Electrolux was the first company to release a domestic robot vacuum cleaner for the public to buy. The original Trilobite was first released in 2001 to great acclaim. The thing that immediately struck me about it - and which still sets it apart from the competition - is that it is a smart robot.
Unlike some robot cleaners you can buy, the Trilobite doesn't rely on a "random walk". Intead to uses its on-board sensors to build up a map of the room. This allows it to ensure that the entire room is properly cleaned rather than risking missing small sections. Of course, whether or not it's worth spending the extra money for a relatively small improvement in floor coverage is an individual decision.
If you don't have time for a comprehensive clean, the Trilobite also has the option for a Quick clean much like the random walk of competitors. There is also a spot clean option.
The Trilobite has bump sensors, of course, however unlike some less sophisicated makes it doesn't rely solely on these. It also uses its sonar sensors to try to avoid hitting things in the first place. Whilst this can be useful, the trade-off is that it doesn't aways clean right to the edges if it senses an obstacle ahead.
Another advantage of the Trilobite is that it is self-recharging. When it senses that its power of running low it uses its sensors to find where the base station is located then returns and docks itself.
The Mark 2.0 version of the Trilobite - snappily named the ZA2 - contains over 200 improvements on the original.