Having some experience with quadcopters, they all use something called an IMU – inertial measurement unit – which gives you the pitch, roll and yaw of the craft. These two values are generated by a gyroscope and accelerometer working together cancelling out each others possible errors. Additional measurements are normally available, a compass for direction and a barometer for altitude readings. With a GPS, the compass (magnometer) allows you to plot a course and have the vehicle follow waypoints; sounds like its worth a look.
An IMU board is now pretty cheap to get your hands on, in fact you can get a complete quadcopter ‘brain’ for $35 here, which contains an Atmel ATMEGA2560, with all of the above sensors ready to use. For my boards, a pre-made I2C board would be ideal which is exactly what I found; the GY-80.