BensLabFourRobot
Here is where I learn myself how to use th' Wiki.
Anyways:
I had a bunch of fun playing with designs but eventually settled on something relatively simple, because I didn't think I would be able to actually build something with feet or waterwheels or grappling hooks or whatnot. In the end, I've gone with a three-wheeled cart.
The two things you need to get a wheeled vehicle running are goforwardability and turnyness (technical terms). My solution is two powered wheels turning about the same axis, but each with its own motor. It works like a wheelchair: if you want to go forward, you spin both tires at the same speed. Pushing one wheel faster than the other makes you swerve, and you can just about turn on a dime by running the wheels in opposite directions.
For stability I added a third "wheel" which is basically one of those spinny things like supermarket carts have.
Attaching the Handyboard isn't complicated: just bolt it on. The board has a hole in each corner, centered about 3/8" from both edges. In theory I'd use plastic standoffs to keep the board raised above the cart but reality is cruel and I couldn't find four standoffs that fit.
Here are some photographs of my prototype, built mainly from whatever I could scavenge in my secret underground laboratory. (Some structural parts were imported from England!)
The last two pictures are upside-down views. The parts of the motors are played by two 35mm film canisters, which are about the right size. They're just bolted to the bottom of the platform.
The whole thing is roughly 7.5" by 10", which leaves space for everything. The board needs some clearance on the edges for wires to stick out and such, and a battery pack could be mounted behind it (the two "motorized" wheels are the front). There is room in front of the board to mount some kind of sensor. While I didn't bother with side walls, I did leave enough room to put them in later.
Does this actually work? It seemed to. You spin the wheels and it goes. Spin them in opposite directions and the thing rotates in place: that's pretty neat. The rear wheel thing worked even better than I expected it to. My cat thought it was fun to play with. What more could you ask for?
I didn't go any farther than this: no laser-cut plastic version for me. As a proof-of-concept, the cardboard model worked quite well. I didn't expect to go any farther with this, though, so cutting out a new base and attaching real motors seemed like a waste of expensive materials. The laser cutter is fun to play with though and I'm confident that I won't have a problem when I need to use it later on.