Determining feasible contact states of pairs of spatial polyhedra

Recent research uses qualitative contact models for compliant motion planning and control. Although these methods have great potential, generation of qualitative contact models of nonconvex polyhedra is difficult. Qualitative contact models could be generated in a generate-and-test fashion if a predicate were available for verifying contact hypotheses. In general, a contact hypothesis does not fully constrain the relative configuration of the objects making verification of the hypothesis difficult. This paper presents an optimization-based method to verify geometric feasibility of contact hypotheses that do not fully constrain the relative configuration. This method has been implemented and applied to test contact hypotheses of nontrivial object pairs.