UNIT QUATERNION AND CRV: COMPLEMENTARY NON-SINGULAR REPRESENTATIONS OF RIGID-BODY ORIENTATION

摘要

Euler's angles, commonly used to represent orientation or rotation of a rigid body, suffer from "representational singularities," creating difficulties in the numerical computation of smooth paths in the vicinity of the singular points in the parameter space. The unit quaternion is a 4-parameter 3-degree-of-freedom singularity-free representation of orientation; multiplying unit quaternions is useful operationally for combining changes in orientation. The conformal rotation vector (CRV) is the unique conformal mapping from the manifold occupied by the unit quaternions to a 3-space; the CRV is useful for interpolating between orientations. Rotations about fixed axes, the minimum angular displacement transformations between body orientations shown by Juttler (1998) to be great circles in quaternion space, are shown here to be a family of planar circles in CRV space.