Verifying contact hypotheses of planar, polyhedral objects using penetration growth distance

The contact between two planar, polyhedral objects can be represented with a set of elementary contacts - face-vertex contacts. However, not all possible contact representations are geometrically possible. Verification of whether a set of elementary contacts is geometrically feasible is in particular difficult if the elementary contacts do not fully constrain the relative configuration of the objects. These are exactly the contact descriptions that allow the objects to move compliantly with respect to each other and are therefore important for motion planning. An equivalent optimization problem is posed to verify geometric feasibility of contact descriptions that do not fully constrain the relative configuration. A trajectory following algorithm has been implemented and applied to test feasible and infeasible contact representations. The results of this work can be used to implement a predicate that verifies whether a contact representation is geometrically possible.