It appears that the software controlling the robots is providing feedback to a media server about its position and therefore the position of the screens. The projector is probably static but is shooting an area large enough to encompass all of the screen positions. When the robot moves the screen the media server moves the content within the projectors view to keep it on the screen.
One of the awards shows did something similar several years ago with moving video screens across the stage while the servers kept the content on the screens.
Want to do something similar?? Let me know. We've just acquired a D3 Quad server which allows these very effects to be realized. Check it out. http://www.d3technologies.com