Efficient Penetration Depth Approximation using Active Learning

Given two objectsA andB, we denote their configuration space as C-space and each configuration or point in C-space corresponds to relative configuration (i.e., position and orientation) of A w.r.t B. In the rest of the paper, we assume that A is movable and B is fixed. For 2D objects, C-space has 2 degrees of freedom (DOF) if A can only undergo translation motion, and 3-DOF if we take into account translational and rotational motion. For 3D objects, C-space has 3-DOF for translational motion and 6-DOF for both translational and rotational motion. Cspace is composed of two components: collision-free space Cfree = {q : A(q)∩B = ∅} and in-collision space Cobs = {q : A(q)∩B 6= ∅}, where A(q) corresponds to A located at the configuration q.