Smooth interpolation of orientation by rolling and wrapping for robot motion planning

Abstract

This paper investigates a novel procedure to calculate smooth interpolation curves of the rotation group SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , which is commonly considered as the standard representation of rigid-body's orientations. The algorithm is a combination of rolling and wrapping with the pull back/push forward technique. One remarkable advantage of this approach is that interpolation curves are given in closed form, which brings convenience for implementations on real-time control systems. A numerical example along with some visualization results is presented as well