Hey Homan,
You could try something like this:
http://www.sparkfun.com/products/9453
It's a reflectance sensor with analog output. You'd need to try it on
the bottom of the bot somewhere (maybe the flat spot on the motor
gearbox) and see what values it gets on a table vs looking over the
edge. With several of these you could also do line following, but at
$3 each these individual modules might not be the best way to go for
that.
Glad the gearbox is running quietly now!
M.