General Identities for Parameterizations of SO(3) With Applications

2014 ◽  
Vol 81 (7) ◽  
Author(s):  
Anton H. J. de Ruiter ◽  
James Richard Forbes
Keyword(s):  
Rigid Body ◽  
Orthogonal Group ◽  
Attitude Determination ◽  
Unit Length ◽  
Spacecraft Attitude ◽  
Euler Angles ◽  
Motion Equations ◽  
Rotation Matrices ◽  
Special Orthogonal Group ◽  
Lagrange’S Equation

Rotation matrices, which are three-by-three orthonormal matrices with determinant equal to plus one, constitute the special orthogonal group of rigid-body rotations, denoted SO(3). Owing to the three-by-three nature of rotation matrices plus their orthonormality constraint, parameterizations are often used in favor of rotation matrices for computations and derivations. For example, Euler angles and Rodrigues parameters are common three-parameter unconstrained parameterizations, while unit-length quaternions are a popular four-parameter constrained parameterization. In this paper various identities associated with the parameterization of SO(3) are considered. In particular, we present six identities, three related to unconstrained parameterizations and three related to constrained parameterizations. We also discuss rotation matrix perturbations. The utility of these identities is highlighted when deriving the motion equations of a rigid body using Lagrange's equation. We also use them to examine some issues associated with spacecraft attitude determination.

scholarly journals Combinatory Attitude Determination Method for High Rotational Speed Rigid-Body Aircraft

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Liangliang An ◽  
Liangming Wang ◽  
Ning Liu ◽  
Jian Fu
Keyword(s):  
Rigid Body ◽  
Rotational Speed ◽  
Attitude Determination ◽  
Unscented Kalman Filter ◽  
The State ◽  
Determination Method ◽  
State Equations ◽  
High Rotational Speed ◽  
Motion Equations ◽  
Accuracy Measurement

In this paper, we present a novel multisensor combinatory attitude determination method that enables high-accuracy measurement of the attitude of a high rotational speed rigid-body aircraft. We analyze the external moments of the aircraft during flight and develop the method using theoretical deductions based on the motion equations of a rigid body rotating around the centroid. The proposed method fuses the data measured from GPS, gyrometer, and magnetometer and uses the improved unscented Kalman filter (UKF) algorithm to perform filtering. First, appropriate assumptions and simplifying approximations are made for around-centroid motion equations of a rigid body according to the motion characteristics of the high rotational speed aircraft. Using these assumptions and approximations, the constraint equations between the Euler attitude angles and flight-path angle, trajectory deflection angle are derived to serve as the state equation. Second, the roll angle with error is calculated using the geomagnetic field model and the geomagnetic intensity measured by a three-axis magnetometer and then fused with the angular velocity information obtained from the gyroscope for constructing the measurement equations. Finally, the state equations are discretized using the Runge–Kutta method during the UKF prediction stage, improving the prediction accuracy. Simulation results show that the proposed method can effectively determine the attitude information of the high rotational speed aircraft, achieving high level of reliability and accuracy thanks to the combination of information from GPS, gyroscope, and magnetometer.

A quantum search algorithm for future spacecraft attitude determination

2011 ◽  
Vol 68 (7-8) ◽  
pp. 1208-1218 ◽  
Author(s):  
Jack Tsai ◽  
Fu-Yuen Hsiao ◽  
Yi-Ju Li ◽  
Jen-Fu Shen
Keyword(s):  
Attitude Determination ◽  
Search Algorithm ◽  
Spacecraft Attitude ◽  
Quantum Search ◽  
Quantum Search Algorithm
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