[From Bill Powers (980114.1015 MST)]
Rick Marken (980114) --
Just tried Rick's demo, and it is excellent. It has many realistic properties.
Notice that when a relatively low liner is hit to the fielder, the fielder
doesn't move, as if he "knows" the ball will get to him. When a long fly is
hit that would come down behind the fielder, he backs up rapidly and then
waits for the ball to come down, as if he has predicted the trajectory and
has run to where the ball will land. I think some people will have a hard
time believing that this outfielder is _not_ predicting where the ball will
land. There is a very strong appearance of prediction and execution -- but
in this case we KNOW that there is no prediction in the simulation!
The method that is used by the simulated outfielder is far simpler than
prediction, yet it always ends up with the fielder being at the right place
at the right time, when possible. This demo ought to be a real eye-opener
for those who think that prediction must be involved in all such phenomena.
This demo is well worth publishing!
For the 3-D case, the obvious solution for lateral control is to keep the
apparent lateral velocity of the ball at zero. I suggest a top view to show
the action, possibly with a split screen showing the side view, too.
Another demo that would be worth working out is a predator chasing a prey
that is dashing around in random directions to avoid being caught. The
principle here is control of the bearing of the prey relative to the
direction of running, to keep it constant. Assuming that the speed of
running is maximum and constant, the predator varies its direction of
running to bring the rate of change of direction to the prey to zero. For
added realism you could make the speed drop as the error signal increases
-- animal can't run quite as fast while in a tight turn. Also, the prey
could be organized the same way, so it has to slow down a bit to make a
rapid change in direction. Then we'd see, perhaps, how a rabbit can elude a
big dog that can't turn as fast but can run at a higher speed. For dessert
you can make the rabbit a control system, too, trying to maximize the
distance between it and the dog.
I hope Chapman is still alive. Somebody ought to show him this demo and let
him have a good laugh at the more recent attempts to explain catching
baseballs.
Re David Goldstein's comment on "fear:" The result of having jammed a thumb
or having been hit on the head by a baseball might be acquisition of a
control system with the goal of avoiding the ball. This control system
would, of course, come into conflict with the system trying to catch it,
the conflict growing as the ball gets nearer. The avoidance system, if its
gain is high enough, could prevent the fielder from actually catching the
ball, although he could move to the right position while the ball was still
relatively far away. As soon as the ball got close enougn, he would duck!
Rick could probably simulate this, too. Just have the fielder perceive the
proximity of the ball as the inverse square of its distance. The reference
level for proximity, for simplicity, would be set to zero.
Oh, one last suggestion, Rick. How about working in the "universal error
curve" so when the error gets very large, the outfielder gives up and stops
running? Now if the ball is hit too far over the outfielder's head, or in
the infield, he will "predict that he can't catch it." By adjusting
parameters like maximum running speed, you can limit the area within which
the outfielder will actually try to catch the ball. And all this, still
without any actual predictions of the ball's or the outfielder's trajectory.
Best,
Bill P.