Continuous gradient proximity distance for humanoids free-collision optimized-postures

This paper presents a new method for strictly convex hulls (i.e. bounding volume) generation made by assembling patches of spheres and toruses (STP-BV). This bounding volume allows to compute proximity distances with the guarantee of their gradients´ continuity. This bounding volume is computed off-line; it slightly over-covers the polyhedral convex hull of the geometrical form. Given a pair of convex objects, having only one of them strictly convex (i.e. STP-BV covered) is proved to be sufficient to guarantee gradient continuity of the proximity distance. The distance computation is based on the closest features of the underlying polyhedral convex hull obtained with V-Clip or any other algorithm. The suggested algorithm is exemplified through a free-collision (including free self-collision) optimization-based humanoid posture generation.