Design for a robot vacuum

My dog makes lots of hair. Seriously, you can hoover the kitchen and five minutes later there's fluff all over. I want a robotic vacuum to keep it under control, but I'm not willing to spend £300+ on a roomba

So I'm going to build one.

Maybe.

First issue I can see is navigation - there are a lot of posts and designs that use ultrasonic sensors, IR, GPS :) and all kinds of expensive, fiddly kit that needs a hefty processor to calculate position ...

Well, my kitchen has a tiled floor. Surely I can use that grid for really simple navigation with no floating point maths or stats, all running on an 8-bit microcontroller of choice?

My intitial thoughts are:

Two bog-standard DC motors driving differential steering and forward/backward motion. This should allow the robot to swivel on the spot.

Three light sensors mounted on the underside of the robot will pick up the lines of the grout and determine if the robot is staying straight on the grid line, and detect when it crosses another line.

A bumper sensor (basically a switch) to detect when the robot hits an obstacle

Oh, and a modified hand-held hoover...

Possibly a charging dock also...