We're starting to use an ultrasonic sensor on one of our research robots. This sensor would have been illegal last year; however, with the digikey ultrasonic sensors being discontinued, there may be no options for this type of sensor unless the rules are changed. (HINT. HINT.)
The company which makes this sensor is senscomp (formerly polaroid) and can be found at
www.senscomp.com. They have a variety of options. But, one option is to output an analog value proportional to the distance from your robot.
The range is 6" to 10' (off the top of my head). The sensing angle is a 15 degree cone.
As for deciding whether an object is another robot or part of the playing field...
if it moves without any intervention from you, it's probably a robot. If it stays put, it's either playing field, dead robot, or movable playing field artifact.
I'm not sure how much use mapping would be or using a pre-stored map to help navigate. It's too easy to get knocked off course, run into an impediment, experience sensor failures, set up in a non-aligned initial position, etc. Using odometry and GPS is probably a dead end if the task relies on complex interaction with the playing field.