[Hans Blom, 960219b]
(David Goldstein, 02/19/97)
I don't claim to have tried to understood the mathematics in the
discussion. From what I do understand, a question comes to mind.
Could MCT be an example of how the imagination mode of a PCT control
system works? ... The MCT approach seems to predict (create) what
the perception is from past perceptions. This sounds like the
imagination mode.
David, your question whether the model, on which adaptive control is
based, can be compared to the PCT notion of the "imagination
connection", is a good one. In my opinion, they partly fulfill the
same role. My main problem with the PCT notion is that perception and
imagination are, I think, normally _combined_, in the sense that
imagination fills in what current time perception does not offer --
because perception is absent or noisy. Indeed, the world (or other
actors in it) may actively attempt to deceive us. Especially in that
case we'd better disregard the perceptions and fall back on the
information that is provided by our internal model.
But there are other reasons why an internal model might sometimes
have advantages. One is in very fast movements, where the feedback
might be too slow. One article that deals with this is "MODELS OF THE
CEREBELLUM AND MOTOR LEARNING" by James C. Houk, Jay T. Buckingham
and Andrew G. Barto, which can be found -- along with a great deal of
other interesting articles that have appeared in BBS -- at
http://www.princeton.edu/~harnad/bbs/
Some fragments from this article:
The concept that movement commands are centrally specified and are
then executed in essentially an open-loop manner has evolved from a
long line of studies in experimental psychology (cf. Schmidt, 1988).
According to this motor program concept, the system operates in a
feed-forward mode, as opposed to using sensory feedback from the
periphery. Instead of providing feedback during the movement,
sensory information is used to select the parameters of a motor
program before it is initiated, to initiate the program, and to
guide the subsequent adaptive process that mediates motor learning.
I would maintain that models are not only employed in motor tasks
such as reaching, but in most everything we do.
How come "most investigators" have started to think this way?
Although most investigators find sensory feedback to be ineffective
in modifying ongoing motor programs, except in limited ways, Adams
(1971; 1977) maintains that the endpoint of a movement is sensitive
to proprioception. In support of Adams' conclusion, we found that
the offsets of elemental motor commands recorded from the red
nucleus can be appreciably prolonged by using a brake to prevent the
animal from reaching the intended target (Houk & Gibson, 1987). We
also found clear support for the concept that the program operates
mostly open loop, since application of the brake had relatively
minor effects on discharge frequency during the burst.
An internal model stores "knowledge" about the world. In order to use
that knowledge for control, some kind of "inverse model" is needed,
as Bill pointed out. Some people think that feedforward based on an
inverse model might even provide more accurate control than feedback
control would:
Kawato and Gomi (1992a) proposed that the lateral cerebellum learns
to function as an "inverse model" of the limb controlled system.
Inverse models do the opposite of the forward models discussed in
the previous paragraph; they predict commands when supplied with
sample responses.
If instead of sample responses they are supplied with signals
representing desired trajectories, an inverse model then generates
the appropriate commands. Kawato and Gomi assumed that the motor
cortex and cerebellum are simultaneously provided parietal signals
representing a desired trajectory of a limb movement. The motor
cortex compares the desired trajectory with sensory feedback and
issues a crude command while waiting for the cerebellum to use its
inverse model to compute a precise command.
A partial answer on Bill Powers' question of how the model's
parameters can be "inserted" into a "control law":
... Prochazka (1989) suggested that the role of the
cerebellum is to control the gain of spinal and brainstem reflexes.
The gain-control idea has also arisen in eye movement models that
are discussed later.
Learning is, operationally seen, improvement of performance. Thus
learning is driven by error (between reference and perception and/or
imagination), and learning attempts to minimize error. A model is
perfect if its prediction accurately coincides with the concomitant
perception. If not, the "prediction error" drives the ensuing further
adaptation of the model.
Kawato and Gomi (1992b; 1993) refined and developed Oscarsson's
error hypothesis into a theory of feedback-error learning,
summarized in Figure 11A. According to this theory, the IO transmits
a motor error signal that is generated by a simple feedback
controller. The difference between a desired trajectory and sensory
feedback reporting on the actual trajectory forms a trajectory error
analogous to the error signal in Albus' theory. However, in Kawato's
theory the trajectory error is processed by the feedback controller
to convert it into a motor error signal, which is a vector with
quite desireable training capabilities. The motor error also serves
as a crude motor command that is eventually replaced by an improved
motor command, after the cerebellar cortex has learned the inverse
model that was described in Section 2.4. While this theory functions
well in robot manipulation tasks, its consistency with the anatomy
and physiology of different cerebellar control systems needs to be
examined.
This article is, by the way, a demonstration that the principles of
model-based control _have_ been considered and used in modeling human
behavior.
Greetings,
Hans