In this paper, we propose a new parameterization method to represent rotation matrices using the angles ϕ recovered from the three direction cosines that lie on the diagonal. The map from the possible configuration space of the new variable ϕ to the solid ball model in axis-angle coordinates is constructed. We also introduce a bi-invariant metric and two left-invariant metrics for measuring the distance in configuration space which could be the foundation for path planning in ϕ space. We further analyze the Jacobian matrix and singularities to better understand the manipulability.

This content is only available via PDF.
You do not currently have access to this content.