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

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... is that it does not directly interrelate angles with spatial components. This paper discusses the properties of Radially Constrained Gaussians (RCG's), then presents speci c cases of uncertain rotations, directions, orientations, 2D transformations, and 3D transformations, then indicates their applications to robotics. d 2 (