A Measure of the Distance Between Two Rigid-Body Poses Based on the Use of Platonic Solids

This paper deals with the definition of a measure of the distance between two spatial rigid-body poses (i.e., positions and orientations). First, a platonic solid is attached to the rigid body, then the distance metric is defined as the root mean square distance between the homologous vertices of the platonic solid at the two rigid-body poses. The distance metric thus defined is intrinsically endowed with physical meaning, it depends only on the position and dimension of the platonic solid on the body, while it is independent of the reference systems, of the chosen platonic solid and of its orientation with respect to the body. Finally, some suggestions for the choice of the position and dimension of the platonic solid are discussed.