Well I can see that price being feasible but obviously there are going to be limitations - I'm not sure if I'll be able to undertake the project but if there is until 23rd September that gives a while.
More likely a combination of sensors. The hard part is making it move away from a human but not hit something 
Looks like they may have even used cameras on their device/something taking an image input.
In a way, their empty room is much simpler than placing one in a normal household environment as there's nothing small that may be in the way of its movement (say a chair leg, shoes, anything that could be on the floor)
I'm pretty impressed with what they have made though - not surprised they asked for 5k 
I'll have a think about how I think this project could be feasible with that time scale and the features requested and how best sensors would have to be used/what sensors. If I think I can undertake the project I'll let you know.