Position Coordinate Conversion Based on Quaternions and Euler Angles, and Mutual Conversion Between Euler Angle Control Method and Quaternion Control Method

In flight control systems, there are two primary methods for representing attitude angles: Euler angles and quaternions. Euler angles utilize three angles (pitch, roll, and yaw) to intuitively describe an aircraft's attitude, but they suffer from gimbal lock issues, making them unsuitable for scenarios involving high-speed rotation or large angle changes. Quaternions employ quaternion algebra to represent rotations, avoiding gimbal lock problems and making them suitable for complex motion control.

The conversion from Euler angles to quaternions involves trigonometric operations, constructing quaternions by combining three basic rotations (typically following the Z-Y-X sequence). In code implementation, this can be achieved using functions that compute quaternion components based on Euler angles, such as angle-to-quaternion conversion functions commonly found in aerospace libraries. Conversely, converting quaternions to Euler angles requires extracting quaternion components and solving inverse trigonometric functions. This often involves mathematical operations to compute Euler angles from quaternion values, ensuring accurate angle extraction for control purposes. In control algorithms, the Euler angle control method is generally more intuitive and easier to understand, making it suitable for small angle adjustments, while the quaternion control method offers greater stability in high-dynamic environments.

The mutual conversion between these two methods allows control systems to leverage their respective advantages, enabling intuitive attitude adjustments while avoiding mathematical singularity issues. In aircraft attitude control, a common practice is to use quaternions for internal computations—where numerical stability is critical—and then convert the results to Euler angles for display purposes or external feedback control. This hybrid approach ensures both computational robustness and user-friendly interface design.