A rational Rodrigues' formula to interpolate rotations

TL;DR

This paper introduces a rational Rodrigues' formula that improves the accuracy and efficiency of modeling rotations and their derivatives, with practical applications demonstrated through gyroscope data of a cell phone.

Contribution

A novel rational Rodrigues' formula is proposed, enhancing the precision and computational efficiency of rotation modeling compared to the classic version.

Findings

More accurate rotation modeling in finite precision arithmetic

Efficient computation of rotation derivatives

Successful application to cell phone gyroscope data

Abstract

We propose a rational version of the classic Rodrigues' rotation formula, which leads to a more accurate and efficient modelling of rotations and their derivatives in finite precision arithmetic. We explain how the rational Rodrigues' formula can be used to describe the kinematics of rigid bodies, in a practical example in which we model the rotation of a cell phone using the data obtained from its gyroscope.