Velodyne. Oh wait, motor restrictions... but no money restrictions. A custom Velodyne with a 550 swapped in for the motor.
Fused panoramic cameras
CVTs on the drive motors.
Follower wheels with encoders.
A lot depends on the specific game in question, I think. Fun, and rather informative, thought experiment, though.
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FRC 2046, 2007-2008, Student member
FRC 1708, 2009-2012, College mentor; 2013-2014, Mentor
FRC 766, 2015-, Mentor