[From Joe Lubin (920331.1200)]
Bill Powers (920330.0800), Greg Williams
Some solutions to the trajectory problem came together this morning.
The model needs at least one more level, the transition level,
which I now am convinced could also be called the "path" level.
I liked this idea when you first mentioned it as the "virtual target" in
your post of 920312.1000. It makes more explicit the notion of
continuous control (as opposed to relatively more ballistic components
of a motion).
In the post of 920312.1000 and in subsequent posts you speak of treating
the alpha and gamma efferent reference signals totally independently.
First of all there are two distinct types of gamma efferent: static and
dynamic. Their different effects arise from the fact that they
innervate different types of intrafusal fiber: static nuclear bag fibers
and dynamic nuclear bag fibers with different mechanical responses to
activation which gives rise to part of the static and all of the
dynamic properties of the Ia afferent responses.
From what I have read, alpha and static gamma signals are usually
proportional to one another: this is called alpha-gamma coactivation.
In lower vertebrates, there is no separate
gamma system and the spindles are efferently innervated by colaterals of
the alphas. By separating the system into alpha (skeletomotor) and
gamma (fusimotor) systems, more independent control can be exercised in
adjusting sensitivity (adaptive gain control). I don't yet have a clear
understanding of how the dynamic gammas are used, although it is clear
that they are (i) silent for slow, mellow behaviors, and (ii) very
active for fast or dangerous movements, and for imposed activity (say
when a cat is picked up against its will).
Your switch to the alpha reference seems right to me, although
separation of the two types of gamma signals might have taken care of
your instabilities. Perhaps you could try to mask out the rate response
(this is essentially what happens when static gamma is large and dynamic
gamma is zero, although there always is some dynamic component to the Ia
afferent signal) and try varying your alpha and gamma together and
see if it works.
I think its a bad idea to conflate the extensor and flexor systems. Your
reduction of the two contraction signals via (a2 - a1) does not capture
all the salient aspects of the alpha commands (diagram of 920320.1100).
This gives you no way of modulating stiffness/compliance. For a
well-learned
motion the agonist is contracted and the antagonist is inhibited
rendering it nonresistent: this is called reciprocal innervation.
For new learning of a motion or for a motion that requires stiffness
in its execution, coactivation is used to tense both agonist and
antagonist. In both strategies the same joint angle can be obtained,
the difference lies in the stiffness of the joint. Reciprocal
innervation allows for more rapid, fluid, less energy consumptive
operation, and requires advanced knowledge of loads. Cocontraction is
more exepnsive energetically but can deal better with unknown situations
and heavier loads. I know that this particular modeling effort doesn't
require the added complexity and I know that William of Occam would not
be pleased with my suggestion, but I do think that most neuroscientists
have difficulty abstracting from pure anatomies, so at least an explicit
mapping from the anatomy to your circuit should be presented in your
paper.
I just came across this:
All this really requires modeling the
opposing muscles separately.
Maybe Joe Lubin and his students, plus Greg
Williams, would like to carry this on to version 3.
Yup.
And from Bill Powers (920330.0800):
I can see now that we will be able to make a
prediction: the velocity profile, normalized as in the article, will
also be the same for different spatial separations of initial and
final positions, at least for rapid movements.
It's nice to be able to make predictions and have some data out there to
test these. I'll send you a paper that references velocity profile
invariance data for arm trajectories. Here is the abstract:
Neural Dynamics of Planned Arm Movements:
Emergent Invariants and Speed-Accuracy Properties During Trajectory
Formation
Daniel Bullock and Stephen Grossberg
Psychological Review 1988 95:49-90.
Abstract
A real-time neural network model, called the Vector Integration to
Endpoint, or VITE, Model, is developed and used to quantitatively
simulate behavioral and neural data about planned and passive arm
movements. Invariants of arm movements emerge through network
interactions rather than through an explicitly precomputed trajectory.
Motor planning occurs in the form of a Target Position Command, or TPC,
which specifies where the arm intends to move, and an independently
controlled GO command, which specifies the movement's overall speed.
Automatic processes convert this information into an arm trajectory with
invariant properties. These automatic processes include computation of
a Present Position Command, or PPC, and a Difference Vector, or DV. The
DV is the difference of the PPC and the TPC at any time. The PPC is
gradually updated by integrating the DV through time. The GO signal
multiplies the DV before it is integrated by the PPC. The PPC generates
an outflow movement command to its target muscle groups. Opponent
interaction's regulate the PPCs to agonist and antagonist muscle groups.
This system generates synchronous movements across synergetic muscles by
automatically compensating for the different total contractions that
each muscle group must undergo. Quantitative simulations are provided
of Woodsworth's Law, of the speed-accuracy trade-off known as Fitts'
Law, of isotonic arm movement properties before and after
deafferentation, of synchronous and compensatory "central error
correction" properties of isometric contractions, of velocity
amplification during target switching, of velocity profile invariance
and asymmetry, of the changes in velocity profile asymmetry at higher
movement speeds, of the automatic compensation for staggered onset times
of synergistic muscles, of vector cell properties in precentral motor
cortex, of the inverse relationship between movement duration and peak
velocity, and of peak acceleration as a function of movement amplitude
and duration. It is shown that TPC, PPC, and DV computations are
needed to actively modulate, or gate, the learning of associative maps
between TPCs of different modalities, such as between the eye-head
system and the hand-arm sytem. By using such an associative map,
looking at an object can activate a TPC of the hand-arm system as Piaget
noted. Then a VITE circuit can translate this TPC into an invariant
movement trajectory. An auxiliary circuit, called the Passive Update of
Position, or PUP, Model, is described for using inflow signals to update
the PPC during passive arm movements due to external forces. Other uses
of outflow and inflow signals are also noted, such as for adaptive
linearization of a nonlinear muscle plant, and sequential read-out of
TPCs during a serial plan, as in reaching and grasping. Comparisons are
made with other models of motor control, such as the mass-spring and
minimum-jerk models.
It appears that these people have thought about many of the issues with
which you are grappling.
Joe, How about some details on what your student has accomplished so
far?
His first semester of work consisted only of getting you model to work,
and creating a beautiful graphical interface on Silicon Graphics IRIS
Workstations. He started with about 10 lines of your code and built it.
He has just recently started his second semester of work. First he
cleaned up the code so that one could implement a new level or a new ECS
with ease. We are viewing this as a generalized
vision/sensorimotor/control environment. I plan to use this for a few
years. Our next steps are to implement (i) the lower levels (your
muscle circuits) and (ii) make the visual depth computation less
trigonometric. For this latter we are using a complex cepstral filter
which operates locally on windows the size of ocular dominance
columns in V1. This filter computes local retinal disparities.
···
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Joseph Lubin jmlubin@phoenix.princeton.edu
Civil Eng. Dept. 609-683-5301
Princeton University 609-258-4598
Princeton NJ 08544
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