Motor program sources; Atkeson & Hollerbach

CSGnet Archive CSG1993
1

[From Bill Powers (931029.0750 MDT)]

Greg Williams (931028) --

Very nice job in picking up the quote on motor schemas. Don't
forget to include William James -- the constancy of ends and the
variability of means. All this shows that the problem has been
known for a very long time (100 years), but that the solution has
eluded a continuing search.

The critical misdirection is contained in

Thus whatever is learned and stored in long-term memory cannot
be a specific set of muscle commands but must represent a more
generic or general set of specifications of how to reach the
desired goal.

Behind the idea of "specifications of how to reach the goal" is
still a picture of direct causality: the specification is for
_how_ to reach the goal, instead of _what goal to reach._ You can
see this same idea in Atkeson and Hollerbach:

"A strategy for gaining insight into planning and control
processes of the motor system is to look for kinematic
invariances in trajectories of movement. The significance of
straight-line movements is that they imply movement planning at
the hand or object level." (p. 2318)

In the discussion:

"Taken together, shape invariances for path and tangential
velocity profiles indicates that subjects execute only one form
of trajectory between any two targets when not instructed to do
otherwise. The only changes in the trajectory are simple scaling
operations to accomodate different speeds. ... Different subjects
use the same tangential velocity profile shape." (pp. 2325-6).

And making the problem even clearer:

"A number of issues remain with regard to these dynamic scaling
results. How are the initial torques for the first movement
generated? If the motor controller has the ability to fashion the
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 need be known if the dynamic components
in Equation 6 are stored separately. ... A second possibility is
a modification of tabular approaches (Rabert, 1978) where the
dimensionality and parameter adjustment problem could be reduced
by separate tables for the four components in equation 6." (p.
2327).

The only possibilities being considered are those that involve
open-loop generation of the torques that will produce a pre-
planned trajectory. "Equation 6" is an equation expressing joint
torque as a nonlinear function of scaling factors applied to
torques previously produced for a known movement. As noted above,
the problem is how the torques for the known movement are
generated in the first place. This problem is not solved. What
the authors hope for is that by finding invariants such as
velocity profiles, they will be able to deduce a motor program
that will produce constant results in object space even when
variations in torque are required.

They simply haven't got far enough into the problem to see that
this quest is hopeless. If they did manage to come up with a
motor program that could realistically create several
trajectories of hand movement between different pairs of points,
they would then have to ask how this can work with different
loads. If they solved that problem, they would have to explain
how the trajectories are produced when the loads are vary
unexpectedly and the muscles progressively fatigue. And then they
would have to explain how the right torques can be produced under
varying loads (such as the varying friction between pencil and
paper) and with fatiguing muscles, when the task is to write the
subject's name. And then they would have to explain how a subject
can accomplish the same movements under the same uncertain
conditions for the tip of a pointer held in the hand. In truth,
they are extrapolating a long way ahead, and predicting success,
when they have not even found the simplest motor program of all:
that for moving quickly between two points under undisturbed
conditions. Their projected work simply expresses faith that
somehow the require movements in object space can be generated by
a clever enough motor programming device -- without ever taking
feedback into account, the feedback both kinesthetic and visual
that is _known_ to exist and that is _known_ to be essential for
skilled performance.

There is an explanation for the observed invariances of velocity
profiles that Atkeson and Hollerbach never consider: these
invariances might simply be the natural outcome of physical
processes of control. There might be no need at all for the motor
program to precompute them. The velocity profiles are
individually scaled both as to amplitude and duration in order to
generate the congruence that the authors found. If you do this
for the joint angular velocity profiles in Little Man V2, you
will find similar invariances, even though there is nothing
computing them. It just happens that when a control system is
given a step-change of reference-signal, the trajectory of the
controlled variable naturally scales up or down so that the
velocity rises and falls along the same generic curve. This is
purely a consequence of the mathematical relationships of control
and the passive dynamical properties of the arm; nothing is
acting to make sure that the trajectory follows any particular
path. The trajectory is a side-effect, not a planned movement.
Evidence of trajectory planning would appear only if the actual
trajectory departed from the one that can be explained as a step-
change in the reference signal of a control system from one fixed
value to another. For example, one can easily move a finger from
one point to another along a semi-circle or an S-shaped curve.
_That_ requires a "program" of velocity or position reference
signals. But it still doesn't require precomputing torques.

···

------------------------------------------------
The key idea to look for in all these sources is how the authors
propose to account for the forces that create movements. It's
clear in Atkeson and Hollerbach that the torques are going to be
computed so as to have the required object-space consequences and
that proprioceptive and visual feedback are not considered. All
approaches that propose to use inverse kinematic or inverse
dynamical computations are also attempting to solve the problem
open-loop. In all such approaches, the key idea that is missing
is comparison of the observed consequences with the desired
consequence _in real time_ as the means of producing the required
output signals.
------------------------------------------------
Atkeson, C. G., and Hollerbach, J.M.; Kinematic Features of
Unrestrained Vertical Arm Movements. The Journal oif Neuroscience
_5_, No. 9, pp. 2318-2330. Sept. 1985.
--------------------------------------------------------------
Best,

Bill P.

2

From Tom Bourbon [931029.1615]

[From Bill Powers (931029.0750 MDT)]

Greg Williams (931028) --

Very nice job in picking up the quote on motor schemas. Don't
forget to include William James -- the constancy of ends and the
variability of means. All this shows that the problem has been
known for a very long time (100 years), but that the solution
has eluded a continuing search.

The critical misdirection is contained in

Thus whatever is learned and stored in long-term memory cannot
be a specific set of muscle commands but must represent a more
generic or general set of specifications of how to reach the
desired goal.

Behind the idea of "specifications of how to reach the goal" is
still a picture of direct causality: the specification is for
_how_ to reach the goal, instead of _what goal to reach._ You
can see this same idea in Atkeson and Hollerbach:

Which Bill then quoted and discussed. His post probably deserves
posting again, but I'll skip to his conclusion. Well, I'll cheat
just a little and include an extra (and extra-good) paragraph.

There is an explanation for the observed invariances of velocity
profiles that Atkeson and Hollerbach never consider: these
invariances might simply be the natural outcome of physical
processes of control. There might be no need at all for the
motor program to precompute them. The velocity profiles are
individually scaled both as to amplitude and duration in order
to generate the congruence that the authors found. If you do
this for the joint angular velocity profiles in Little Man V2,
you will find similar invariances, even though there is nothing
computing them. It just happens that when a control system is
given a step-change of reference-signal, the trajectory of the
controlled variable naturally scales up or down so that the
velocity rises and falls along the same generic curve. This is
purely a consequence of the mathematical relationships of
control and the passive dynamical properties of the arm; nothing
is acting to make sure that the trajectory follows any
particular path. The trajectory is a side-effect, not a planned
movement. Evidence of trajectory planning would appear only if
the actual trajectory departed from the one that can be
explained as a step- change in the reference signal of a control
system from one fixed value to another. For example, one can
easily move a finger from one point to another along a
semi-circle or an S-shaped curve. _That_ requires a "program" of
velocity or position reference signals. But it still doesn't
require precomputing torques.

------------------------------------------------
The key idea to look for in all these sources is how the authors
propose to account for the forces that create movements. It's
clear in Atkeson and Hollerbach that the torques are going to be
computed so as to have the required object-space consequences
and that proprioceptive and visual feedback are not considered.
All approaches that propose to use inverse kinematic or inverse
dynamical computations are also attempting to solve the problem
open-loop. In all such approaches, the key idea that is missing
is comparison of the observed consequences with the desired
consequence _in real time_ as the means of producing the
required output signals.
------------------------------------------------
Atkeson, C. G., and Hollerbach, J.M.; Kinematic Features of
Unrestrained Vertical Arm Movements. The Journal oif
Neuroscience _5_, No. 9, pp. 2318-2330. Sept. 1985.
--------------------------------------------------------------

Nicely put. Concerning our discussions about who else (other
than some PCTers) does and does not "get it" on the topic of
motor control, the bottom line Bill identifies is this: Look at
what they say about the creation of the forces that create
movements. If they say the forces (and the kinematics and
dynamics) "just happen" during the control of intended
perceptions, they got it. If they say the nervous system must
first compute the kinematics and dynamics and then command the
desired actions, they didn't get it.

To Bill's analysis I would add another "cut" or "slice" we can
make when we decide who got it. Some people -- no, many people
who write about behavior say *too little* for us to know whether
or not they got it. For all people who say nothing about how the
forces are created, all we can say with certainty is that we
don't know what they think about the subject. That being the
case, I believe we should leave them in their present undefined
state and direct our attention and discussion elsewhere.

(*-------------------------------------------------*)

I am looking at a chapter titled "Cybernetic aspects of the
nervous system and sense organs," by M. Zimmermann, in Robert F.
Schmidt & Gerhard Thews (1983) (Eds), Human Physiology, NY:
Springer-Verlag, pp. 315-328. There are many references to
earlier work.

Zimmermann begins the chapter by paraphrasing Wiener's definition
of cybernetics as a study of the processes of communication and
regulation. After discussing information theory, Z. moves to
regulation, which he explains, "in the language of *control
theory*" (italics in the original). He gets quite a bit of the
language right.

p. 321: "The controlled variable is a *state* that is to be kept
constant (room temperature in our example)." (You can probably
guess his example.) To paraphrase (*--* indicates words he put
in italics), a sensor measures the current state of the c.v. and
sends out "an appropriate *feedback signal*" (hmm, what is that?)
to the controller. The controller compares the current value
with a *reference signal*; if they differ, an *error signal*
causes the controller to initiate corrective measures -- the
controller sends out a *control signal* (?) to an appropriate
device, which is the controlling element or *effector*. "Control
signals are sent out continuously until the feedback and
reference signals match. Factors that cause the controlled
variable to depart from the set point given by the reference
signal are called *perturbations* (e.g., loss of heat from the
room)" (pp. 322-3).

p. 322; a sentence in italics: "The essential feature of a
control circuit is thus the closed-loop arrangement, operating so
that any disturbance of the controlled variable is automatically
corrected." More elaborate control systems can have " ...
*variable gain*; the *gain of the controller* determines its
*sensitivity* to differences between the feedback and reference
signals." (Warms the heart of a PCT person, doesn't it?)

Zimmermann discusses changes in the reference signal. p. 322:
"The controller's response to a change in the *reference signal*
is the same as to a change in the feedback signal; the
*difference* between the two is measured and the controlling
element acts on the controlled variable until it has reached the
new set point."

p. 322: He analyzes a spinal reflex as a control system.

p. 322: He begins an analysis of static control systems by
"opening the loop." He uses a spinal reflex as his example. Nice
treatment of gain. Also, starting on p. 324, in a section on
"closing the loop," he describes a way to identify the presence
of control: if a variable (he uses muscle length, L) is
disturbed, it changes less when control is present than when it
is absent. "The quality of regulation can be described by the
*regulation factor* R:

R = delta L with regulation / delta L without regulation."

(This looks like an approximation of the Stability Factor, S,
doesn't it?)

p. 234: A nice discussion of the results of adjusting the gain in
the muscle-length controller.

p. 324ff: Dynamic control systems. "Here we show that
regulation is fundamentally characterized by the *temporal
properties* of the system: Disturbances should be compensated as
rapidly as possible. The dynamics of a control system or of its
components are studied by imposing well defined disturbance. For
analysis of our muscle control circuit, we shall use a *step
function*." (Some of you will know, immediately, the kinds of
problems that can follow from that fateful selection of
disturbances.) There follows a discussion of oscillations,
damped oscillations, instability of control systems, etc; all of
these might be relevant to developing effective models of
movement disorders.

p. 326: variable reference signals. "When a *movement* -- i.e.,
a change in muscle length -- is to be made, there must be a *set-
point readjustment* in the stretch reflex control circuit." . . .
"It follows that shifting the controller characteristic on
supraspinal command brings the system to a *new muscle length
L*."

p. 327: The chapter ends with a brief section on concatenation of
segmental and supraspinal control circuits. Movement at a hinge
joint, and control of position of a joint, via coupled,
antagonistic control systems; and "intermeshing" of several
joint-position control systems to produce coordinated movements.

CONCLUSIONS?

I don't know how well Zimmermann understood humans beings as
control systems. Long pause.

Now that some of my readers are cooled down, and others are white
hot, let me add just a little additional information about the
chapter. Fig. 15-6A shows a diagram of a control system. (It
was the first thing I checked out when I turned to the chapter.
I make a practice of doing that. Authors say a lot in their
figures -- often more than they realize.) At first glance, many
aspects of the diagram look fine, but there are some possible
problems: there is no "output function" or "input function."
There is a "reference signal;" controller (hmm? comparator?);
control signal (I read it as "error signal," but why does his
choice of a term bother me?); feedback signal (I read "perceptual
signal" -- no big deal); perturbation (in the right place, no
less!); controlled variable (oh, oh -- here it is). The
controlled variable is *inside* the "controlled system." In his
example, the controlled system is the muscle; the controlled
variable is the length of the muscle. This discussion, which is
technically EXCELLENT concerning control systems in general, is
about how the nervous system controls the muscles. The text in
the chapter is consistent with the figure.

Perhaps my conclusion about Zimmermann's chapter is incorrect.
Perhaps he was merely *emphasizing* control of muscle, assuming that
everything else is already accounted for. Maybe he assumes his readers
all know the nervous system uses muscles as the means to control
perceptions, most often, perceptions of something other than muscle. The
fact is, he never talks about the topic of perceptual control. I don't know
what he assumed. I don't know if he got it, or if he did not get it, or if
there is a third (perhaps fractal) state of his knowledge on the topic.

Until later,

Tom