Controlled variables vs. side-effects

[From Bill Powers (950527.0950 MDT)]

Just got back from seeing our daughter Barbara off in the start of the
Iron Horse bike race, Durango to Silverton. The length is 45 miles, the
total climb over two main passes is 5500 feet (the highest pass, Molas,
is about 11,000 feet). Last year (her first, at age 35) she did it in
4:20; this year she hopes for under 4:00. The pro winning time last year
was 2:10. She should be about halfway right now, starting the four-mile
climb to Coal Bank Pass (2500 foot climb to over 10,000 ft). Go Bara!

ยทยทยท

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Rick Marken, Bruce Abbott (continuing) --

When you push on a control system, it pushes back.

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RE: trajectories vs. system organization

In a great deal of modern behavioral research, trajectories of movement
are examined in the hope of finding invariants that will reveal secrets
of behavior. This approach ties in with system models that compute
inverse kinematics and dynamics and use motor programs to produce
actions open-loop. These models assume that the path followed by a limb
or the whole body is specified in advance in terms of end-positions and
derivatives during the transition, so the path that is followed reflects
the computations that are going on inside the system.

It is this orientation that explains papers like

Atkeson, C. G. and Hollerback, J.M.(1985); Kinematic features of
unrestrained vertical arm movements. The Journal of Neuroscience _5_,
#9, 2318-2330.

In the described experiments, subjects move a hand in the vertical plane
at various prescribed speeds from a starting point to variously located
targets, and the positions are recorded as videos of the positions of
illuminated targets fastened to various parts of the arm and hand.

The authors constructed a tangential-velocity vs time profile of the
wrist movement for various speeds, directions, and distances of
movement. They normalized the profiles to a fixed magnitude, then to a
fixed duration, and found that the curves then had very nearly the same
shape. Using a "similarity" calculation, they quantified the measures of
similarity.

They were then able to compare these normalized tangential velocity
profiles across various directions and amounts of movement and show that
the treated profiles were very close to the same. They conclude:

     Taken together, shape invariance for path and tangential velocity
     profile indicates that subjects execute only one form of trajectory
     between any two targets when not instructed to do otherwise. The
     only changes in trajectory are simple scaling operations to
     accomodate different speeds. Furthermore, subjects use the same
     tangential velocity profile shape to make radically different
     movements, even when the shapes of the paths are not the same in
     extrinsic coordinates. Different subjects use the same tangential
     velocity profile shape.

     ... this would be consistent with a simplifying strategy for joint
     torque formation by separation of gravity torques from dynamic
     torques and a uniform scaling of the tangential velocity profile
     ... (p. 2325)

     ... if the motor controller has the ability to fashion correct
     torques for one movement, why does it not use this same ability for
     all subsequent movements rather than utilize the dynamic scaling
     properties? Among the possibilities we are considering, the first
     is a generalized motor tape where only one movement between points
     must be known if the dynanmic components in equation 6 are stored
     separately....A second possibility is a modification of tabular
     approaches [ref] where the dimensionality and parameter adjustment
     problem could be reduced by separate tables for the four components
     in equation 6. (p. 2326)

This paper was sent to me by Greg Williams as a source of data about
actual hand movements, for comparison with the hand movements generated
by Little Man v. 2, the version using actual arm dynamics for the
external part of the model. The model's hand movements were, as Greg
will attest, quite close to those shown in this paper, being slightly
curved lines connecting the end-points. Forward and reverse movements
followed somewhat different paths, and by adjustment of model parameters
this difference, too, could be reproduced.

What is interesting is that the fit between the Little Man and the real
data was found without considering tangential velocity profiles or doing
any scaling or normalization. In other words, the invariances noted by
the authors were simply side-effects of the operation of the control
systems of the arm interacting with the dynamics of the physical arm. In
the Little Man there is no trajectory planning, no storage of movement
parameters, no table-lookup facility, no computation of invariant
velocity profiles. The observed behavior is simply a reflection of the
organization of the control system and the physical plant.

The path which Atkeson, Hollerbach (and many others at MIT and
elsewhere) are treading is a blind alley, because no matter how
carefully the observations are made and the invariances are calculated,
there will be no hint of the control-system organization, the SIMPLE
control-system organization, that (I claim) is actually creating the
observed trajectories. No doubt a sufficiently complex trajectory-
control model, with just the right tables of coefficients and velocity
profiles, would ultimately be able to match the behavior. But this line
of investigation, with its underlying assumptions, will never lead to
the far simpler and anatomically correct PCT model.

In terms of the current discussion on the net, the observations made by
the authors were interesting as checks on the model, but were actually
irrelevant to what the control systems were doing. The control systems
(the first two levels of the Little Man model) controlled only three
kinds of variables that underlay the perceptual signals: angular
positions, angular velocities, and angular accelerations. They received
no information about wrist position in laboratory space. They contained
no provision for computing tangential velocities, or for computing
positions of points on the physical arm in space, or for computing
space-time invariants. The behavior of the control systems, in other
words, took place in a proprioceptive perceptual space that no outside
observer could see. In order to translate from this perceptual space
into variables that were observable, the computer program generated the
resulting arm positions and plotted them in a form suitable for visual
inspection. So a side-effect of the actual control process was presented
for comparison with a corresponding side-effect of the real control
process, as visible to an outside observer.

The approach of Atkeson and Hollerbach appears in many guises. We have
already talked about the apparent scaling and normalization of
trajectories seen when two hands move rapidly and simultaneously to
targets at different distances. In operant conditioning experiments, we
have seen how the control of reinforcement by behavior is obscured by
the fact that variations in behavior tend to stabilize reinforcement
rates, thus making reinforcement rate appear to be the independent
variable.

We have also seen a few -- a very few, so far -- studies in which the
PCT orientation was used, Srinivasan's being the most recent. What is
the difference? I think the difference is in whether the emphasis is on
seeing the behavior from the behaving systems's point of view, as best
we can imagine it, and seeing it strictly from the human observer's
point of view.

From the human observer's point of view, it seems that we must account

for the detailed movements and physical interactions that are seen to
occur. This leads to trying to find invariances or striking mathematical
regularities of some sort in the observed behaviors. It leads to
imagining an internal system that is producing explicitly what we are
observing; if we observe a trajectory, there must be some generator that
is specifically calculating that trajectory.

But from the behaving system's point of view, we can consider only the
information that is available to the behaving system; we must look for
our explanations there. The trajectories of movement that result from
the system's operation are basically side-effects; they are not planned
and they are constant only in a constant environment. Furthermore, they
are unknown to the behaving system and play no part in the production of
behavior. We can deduce from the model of the behaving system what the
observable side-effects would be in a given environment, and so can
compare those side-effects with our external observations of the
behavior. But our explanation of the behavior is not based on those
side-effects.

Most important, when we simply describe behavior as a sequence of
physical happenings and relationships, we have no way of knowing whether
we are describing controlled variables or side-effects. When we see a
fly landing on a ceiling, it is perfectly possible that NOT A SINGLE
ASPECT OF WHAT WE SEE is perceived and controlled by the fly. When we
see the fly extending its legs just prior to landing, the fly may have
no perception of the configuration of its legs; to the fly, all that is
controlled may be two or three joint-angle signals, not even identified
by the fly as representing joint angle. When we see the wings stop
flapping, to the fly all that may be controlled is a sensation of
vibration. When we see the fly's body making a steep angle with the
surface, the fly may simply be experiencing a visual signal indicating,
as Rick guessed, a gradient of illumination or texture. Not one of the
variables we are observing may ever appear in the ultimate model of the
fly's internal organization, just as in the Little Man the actual arm
configuration and hand position never appear in the model of the first
two (kinesthetic) levels of control. Once we have the right model, we
can always compute how its operation will appear to an observer who is
focusing on various side-effects of the actions. But the model itself
says nothing about those appearances, and makes no use of them.
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Best to all,

Bill P.