Error propagation on the Euclidean group with applications to manipulator kinematics

Error propagation on the Euclidean motion group arises in a number of areas such as errors that accumulate from the base to the distal end of manipulators. We address error propagation in rigid-body poses in a coordinate-free way, and explain how this differs from other approaches proposed in the literature. In this paper, we show that errors propagate by convolution on the Euclidean motion group, SE(3). When local errors are small, they can be described well as distributions on the Lie algebra se(3). We show how the concept of a highly concentrated Gaussian distribution on SE(3) is equivalent to one on se(3). We also develop closure relations for these distributions under convolution on SE(3). Numerical examples illustrate how convolution is a valuable tool for computing the propagation of both small and large errors.