Second-Order Theory of Error Propagation on Motion Groups

Error propagation on the Euclidean motion group arises in a number of areas such as and in dead reckoning errors in mobile robot navigation and joint 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. In this paper we show how errors propagated by convolution on the Euclidean motion group, SE(3), can be approximated to second order using the theory of Lie algebras and Lie groups. We then show how errors that are small (but not so small that linearization is valid) can be propagated by a recursive formula derived here. This formula takes into account errors to second-order, whereas prior efforts only considered the first-order case [8, 9].