My original thought was, what would it take to get a robot to roll a mile, autonomously? I'm not talking GPS-directed, oblivious to its surroundings. It would need to be able to navigate terrain and avoid obstacles. Simply crossing streets would be a challenge -- how would it know if there was traffic? And would the robot need some sort of anti-theft component to keep it from being purloined?
Even more interesting but imagine a robot that was made to traverse underground. It would be unrecoverable if lost, so I'd want to do it right. It would need to be able to stay charged somehow, and you'd want to remain in contact with it despite it being underground. One solution to both of these would be for it to trail a power/data line behind it. Clunky, but what else could you do?
It would need the ability to map a given area out and determine the correct way to traverse it. The bot would need to resist moisture and see in the dark. It would need the ability to climb a chimney-shaped vertical shaft up or down, to pass through narrow spaces, and maybe even clear debris.
My idea for a form factor would be a snake-like shape, or more accurately, a train. The bot would consist of a string of modules, each with a specific purpose. For instance, the tail end would have a spool holding the power/data line. Maybe another module would have a couple of mechanical arms to assist with the chimney climbing. The lead module would be peppered with sensors.
Even better would be an autonomous bot, but I couldn't even imagine how difficult that would be.