Fused Angles: A Representation of Body Orientation for Balance

TL;DR

The paper introduces fused angles, a new mathematical representation for 3D body orientation, specifically designed for balance applications, with thorough analysis and comparison to existing methods.

Contribution

It presents a novel fused angles parameterisation for 3D rotations, including a related tilt angles representation, with detailed mathematical and geometric properties.

Findings

Fused angles provide a robust and intuitive way to represent body orientation.

The representation is thoroughly analyzed and compared to existing methods.

Tilt angles naturally emerge from the fused angles framework.

Abstract

The parameterisation of rotations in three dimensional Euclidean space is an area of applied mathematics that has long been studied, dating back to the original works of Euler in the 18th century. As such, many ways of parameterising a rotation have been developed over the years. Motivated by the task of representing the orientation of a balancing body, the fused angles parameterisation is developed and introduced in this paper. This novel representation is carefully defined both mathematically and geometrically, and thoroughly investigated in terms of the properties it possesses, and how it relates to other existing representations. A second intermediate representation, tilt angles, is also introduced as a natural consequence thereof.