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

Abstract

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.

References in corpus (6)

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Cited by in corpus (6)

• Systematic Convergence of Nonlinear Stochastic Estimators on the Special Orthogonal Group SO(3)
• Nonlinear Stochastic Estimators on the Special Euclidean Group SE(3) using Uncertain IMU and Vision Measurements
• Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping
• Attitude Determination and Estimation using Vector Observations: Review, Challenges and Comparative Results
• A Critical Comparison on Attitude Estimation: From Gaussian Approximate Filters to Coordinate-free Dual Optimal Control
• Asymptotically Stable Observer-based Controller for Attitude Tracking with Systematic Convergence