Practical Parameterization of Rotations Using the Exponential Map (Grassia)

This paper discusses the Exponential Map as a practical
parameterization of rotations for various situations (e.g.
differential control and dynamics simulation, interpolation, and
certain kinds of spacetime optomization). It also goes over the
limitations of this parameterization and compares it to other popular
parameterizations including 3x3 rotation matrices, Euler angles, and
quaternions.

Problem: To develop a compact, useful representation for orientations
posessing desirables qualities (including but not limited to being
able to compute derivatives, integrate ODEs, interpolate,
composition).

Key ideas/contributions:

1. A rotation parameterization in R^3 that does not suffer from Gimbal
lock in most useful situations, is differentiable, can be used in
ODEs, and can be interpolated. This parameterization is the
exponential map.

2. A means of converting between exponential maps and quaternions.

3. An analysis of which parameterizations are appropriate for which situations.

Questions:

None