[Bongle]

I think an ultrasonic sensor combined with dead reckoning and pre-programmed knowledge of the field would do the trick. However, you don't want to get too cautious: if a game piece falls in front of you, you don't want to waste your time driving around it (unless they are heavy). I know there were robots (specifically lap bots) that could drive around traffic in autonomous mode last year.

Another idea I've had in the past was a microphone or microphone array, but being passive sensors, they would not work to detect a robot that has crashed and is just sitting there stalling its motors. They'd be more effective as a defensive autonomous mode, hunting out opposing robots and bumping them.

Other less-active options are to have a bunch of routes or delays that you can select from before the match to give maximum flexibility. If your alliance partners can only take a certain route, then delaying for a few seconds before starting your own autonomous might give them time to get out of the way. This can be achieved with banks of switches and potentiometers on the side of your robot, allowing for the run-time selection of varied modes.