Review of Attitude Representations Used for Aircraft Kinematics

Abstract

Adetailed survey ispresentedoftheliteratureonattituderepresentationdatingfromtheearlyworkofEulerand Hamilton to recent publications in e elds such as navigation and control. The scope is limited to the development of the aircraft kinematic transformation equations in terms of four different attitude representations, including the well-known Euler angles, the Euler-axis rotation parameters, the direction cosines, and the Euler ‐Rodrigues quaternion.Theemphasisisdirectedattheapplicationofthequaternionformulationtoaircraftkinematics.Results are presented that reinforce observations that the quaternion formulation, typically implemented to eliminate singularities associated with the Euler angle formulation, is far superior to the other commonly used formulations based on computational efe ciency alone. A development of quaternion constraints necessary to independently constrain roll, pitch, yaw, bank angle, elevation angle, and/or azimuth angle is presented. For verie cation of simulation codes, a general closed-form solution to the quaternion formulation, for the case of constant rotation, is also presented. Additionally, a discussion is provided of numerical integration methods and numerical errors for the quaternion formulation. This discussion is especially important for simulations that may still utilize a common error reduction scheme originally developed for analog computers.