Quaternion to Euler angles conversion: A direct, general and computationally efficient method.

Area of Science:

• Robotics
• Computer Graphics
• Aerospace Engineering

Background:

• Existing methods for quaternion to Euler angle conversion are complex, often requiring multiple steps or sequence-specific implementations.
• These methods can be computationally intensive, involving intermediate matrix conversions.

Purpose of the Study:

• To present a general, direct formula for extracting Euler angles from a unit quaternion.
• To support all 12 possible rotation sequences for both Proper Euler angles and Tait-Bryan angles.
• To offer a computationally efficient alternative to current conversion techniques.

Main Methods:

• Development of a closed-form formula for direct quaternion to Euler angle extraction.
• The algorithm avoids intermediate conversion steps like quaternion-to-matrix.
• Comparison with a standard matrix-to-Euler angle algorithm involving quaternion-to-matrix conversion.

Main Results:

• A general formula capable of extracting Euler angles in any of the 12 possible sequences was derived.
• The new algorithm demonstrates a significant speed improvement, being up to 30 times faster than classical methods.
• A concise, single-page pseudo-code implementation is provided, highlighting ease of use.

Conclusions:

• The proposed direct conversion method offers a more efficient and straightforward approach for quaternion to Euler angle transformations.
• Its speed and generality make it highly valuable for applications requiring rapid and accurate orientation representation.