Biomedical Engineering Reference
In-Depth Information
17.5 Controlling unstable plants
There has been interest in recent years in the motor control of unstable tasks, partic-
ularly in two specific paradigms:
•
Stabilisation of the human inverted pendulum in quiet standing [3, 38, 39, 48,
49, 69];
•
Arm trajectory formation in an artificial, unstable force field [14].
In both cases the instability is associated with a potential field which has a maximum
value around the reference state and feeds a diverging force field, thus having an
antagonistic action with respect to the converging force field associated with mus-
cle stiffness. In general, there are three possible mechanisms of stabilisation of an
unstable load:
1.
Reflex Mechanism
, determined by a number of different sensory feedbacks;
it is unfeasible in this context because it tends to worsen the instability as a
consequence of the substantial delays in the control loop.
2.
Stiffness Mechanism,
related to the mechanical properties of muscles: it op-
erates without delay, and can be modulated by means of coactivation, which
is applied uniformly to all the muscles of a functional group, or by a more
subtle re-distribution of activities in order to match the peculiar features of the
task/load.
3.
Anticipatory feedforward/feedback mechanism,
which has an integrative cen-
tral nature: it is based on two types of internal models: a) a model for multi-
sensory fusion, thus compensating by means of
prediction
the transducton and
propagation delays of sensory information, and b) a model for the generation
of motor commands that anticipate the destabilising consequences of the load.
In any case, the divergent force field can be viewed as a
negative spring
and the
rate of growth of the field, away from the equilibrium point, sets a
critical level of
stiffness
. Above this level stiffness alone can stabilise the plant; below this level the
effect of stiffness must be complemented by anticipatory control mechanisms.
17.5.1
Stabilisation of the standing posture: evidence of anticipatory
compensation
In spite of its apparent simplicity, the nature of the control mechanisms that allow
humans to stand up is still an object of controversy. Visual, vestibular, propriocep-
tive, tactile, and muscular factors clearly play a role in the stabilisation process and
different authors have stressed one or the other. In particular, a model has been pro-
posed by Winter et al. [69] that attributes to muscle stiffness alone the capability
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