Fused Angles: A Representation of Body Orientation for Balance
This work addresses the specific problem of orientation representation for balancing bodies in robotics or biomechanics, but it appears incremental as it builds on existing rotation parameterisations without demonstrating broad applications or performance gains.
The paper tackles the problem of representing body orientation for balance by introducing the fused angles parameterisation, a novel rotation representation, and also presents tilt angles as an intermediate representation, with both defined mathematically and compared to existing methods.
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.