Distance Bound Smoothing under orientation constraints

Distance Bound Smoothing (DBS) is a basic operation originally developed in Computational Chemistry to determine point configurations that are within certain pairwise ranges of distances. This operation consist in the iterative application of filtering processes that reduce the given ranges using triangular and tetrangular inequalities. Standard DBS has a limited range of applications because it does not take into account constraints on the orientations of simplices (triangles or tetrahedra, depending on the dimension of the problem). This paper discusses an extension of DBS that permits incorporating these constraints. This paves the way for the application of DBS techniques to a broad range of problems in Robotics.