[Avery Andrews 930316.1200]
Perhaps one reason that the Arm demo hasn't made the impression that
one might have hoped for is that the actual principles underlying its
operation are somewhat more subtle than is immediately apparent, and
there needs to be rather more in the way of purple prose than there
is to explain how it works. And, I suspect, more on the way of
simpler `sub-demos' to illustrate specific principles.
For example, after observing the rather stupid-looking trajectories
created by my shoulder-centered polar coordinate arm (when the target
is above the elbow the hand goes up to far, then circles back and over
approaching the target in a sort of spiral), I thought, well what would
happen if the polar coordinates had their origin in a more eye-like
position, such as above the shoulder (at half the length of the
forearm). Voila, the trajectories looked much more sensible, without
any compensations. Whether they are realistic I don't know - haven't
gotten around to checking out that part of the literature yet.
But the reason why they are more sensible is easy to see:
x T
S --------- E -------- H
In a situation like this, the apparent angular error at the start
of the movement will seem to be much less if the origin is at x
(eye-position, sort of) rather than at S (shoulder position), so
the inappropriate shoulder elevation will be reduced or even
eliminated, depending on the details of the circumstances.
I think the shoulder-centered coordinates may have their virtues,
however. For example, changes in shoulder yaw and pitch will have
a very pleasant relationship to changes in the azimith and elevation
of *any point* on the arm, namely, the identity relation. This isn't
true for eye-centered polar coordinates. Coordinate
transformations aren't really that hard to compute, & there's no
reason why people couldn't make use of many coordinate systems
simultaneously (indeed I think I recall an article in Synthese
(or maybe BBS) arguing that they used six different ones at once).
More generally, I agree entirely with everything that Bruce Nevin said
recently about PCT presentation - I don't think that people are all
necessarily as block-headed as Rick Marken thinks they are, but they
will act that way if the presentation isn't tailored to their current
state of mind. In this vein, the theme that the eye-hand-arm system
is set up so as to make effective perceptual control easy is one that
might appeal to people who are attracted to Gibson, Kugler, Turvey,
etc.
If anyone is interested, I can provide TC code for the `jacobian'
and `polar' schemes, though it's pretty grotty. I would think that
the basic points could be made with a spreadsheet, if trig functions
are available (such as atan2, to go from xyz to polar).
Avery.Andrews@anu.edu.au