A New Formalism to Characterize Contact States Involving Articulated Polyhedral Objects

In this paper a novel formalism to characterize contact states between an articulated polyhedral object and a polyhedral environment for the generation of the graph of feasible contact states between them is presented. This formalism is based upon a particular representation of the stratification of the configuration space of the articulated object by means of oriented matroid theory. A stratification is a decomposition of a set into a collection of manifolds which in our case correspond to the different contact states between the articulated object and the environment. In the representation of the stratification of the configuration space using oriented matroid theory the topological properties of the different strata are represented at a purely combinatorial level. An algorithm to enumerate the existing strata and to find the adjacency relationships among them is proposed. It will be shown that the symbolic computation based on oriented matroids simplifies and in some cases even replaces the computation with coordinates.