Hi, Isaac --
I finally found the reference to which I alluded, in
McMahon, T.A. (1984); Muscles, reflexes, and locomotion. Princeton, NJ:
Princeton University Press). p. 149:
"It was supposed originally that the tendon organs did nothing until safe
muscle loads were exceeded, but later evidence showed that tendon organs
responded to less than 0.1 g of force applied directly to the base of the
capsule (Houk et. al. 1971). An organization like that diagrammed in fig.
6.4 [note: exactly the model used in the Little Man] has been suggested,in
which afferent activity from both spindle receptors and tendon organs
balance in such a way that neither muscle force nor muscle length should be
considered a controlled quantity -- rather, it is their ratio ..."
This goes on to a bad conclusion, but the basic point is made, that the
tendon feedback is continuous down to very small forces.
The Houk reference is
Houk, J. C., Singer, J. J.,and Henneman, E. (1971); Adequate stimulus for
tendon organs with observations on the mechanics of the ankle joint. J.
Neurophysiol. 34; 1051-1065.
The Little Man simulation shows what the roles of tendon and spindle
feedback are. The tendon feedback is inhibitory, and constitutes a force
feedback which is equivalent to torque feedback; both are equivalent to
angular acceleration feedback. The reference signal entering the motor
neuron is compared against the acceleration feedback, so the controlled
variable at this level is (angular) acceleration. An interesting feature of
this control system is that if a disturbance is applied to a limb when the
alpha reference signal is zero and there is no gamma system, the limb
ACTIVELY COMPLIES with a positional disturbance, the muscles changing their
length to make limb movement compliant with whatever is pushing on the
limb. To see this clearly you have to take opposing muscles into account;
in the Little Man model, the two opposing control systems are boiled down
to a single equivalent bidirectional system. It's easy to overlook these
feature of the Little Man, because they are handled by just a couple of
lines of code and don't stand out as anything important.
The effect of the tendon feedback is to make the limb seem nearly massless,
to higher-level control systems and external positional disturbances.
The net reference signal entering the motoneuron consists of the alpha
efferent signal PLUS a signal representing the mechanical error signal from
the muscle spindle (length) control system. There is a phasic and a tonic
component in the spindle error signal (McMahon, p. 153). Considering only
the phasic signal, we have something close to velocity feedback, the error
signal becoming the reference signal for sensed torque (which is
proportional to angular acceleration). And the tonic component becomes the
next level of feedback providing position control, which acts by setting
the reference level for the velocity control level. That decomposition of
the three levels of control -- acceleration, velocity, and position -- is
an algebraic artifice, but entirely equivalent to the actual arrangement.
Nature has simply collapsed two of the levels into one, a neat and
efficient arrangement. I have found that this arrangement provides stable
control of angle without any added compensation, even with massy limbs.
The alpha efferent signal serves as a force reference signal, which is the
mode of control that occurs when the limb is pressing against the ground or
a massive object (isometric case). The gamma efferent is primarily a muscle
length control system, which is effective when the limb is free to move.
Richard Kennaway and I are working out how to apply these principles to
archy the bug's legs, with the added feature that sensors on the feet
provide added force feedback (those sensors are known to synapse to the
motoneurons, too, in the inhibitory sense, just like the Golgi sensors).
If you look at earlier chapters in McMahon, you will see that the Little
Man's muscle model is very close to what McMahon shows -- see especially
the lower part of Fig. 3.7, p. 67. The LM model is really as realistic in
all its details as I could make it. Any major departures of its behavior
from real behavior (as in "reaching" in a spinning room) are most likely to
arise from higher levels of organization.