A general representation for orientational uncertainty using random unit quaternions

Previous work in representing transformational uncertainty used a linearized perturbed-transform method which assumes small angle errors. This paper presents an alternative representation using random unit quaternions that makes no strict small angle error assumption. The approach uses a novel family of probability density functions derived by placing a unit-length constraint upon some or all of the degrees of freedom of a Gaussian in Euclidean space. An important property of this representation is that it does not directly interrelate angles with spatial components. This paper discusses the properties of radially constrained Gaussians, presents specific cases of uncertain rotations, directions, orientations, 2D transformations, and 3D transformations, and then indicates their applications to robotics