[From Bill Powers (931220.1120 MST)
Martin Taylor (931219.1740) --
Wow, what a great job on pull-only control systems! That needed
to be done, and you have done wonderfully with it. You must have
found a no-mistake mode, because I didn't find any. For however
much comfort THAT is, from an error-prone fumbler.
There is a direct demonstration of the principles you bring out
in my Byte article, Aug. 1979 p. 94 ff.. This runnable computer
model uses linear output functions, and it is pull-only at the
muscle level but not at the higher level. However, it shows that
by using three muscles at arbitrary (but not collinear) angles,
it is possible to obtain independent control in the x and y axes,
as well as control of muscle tone. The BASIC program is very
clumsy and slow, probably not worth translating into C, but on
pp. 112-114 there are some printouts showing how the six control
systems converge toward zero error. It works just the way you say
it should.
It helps to have a single muscle-tone system that controls the
sum of all tension signals. This automatically sets the level of
opposing tensions and limits the amount of conflict. Varying the
muscle-tone reference signal then adjusts the loop gains of all
the square-law systems. This is definitely going into Little Man
Version 3.
The remarks on redundancy are most interesting, and I think
you're right. There may even be a possible generalization of your
principles, in that the major muscle groups are really less
chunked than the textbooks suggest. The attachments spread out a
lot, so that by selectively using parts of the same muscle,
different force vectors can be generated. One can almost
visualize all the thousands of individual spinal control loops as
being usable to create fine subdivisions of effort vectors, with
no clearly preferred axes (except what the joints impose). That
one would really need a team effort, with kinesiologists,
physiologists, neurologists, and control theorists. A lovely big
project, but beyond us now. Just the thing for a bunch of young
enthusiastic post-docs to get their teeth into.
ยทยทยท
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Best,
Bill P.