This paper presents a method to calculate the attitude quaternion of a quadcopter with few calculations. The quaternion calculation is based on accelerometers and gyroscopes from an Inertial Measurement Unit (IMU). The quaternion from the accelerometer is calculated as the shortest rotation arc from the gravity vector in the navigation frame. The quaternion from the gyroscope is calculated based on equations of the quaternion derivative. A complementary filter is combining the two quaternions with a componentwise comparison. The attitude estimation is calculated without any trigonometric functions. The quaternion is directly used as an input to the attitude controller. The attitude controller is a PD controller running at 400Hz. A model of the quadcopter in Matlab verified that the control system worked as intended. The estimator was verified with a Stewart platform, by mounting the quadcopter on top of it and comparing the angles from the Stewart platform with the angles from the filter. Finally the algorithms were implemented on a quadcopter controller board, and the attitude estimator were compared with the attitude estimation from a high-end IMU from MicroStrain. The complete control system was also tested on a 8-bit microcontroller running at 16 MHz. The relatively slow processor on the microcontroller was also able to do every calculations within 2.5ms.
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