Page 40 - Human Inspired Dexterity in Robotic Manipulation

36 Human Inspired Dexterity in Robotic Manipulation

the current trial. Specifically, A ¼ [A, 0; 0, 1] and B ¼ [B, 0] for context A,
or A ¼ [1, 0; 0, A] and B ¼ [0, B] for context B. Eq. (3.2) assumes that neg-
ligible generalization occurs across contexts during learning, which has been
demonstrated in the TF group. It assumes that the “retention rate” A is also
context dependent. That is, no decay of the inactive context should occur,
which is a phenomenon that is supported by our experiment showing long-
term recall of the learned context (RT groups). Both of these assumptions
are consistent with the finding that the error-based update of the internal
model is context dependent [37]. Similar to the DRMC model, we also
T
set the initial value of x(1) to (180, 180) to match the data-revealing
subjects’ ability to visually initialize the internal representation.
The novel feature of our DPNI model is the use-dependent memory
that generates a nonlinear bias to the motor output in the subsequent trial.
Specifically, we defined the use-dependent memory u(n) as a simple aver-
aging process of previous manipulations:

ð
un +1Þ ¼ 1 CÞ•un ðÞ + C•T target n ðÞ (3.3)
ð
where C denotes the contribution of the previous trial in the averaging pro-
cess. This equation is conceptually similar to the use-dependent learning
model [16]. However, unlike reaching movements, which are single ballistic
motor actions, our task (and other object-manipulation tasks) essentially
consists of two phases: a lifting phase and a 2-s holding phase. While the
maximum error occurred during lifting, subjects had to consistently exert
the compensatory torque corresponding to the T target during the holding
phase to maintain zero-object roll based on real-time sensory feedback.
It has been demonstrated that grip-force bias can be generated with only
squeezing objects without lifting them [25]. Therefore, we use the T target
to build up the use-dependent memory. The same study also demonstrated
that such use-dependent memory was possibly independent from the con-
text of the task. Therefore, we assume use-dependent memory to be the
source of context-independent bias that generates the interference in our
experimental paradigm [31].
Most importantly, we think that the bias caused by use-dependent mem-
ory is also a function of the internal state x that is actively engaged for the
context in the current trial. Specifically, this bias is small when the direction
of the use-dependent memory of the torque is the same as the engaged
internal state, whereas the bias is large when they have opposite directions.