[From Bill Powers (920308.0400)]
Greg Williams, thanks very much for the articles by Cruse (two-part article
on "Quantitative model of walking... ", 1980) and Graham ("Simulation of a
model for coordination of leg movement...," 1977), from Biological
Cybernetics. As I suspected, I have been reinventing a number of wheels,
but it's nice to see that I haven't misconstrued the problems that others
have been trying to solve. These papers offer models containing many
features that I've incorporated into mine -- Cruse even proposes negative
feedback control systems for leg position. The main gait-control solutions
(as in Beer's model) entail circuits for resetting the legs to a forward
position after a complete stride, with the reset from one leg circuit
inhibiting and then initiating the reset for the next leg forward (or
backward), and with contralateral circuits interacting to make lateral
pairs of legs alternate steps.
While there are, as I've been discovering, many circuits that will produce
these effects, the least complex methods seem to boil down to some basic
logic that's pretty much forced on the designer. The trigger for a forward
swing can come from limit-detecting sensors, from comparing leg position
sensory signals with upper and lower limit values, and even from comparing
the muscle driving signal with upper and lower limit values (this last is
the equivalent of a central oscillator). All three methods might be
present. Of course the legs must lift during the reset. The speeds of
forward and backward swings can be produced by an integrator with variable
input currents, the design with which I began. Neither author used my
method based on negative feedback control of angular rate of change (Beer
used an assumed force-velocity relationship in the legs or body to produce
variable speed). I'm not sure that negative velocity feedback is the best
solution -- it may be overkill for bugs.
Experimental data seem to require negative feedback control of leg
position: for example, the force exerted by a leg rises when the insect
drags a weight, ruling out open-loop motor outputs. This was the only
control-system experiment done, if I remember right. No data on control of
velocity was presented in either paper; velocity might be under control or
just produced open loop.
I think it's possible to make a case for a configuration level (position
control), a transition level (velocity control), an event level (lift-
swing-drop during reset), a relationship level (signal limit detection), a
sequence level (propagation of resets from one leg to another) and a logic
level (logical conditions on mutual inhibitions among events). No category
level that I can see. These are not complete control systems, necessarily
-- some may be considered open-loop (I could also be imagining them). The
reset event, for example, is stereotyped and there's no need for the bug to
sense it or recognize it -- only to produce it. This is very interesting
from the standpoint of development or ontogeny. Could control of different
levels of variables grow out of an initial capacity to vary them open-loop?
In simple enough systems, which limit themselves to simple niches, higher-
level variables like reset events really aren't subject to disturbance
under normal conditions, and there's no requirement for precision.
Something to think about seriously.
Cruse is using the method of modeling in the right way: trying to build a
model that will account for observed aspects of behavior. The modeling does
have a forcing effect on the data, however. I am still dubious about the
notion of a central oscillator, for example, because the data really show a
LOT of variation in phase relationships between legs, which a central
pattern generator shouldn't produce. I still favor looking for an
asynchronous model in which velocity can be smoothly varied between maximum
forward and maximum reverse with resets occurring automatically. Maybe both
methods are used.
ยทยทยท
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I had occasion to do a behavioral experiment today. We have little brown
and gray bugs that come in with the firewood -- they look like "shield
bugs" but not quite; about 1 cm long, with long thin curved feelers in
front. I saw one today climbing a glass door and applied a few gentle
disturbances. This bug, fortunately, was either cold, lethargic, or stupid
because it let me fool with it for a while without panicking. I hope they
don't carry some deadly disease.
It moved slowly when I barely touched it from behind -- sometimes several
touches were required to keep it moving long enough to see its gait. This
was not a terrified bug, or else it was terrified into near-paralysis. I
couldn't tell whether the reset was propagating forward or backward, but it
may have been forward. Resets were not very fast. The legs did NOT reset
one after the other in a fixed time, 1-2-3, so the model with a fixed
temporal sequence of resets wouldn't work for this bug (unless I was seeing
its fastest gait!). Contralateral legs did produce alternate steps: you
could see each pair of legs waddling along.
The most interesting phenomena showed up when I applied a disturbance from
in front, with the bug stationary or moving. Touching an antenna on one
side only, from directly ahead, resulted in immediate swiveling of the
front of the body in the other direction, around a pivot near the hind
legs, without backing up or with only a small withdrawal. Touching both
antennae at once caused a stop, and pushing resulted in a very nice
reversal, straight back, similar to the forward stepping pattern but not as
coordinated-looking. I could get it to back up only a few steps before a
different behavior appeared.
After a couple of head-on pushes, the bug went into a sideways crab-like
movement, its body remaining oriented straight into my finger but moving
exactly sideways. All three pairs of legs went through steps with resets
just as if it were moving forward, but only lateral leg movements were
occurring. Contralateral legs still alternated steps, as before. I couldn't
see the sequence fore-and-aft -- I was too astonished by the crab gait.
When I persisted, the bug turned its body by crabbing the hind legs one way
and the forelegs the other way, with the middle legs hardly doing anything.
It pivoted about its own center. There is clearly independent control of
the leg-pairs.
All this was taking place on a vertical glass surface with the bug moving
mostly diagonally upward. When I finished, I realized that this bug (which
I was originally going to squash) had become a pet, so I had to scoop it up
on a piece of paper and deposit it in the great Outdoors, where it was
probably eaten within 5 minutes. But thanks for the game, bug.
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I now realize that there are sideways gaits with resets, and that there are
several ways to use them to produce turns with radii down to zero. The same
kind of circuit should be usable for crab motion as for forward motion, but
using the lateral muscles. I don't know if this is observable in other
species, or even other examples of my bugus minimus. One thing I am sure
of: in the bug I observed, collision with an obstacle does NOT result in a
stereotyped backing and turning, but in clear control of pressure on the
antennae by means of perfectly appropriate reversing, turning or crabbing
movements, just sufficient to reduce the pressure to zero. I don't know
what a more excitable bug would have done.
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All of this, plus reading the literature you sent me, reaffirms my view
that before a definitive model can be constructed, behavioral experiments
have to be done, and specifically experiments aimed at revealing controlled
variables. Heroic measures like amputations and deafferentation may tell us
something, but I feel that working with intact animals is likely to mislead
the least. The details of neural circuitry in these models are not very
constrained by knowledge about actual nervous systems -- it's mostly a
matter of coming up with a design that will reproduce various features of
the behavior. Some of these features -- like how long a leg remains up
during the reset phase -- aren't very important, yet it's easy to get hung
up on trying to get perfect reproduction. There are too many ways to
reproduce such details; I think it's best to try to get the major aspects
of the behavior right, and let modifications be added by those who are
truly interested in bug neurology for its own sake. There are a jillion
reset circuits that would all work the same way. I'd just as soon pick one
that works reasonably well and get on to more interesting (higher level)
behaviors. When somebody actually traces the real reset circuits, we can
just rub out that part of the model and fill in the right circuit. It won't
DO anything remarkably different.
One thing this modeling can do: it can help circuit-tracers recognize what
they're looking at. So it's good to have several possibilities for the
various functions.
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Also, I keep remembering the large variability in neuroanatomy from one bug
to another of the same species. Looking for THE gait-control circuit may be
a wild goose chase. Maybe bugs just reorganize until they have A gait-
control system that serves their higher-level purposes. In that case, we
might find that ALL the models proposed, that work, will be found in one
bug or another, even in one species. I doubt that all these behavioral
experiments mentioned by Cruse were done with many individual bugs, to
check that they all work the same way in detail. Cruse mentions that some
of the observations are contradictory. Maybe that just results from the
fact that when you've seen one bug, you have NOT seen them all. If Beer's
"genetic algorithm" modeling succeeds in creating functional bugs, it will
stop with the first design that meets the criteria -- and it might never
produce the same design twice, even though all the designs "do" the same
thing.
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Best,
Bill P.