Adding a live video camera to your robot, and having it provide real-time video that can be displayed on a standard television is very straightforward. It is also FIRST legal (within certain limits). Several teams have done it in the past.
Get a 2GHz-band video camera and transmitter. The one that I have used is the
X-10 XCam2 remote camera kit, which sells for less than $80. The camera module connects to a 12 volt power supply. Clip the power lead, and connect it to your robot power system (which is - yippee - 12 volts!). Connect the received unit to a TV, turn to Channel 2 or 3 (switch settable), and away you go. You get to see the world from the robots point of view!
Now for the "certain limits." If you are going to use the camera during a competition, you must clear it with FIRST (see Rule <R94>). Also, you will not be allowed to display the video at the Alliance Control Station. FIRST may receive the transmitted video at the scoring table, and pipe it on to the "Jumbotron" for all the teams and audience to see, but you will not be able to use it just for a competitive advantage for your team.
-dave