Singularity and attitude estimation
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abstract
This paper deals with the problem of how to avoid singularity associated with a minimum-element attitude parameterizations. The proposed methods are derived from the sequential rotations technique ( rotations of the reference directions about coordinate axes). The paper introduces also: 1) /2 rotations about the coordinate axes, 2) rotations about bisectors of the coordinate planes, and 3) 2/3 rotations about the trisectors of the coordinate octants. These rotations, together with the rotations of the observed directions, actually complete the most interesting sequential rotations set: all the rotation matrices made of all zeros except three unitary elements. In fact, most of the sequential rotations using one of these matrices, do not require additional computations. Finally, two applications are presented to show how to avoid the singularity when using the principal axis and angle or when using the Rodrigues vector, respectively.
