Improving the precision and speed of Euler angles computation from low-cost rotation sensor data

Area of Science:

• Robotics
• Navigation Systems
• Sensor Fusion

Background:

• Accurate estimation of object attitude is crucial for navigation and control systems.
• Gyroscopes provide angular rate data but are prone to drift and errors over time.
• Euler angles are a common representation of object orientation.

Purpose of the Study:

• To compare the computational efficiency and accuracy of three algorithms for computing Euler angles from gyroscope data.
• To evaluate the suitability of different algorithms for real-time attitude estimation.
• To propose sensor fusion strategies for mitigating gyroscope errors.

Main Methods:

• Comparison of algorithms based on rotational matrix, time derivations of Euler angles, and unit quaternions.
• Analysis of computational efficiency (clock cycles) and accuracy of Euler angle estimation.
• Implementation of sensor compensation techniques using magnetic compass and accelerometer data.

Main Results:

• The quaternion-based algorithm demonstrates similar accuracy to the matrix-based algorithm but is approximately 30% more computationally efficient on an 8-bit microcomputer.
• The algorithm integrating Euler angle time derivations exhibits singularity issues, limiting its accuracy across the full attitude range.
• Sensor fusion using a matrix-based algorithm can yield a system approximately 10% faster than quaternion-based systems for compensated sensor data transformation.

Conclusions:

• For gyroscope-only attitude computation, the quaternion-based algorithm is recommended due to its balance of accuracy and computational efficiency.
• Euler angle time derivation integration is unsuitable for full-range attitude estimation.
• Sensor fusion with additional sensors (magnetometer, accelerometer) is essential for robust and accurate attitude estimation, with matrix-based transformations offering potential speed advantages in compensated systems.