# Special Orthogonal Group SO(3), Euler Angles, Angle-axis, Rodriguez Vector and Unit-Quaternion: Overview, Mapping and Challenges

arXiv: https://arxiv.org/abs/1909.06669 · HTML: https://mlsanity.com/paper/1909.06669/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [Optimizing Active Perception for Learning Simultaneous Viewpoint Selection and Manipulation with Diffusion Policy](https://mlsanity.com/paper/2409.14615/) (2024)
- [Kinematics and Dynamics Modeling of 7 Degrees of Freedom Human Lower Limb Using Dual Quaternions Algebra](https://mlsanity.com/paper/2302.11605/) (2023)

## Abstract (arXiv)

The attitude of a rigid-body in the three dimensional space has a unique and global definition on the Special Orthogonal Group SO (3). This paper gives an overview of the rotation matrix, attitude kinematics and parameterization. The four most frequently used methods of attitude representations are discussed with detailed derivations, namely Euler angles, angle-axis parameterization, Rodriguez vector, and unit-quaternion. The mapping from one representation to others including SO (3) is given. Also, important results which could be useful for the process of filter and/or control design are given. The main weaknesses of attitude parameterization using Euler angles, angle-axis parameterization, Rodriguez vector, and unit-quaternion are illustrated. Keywords: Special Orthogonal Group 3, Euler angles, Angle-axis, Rodriguez Vector, Unit-quaternion, SO(3), Mapping, Parameterization, Attitude, Control, Filter, Observer, Estimator, Rotation, Rotational matrix, Transformation matrix, Orientation, Transformation, Roll, Pitch, Yaw, Quad-rotor, Unmanned aerial vehicle, Robot, spacecraft, satellite, UAV, Underwater vehicle, autonomous, system, Pose, literature review, survey, overview, comparison, comparative study, body frame, identity, origin, dynamics, kinematics, Lie group, inertial frame, zero, filter, control, estimate, observation, measurement, 3D, three dimensional space, advantage, disadvantage.