Modelling Motor Control Paradigms - Computational Neuroscience: A Comprehensive Approach - page 553

17.5.2 Arm trajectory in a divergent force field: evidence of stiffness

modulation

In the manipulation of objects or tools people must control forces arising from inter-
action with the physical environment. Recent studies indicate that this compensation
is achieved by learning internal models of the dynamics, that is, a neural represen-
tation of the relation between motor command and movement [34, 36, 44, 64, 71].
In these studies interactions with the physical environment are stable and a learning
paradigm such as feedback error learning is capable to acquire a working internal
model of inverse dynamics to be used in feedforward compensation. However, in
many common tasks of everyday life (e.g., keeping a screwdriver in the slot of a
screw) the interaction forces are divergent from the working point and thus represent
an unstable load. In most situations, as in the case of the standing posture, we can
rule out a reflexive feedback mechanism of stabilisation. Therefore the stabilisation
can only be obtained by any or either of two mechanisms: 1) skillful modulation
of the mechanical impedance of the arm, 2) anticipatory control based on internal
models.

That the former mechanism can solve the stabilisation problem was demonstrated
in a recent study [14] in which the human arm of the subject was immersed in an
unstable force field generated by a robotic manipulator. The subjects performed
forward/backward movements on the horizontal plane between two targets. The in-
stability was the result of an artificial, divergent force field, perpendicular to the line
of action of the nominal trajectory and proportional to the lateral displacement of
the trajectory. In this way the robotic manipulator simulated a sort of inverted pen-
dulum. The subjects were able to learn the task after a sufficiently long set of trials
and the solution was achieved by a modulation and rotation of the stiffness ellipses
in such a way to neutralize the divergent field. This is a more complicated strategy
than the simple co-contraction of all the muscles that would increase the size of the
ellipses without altering their orientation. Re-orienting the ellipses requires a subtle
re-organisation of the pattern of muscle activation within a group of synergistic mus-
cles and requires extensive training. The motivation for adopting this strategy is to
optimise the mechanical impedance while keeping the metabolic cost at a minimum
value.

However, it remains to be seen whether the stabilisation of unstable dynamics by
means of optimal impedance matching is a general problem solving approach or is a
rather special purpose paradigm limited to over-trained control patterns. The prob-
lem was addressed in a pilot study [51] in which a physical inverted pendulum could
be grasped by the subjects at different heights ( Figure 17.15) and the oscillations of
the pendulum were measured by a pair of potentiometers, linked to the tip of the
pendulum by means of a suitable articulation. The task of the subject was simply
to keep the pendulum standing and the oscillations of the pendulum were recorded
together with the EMG activity of two muscles of the arm: biceps and triceps (Fig-
ure 17.16) . In this experimental setup it easy to demonstrate that the critical value
of hand stiffness for the stabilisation of the unstable plant depends upon the point of