Higher-Order Cayley Transforms for SE(3)

Abstract

This paper presents a new pose parametrization technique based on n-th order Cayley transforms. Our study is built on the properties of maps that link the dual vectors with the special Euclidean displacement Lie group SE(3) and the Lie group of the orthogonal dual tensors. The resulted parametrization framework is complete and embeds multiple of the reported attitude parameterization Cayley maps, while extending them towards pose parameterization.