Propagation of errors in hybrid manipulators

Error propagation in hybrid manipulators is addressed here within a rigorous mathematical framework. Understanding how errors propagate in serial manipulators and cascades of platform manipulators is important for developing better designs. 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). Numerical examples illustrate that convolution and covariance propagation provide the same answers for small errors