Gyrometer
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Theory
A Gyrometer (or gyroscope) is a device for measuring orientation along one or several axis. In our case, we want a gyrometer to measure the rotation of the robot on the vertical axis to determine its orientation wrt the playing field.
To do so, we will need a Yaw gyrometer. Pitch and Roll are not necessary if we plan to stay on a horizontal surface, but can be useful to determine whether the robot is on a plane or not (for instance, auto-shutdown if it is held in someone's hand).
Components
STMicroelectronics
Some interesting products:
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LY550ALHLPY503AL Pitch and Yaw,+/-500deg/s+/-30 deg/s ($8, sparkfun) -
LPR550ALLPY530AL Pitch& Roll, +/-500 deg/s
Only the LY530AL is available for now, though.