Bicycle front end geometry is optimiized for steering and self-
steering - the opposite of what you want. Bicycle steering axis
inclination is in the range of 70-75 degrees. You want 90 degrees
(vertical) with all of the trail behind the vertical spindle.
I'm pretty sure that trail is usually in the range of 1 to 6 inches
from very small to about 30 inch wheels for practically any
application. The key is to achieve stability and self alignment in
your speed range. A shimmy is the mass of the wheel assembly itself
oscillating around the spindle axis. Friction in the bearings and the
tire contact will help dampen the oscillations up to the point that
speed introduces too much input forces for them to control. Trail
provides a lever arm for the forward momentum of the vehicle to act
against the road surface. You have to have some trail in order to get
a self-centering effect. Too much trail and speed makes for an
excessively strong self centering effect that causes the mass of the
assembly to overshoot center and create a self-sustaining shimmy at
certain speeds.. At the walking speed you are talking about very
small changes in the trail should make big differences in the
oscillation dynamics. Tuning of a particular system has to take into
consideration (at minimum) the polar moment of inertia around the
spindle axis, trail, design speed, and dampening characteristics of
the tire (somewhat variable with inflation.) More weight on the wheel
and less tire pressure will give you more dampening friction.
Moving the rear wheels further back from the center of gravity of the
entire vehicle will transfer more weight to the front wheels. I don't
know exactly how much trail you need with a 20 inch trailing wheel,
but your speeds are low enough that it should be possible to try some
experimenting. You want to avoid making the front wheels any further
forward of the CG than necessary. Changes of as little as one
centimeter can make a noticeable difference. I will guess it should
be in the 2-3 inch range.
Take a 20 inch bicycle and remove the bars. Then turn the fork around
so you have the offset to the back, hold up the rest of the bicycle
and roll it along on the front wheel. Raise the back of the bike
until the headset is near vertical. Experiment with various angles to
see what works. Although your actual spindle axis should be vertical,
you can change the effective trail by this method. Once you have a
rough idea of what works - you could build something more precise to
experiment with - still easier than getting it wrong on your vehicle.
Here is a very technical discussion (beyond me) for what you can glean
from it:
http://www.rehab.research.va.gov/jour/00/37/3/kauzlarlich.htm
Some on-line discussions of tail-wheel airplanes suggest that the
pivot axis needs to be very SLIGHTLY inclined forward (same direction
of angle as a bicycle.). I suspect that solution is unique to the
airplane suspension and would not be an advantage for you.