Fused Angles and the Deficiencies of Euler Angles
This work addresses orientation representation issues in robotics, particularly for balancing tasks, but is incremental as it builds on existing parameterizations.
The paper tackled the problem of representing 3D rotations for balance-related applications, such as walking bipedal robots, by introducing fused angles as an alternative to Euler angles, highlighting their advantages in singularity locations, parameter sensitivities, independence, and axisymmetry.
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.