TY - JOUR
T1 - Short Communication
T2 - Determining the average attitude of a rigid body
AU - Challis, John H.
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2020/1/2
Y1 - 2020/1/2
N2 - Three-dimensional angular kinematics exist on the surface of a unit hypersphere, therefore the average attitude cannot always be accurately computed by averaging Cardan angles. This study derives and evaluates a method for determining average body attitude, by exploiting the singular value decomposition of the average of a set of attitude matrices. To test the method 1000 criterion attitudes were determined, and for each attitude 10 noisy attitude matrices generated. The new method and the averaging of Cardan angles extracted from the 10 noisy attitude matrices were evaluated for their ability to estimate the criterion attitude. At low attitude variance the two approaches provided equivalent results, but with increasing attitude variance levels the new procedure was superior. The method provides superior estimates of average attitude compared with averaging Cardan angles, by accounting for the geometric distribution of rigid body attitudes on the surface of a unit hypersphere.
AB - Three-dimensional angular kinematics exist on the surface of a unit hypersphere, therefore the average attitude cannot always be accurately computed by averaging Cardan angles. This study derives and evaluates a method for determining average body attitude, by exploiting the singular value decomposition of the average of a set of attitude matrices. To test the method 1000 criterion attitudes were determined, and for each attitude 10 noisy attitude matrices generated. The new method and the averaging of Cardan angles extracted from the 10 noisy attitude matrices were evaluated for their ability to estimate the criterion attitude. At low attitude variance the two approaches provided equivalent results, but with increasing attitude variance levels the new procedure was superior. The method provides superior estimates of average attitude compared with averaging Cardan angles, by accounting for the geometric distribution of rigid body attitudes on the surface of a unit hypersphere.
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U2 - 10.1016/j.jbiomech.2019.109492
DO - 10.1016/j.jbiomech.2019.109492
M3 - Article
C2 - 31733819
AN - SCOPUS:85075400961
SN - 0021-9290
VL - 98
JO - Journal of Biomechanics
JF - Journal of Biomechanics
M1 - 109492
ER -