Pseudo minimum translational distance between convex polyhedra(I) - Definition and properties

Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiable almost everywhere w.r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.