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electronic compass
I would reccomend using an electronic compass from Digi_Key, I know they have them (though they may not be cheap). In 2 min I would be worried about decay of the numeric integration of even a very good rotation sensor.
Also, a note on the system you are trying to build: They are very mechanically complex and use many motors. Only pursue it if you really think it is worth the time, effort, motors, and weight to get that advantage over a less complex steering/drive system. IMHO time is better spent on manipulators than a super maneuverable drivetrain this year.
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