Biomedical Engineering Reference
In-Depth Information
the intended direction and speed of the end-effector. Relaxation is a direct, not an
inverse computational process and it can be implemented in a very natural way in
terms of neural networks by means of interactive self-organised cortical maps [47].
17.3.2
The viscous-elastic properties of the human muscles
Perhaps the most marked difference between the robotic and the biological perspec-
tive in the field of motor control is that in contrast with the typical robotic actuators
(torque motors), which are force-controlled and uni-directional (in torque motors the
output torque only depends on the applied current, independent of the load reaction),
the biological actuators (striated muscles) are position-controlled and bi-directional:
the actual force delivered by the muscle to the load is a function of the descending
motor command and of the reaction of the load. This bi-directional relationship is
characterised by two main components:
•
A length-dependent component, which is equivalent to an energy-storage elas-
tic characteristic of the muscle [17, 56];
•
A velocity-dependent Hill-type component, which captures the dissipative,
viscous characteristic of the muscle [70].
What is important, from the motor control point of view, is that the length-tension
curves of the muscles cannot be approximated in a linear way but have a charac-
teristic exponential course, related to the progressive recruitment of motor units).
This means that muscle stiffness is not constant but is a function of the particular
equilibrium point. In fact, the descending motor commands determine the point of
intersection m of the exponential curves with the horizontal line: see
Figure 17.8.
In this model m is the controllable parameter, or m-command, that sets the activa-
tion threshold of the monosynaptic stretch reflex and thus determines the
rest-length
of the muscle-spring. In this sense muscles are position controlled and by exploit-
ing the fact that each joint is activated by antagonistic groups of muscles the brain
can determine independently the overall equilibrium point (via a pattern of
recipro-
cal
m-commands to antagonistic muscles) and the overall stiffness (via a pattern of
coactivation
m-commands to synergistic muscles).
Such bi-directional characteristics of the muscles in a kinematic chain, such as
the arm, are combined together determining an elastic interaction between the end-
effector and the load which has markedly anisotropic features (see the stiffness el-
lipses of
Figure 17.9)
.
This ellipse can be computed experimentally by generating
small disturbances in different directions and measuring the restoring force vector.
As seen in the figure, the orientation of the stiffness ellipses appear to be charac-
terised by a polar pattern, with the long axis (where the hand appears to be stiffer)
aligned along the shoulder-hand direction. The size of such ellipses is easily un-
der voluntary control by modulation of the overall coactivation of arm muscles. On
the contrary, the orientation of the ellipses does not appear to be under immediate
voluntary control, with the exception of highly learned movements [14].
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