This state-of-the-art vacuum cleaner robot, 360 Eye, was released by Dyson few months ago. From the official website, it can be seen that the robot uses V-SLAM technique which dramatically increases the computational overhead. To fit the computational load, I think the processor of this robot should be at least a Cortex A8 running at 1GHz or an ARM-DSP SoC, like TI DaVinci DM64xx. I think the innovative part which makes this robot unique, is the use of tank-like structure and a 360 degrees camera for video navigation:
Figure. 360 Eye Vacuum Robot by Dyson (picture from IEEE Spectrum)
The tank structure makes this robot robust to small scale obstacles such as your carpet on the floor and small rising edges. For the idea of using a 360 degrees camera, well, I have to say it is a genius concept. A full view camera promises more contrast features and corners for the robot to navigate while it also reduce the possibility that the view of the robot is blocked by large obstacles like a human.
This is no doubt that this is the most advanced vacuum cleaner robot so far and only the newest technology of micro-processors can ensure this aggressive design. The only problem is, the cost of this robot is also considerable, thus its selling price is more than 900 dollars.
Last thing that I am wondering about is, what if this robot encounters a mirror?