Segcar

The short-short summary: build a two wheeled, self balancing car, similar in size and shape as a regular car, except with one wheel on each side, instead of two on each side.

Now, I know that someone's going to object that a segway-like vehicle must tilt forward to accellerate forward (or to slow down, if it's moving backwards) and tilt backwards to accellerate backward (or to slow down, if it's moving forwards), resulting in the front or rear bumper scraping the road when high accelleration is needed, but... I have a solution.

Specifically, instead of moving the center of gravity forwards and backwards by tilting the car, move it some other way.

There are tree obvious ways of dynamically shifting the center of gravity without tilting the vehicle.

The first, is move a heavy mass forwards and backwards within the car, using the space where the driveshaft would normally go (if you use electric motors, one for each wheel, then you don't need a driveshaft). The problem of course is that this adds weight to the car that isn't really doing anything useful besides balancing, and it takes up quite a bit of space.

The second is to have a front and rear reservoir of some dense liquid, and pump this liquid forwards and backwards to move the vehicle's center of gravity. This has a variety of drawbacks (moving the liquid fast enough to balance the car, the added weight which isn't doing much useful, and leaks).

The third, and coolest idea, is to mount the two wheels (and perhaps their motors) on a pair of linear bearings (tracks or rails or rolamite), and move the entire vehicle forwards and backwards on them.

One important side effect of moving the center of gravity without in this manner is that we no longer need to turn the wheels to balance; the car can balance itself even if it's in park or neutral, or with the emergency brake on, or (and perhaps most importantly) even if it's skidding around on an icy surface.

Another advantage is that the computer circuitry for balancing can be made independant of the rest of the car's computer circuitry, making it more robust and crash resistant (no pun intended). In a segway, balancing and accelleration are and must be integrated.