I was showing some rubber-band demos to a friend, and that started me thinking about how to diagram a model. I realized that it's surprisingly complex. There are some important reasons to develop a model. The physical setup is very clear and agreed upon. Very interesting instances of internal and external conflict can be set up without distraction by imagined scenarios subject to differing interpretations.
Starting with simple control of knot over dot, we have the relationship knot over dot with inputs from two configurations, knot and dot. Then we have a physical connection in the environment, the rubber band between the knot and the controller's finger, and between the knot and the disturber's finger; or more simply between the two fingers with the knot in the middle of the rubber bands however they stretch (assuming equal elasticity).
But what about those fingers? Each is at the end of an arm and is moved by arm movements. So we have the arm demo controlling the fingertip. Maybe we don't need to specify the control of the fingertip into a hook configuration. Movement is constrained to the horizontal plane, but it's not clear to me that this constraint enables the arm demo to be simplified to fewer degrees of freedom at, say, the shoulder joint. The demo would have to be modified so that the relationship between knot and dot is what is controlled, rather than the relationship between fingertip and target.
In the special issue of International Journal of Human-Machine Systems
edited by Martin Taylor.
I'm working slowly with Richard Kennaway to introduce more realistic muscle
models (with exponential spring constants as in real muscles) into the arm
model, and to bring in force signals as well as positional sensory signals.
The force signals are important because in the rubber-band demo the stretch
of the rubber-bands is a function of applied force. People can often
control in either of two modes: position or force. In force control,
position is not controlled; it is varied so as to maintain whatever force
is desired, independently of position. An example can be seen by having
someone hold out a hand palm up while you press on it palm down. Bring the
sensed amount of skin pressure to some small value, then ask the other
person to raise and lower the hand while you maintain the same pressure.
Skin pressure signals go directly from pressure sensors to the spinal motor
neurons. But there is more to it than that, as you can see from this example:
Press downward with the palm of your hand on the tabletop, bringing the
sensation of skin pressure to some specific level. Remember that pressure.
Now turn your hand over with palm up and press _up_ on the underside of the
table with the same amount of pressure. Note that in the first case one set
of muscles, including the triceps, was being used to control the skin
pressure on the palm of the hand. In the second case, a different set
(biceps) was being used to control the _same_ skin pressure sensations.
Obviously, the connections from the skin sensors to the spinal motor
neurons were not physically re-routed just by turning your hand over. Yet
they were _functionally_ re-routed.
I can see only two solutions, neither of which is of much help. (1) Signals
descending the spinal cord can be used to vary the weights in the feedback
connections at the spinal level, adjusting which sensors are connected to
which spinal motor neurons, or (2) the actual feedback loops are much
higher in the brain, where similar effects are produced (the central
sulcus). The same signals that rotate the forearm must adjust these
weightings -- otherwise, simply turning your palm over would change
negative feedback to positive feedback.
I wish we had a lot more people working on the arm model.