This is a video of Roomba Pac-Man in action. A few clarifications:

The red tape on the floor is simply so the user can visualize the map in the real world. The robots are unaware of the tape, and are rather constrained by a virtual boundary embedded in their programming.

The "dots" on the floor are pieces of paper the the Pac-Man Roomba must vacuum up to complete the map.

The ghosts actually autonomously search for Pac-Man, and when they get close enough to "sense" Pac-Man, chase him according to a set of probabalistic rules.

The human controller cannot force the Pac-Man to cross any boundaries, it will only allow inputs in valid directions.

For more in depth information check out the "hardware" and "software" sections.