individual subjects was too noisy to obtain
reliable fits. Confidence intervals for parameter estimates were calculated
using a boot-strap procedure [5,13] that resampled the experimental data
with replacement data to obtain 1000 boot-strap data sets. The model
was fitted separately to the mean T com of each of these data sets. The
95% confidence intervals were calculated as the 2.5 and 97.5 percentile
values from the distribution for each parameter obtained across the 1000
individual fits.