Fused Angles and the Deficiencies of Euler Angles

TL;DR

This paper compares fused angles and Euler angles, highlighting the advantages of fused angles in representing orientations for balancing robots due to their better singularity properties and parameter independence.

Contribution

It provides a detailed analysis of the differences between fused angles and Euler angles, emphasizing fused angles' suitability for balance-related applications.

Findings

Fused angles have fewer singularities than Euler angles.

Fused angles exhibit better parameter independence.

Fused angles are more axisymmetric and less sensitive to parameter changes.

Abstract

Just like the well-established Euler angles representation, fused angles are a convenient parameterisation for rotations in three-dimensional Euclidean space. They were developed in the context of balancing bodies, most specifically walking bipedal robots, but have since found wider application due to their useful properties. A comparative analysis between fused angles and Euler angles is presented in this paper, delineating the specific differences between the two representations that make fused angles more suitable for representing orientations in balance-related scenarios. Aspects of comparison include the locations of the singularities, the associated parameter sensitivities, the level of mutual independence of the parameters, and the axisymmetry of the parameters.