Page 84 - Human Inspired Dexterity in Robotic Manipulation

80 Human Inspired Dexterity in Robotic Manipulation

In our opinion, the two models previously discussed can be two
extremes of a yet unknown computational model. While the first is
applicable when the hand dynamics are already “prewired” in the
CNS with reasonable accuracy, the second may take place at earlier stages
of learning when the hand dynamics are acquired/rewired together with
the novel environment. More experiments, conducted for a wider vari-
ety of dynamic environments (different movement times, different
masses, and stiffness coefficients) and with a larger number of human sub-
jects, are necessary to clarify the dynamics of the learning process. One
apparent limitation here is the affordable learning time as we are dealing
with highly skillful movements, and for some environments the reaching
task can be very nontrivial, exhibiting multiple peaks in the hand velocity
profiles [27].
2. Deterministic vs. stochastic. The model developed in this chapter is deter-
ministic. A stochastic formulation of the optimal control problem may
be more appealing as the computing elements and actuators in biolog-
ical systems exhibit a certain degree of stochasticity. It has been sug-
gested [28, 29] that the minimization of end-point errors in the
presence of motor command noise is a major determinant of motor
planning. On the other hand, it has been shown [30]thatthe
minimum-variance model with signal-depended noise is equivalent
to the minimum-effort model (5.13) if the plant dynamics (5.11),
(5.27) have zero eigenvalues, which apparently holds true in our case.
To explore the differences between the two approaches to a greater
extent, it would be necessary to introduce damping elements in the
structure of the flexible object.
3. Comfortability and the natural boundary conditions. In our experiments the
subjects were instructed to produce reaching movements in a comfort-
able way, operating without undue stress, away from the limits of neu-
romuscular performance. This instruction is, presumably, transcribed by
the CNS into the zero-boundary conditions for the hand acceleration at
the start and end points. Still, it is not clear if (and if yes, how well) the
CNS can control the higher derivatives of the hand position. If the
movement gets closer to the constraints imposed by the neural and mus-
culoskeletal hardware (a shorter movement time or higher accuracy of
reaching, or a lower natural frequency of the flexible objects), the
assumption of zero initial and final acceleration is likely to be violated
[31]. Removing this assumption from our optimization problems will
result in the so-called natural boundary conditions (λ 7 (0) ¼ 0 and