Force-assembly with friction

Previously, force-assembly has been defined as an assembly process for which a single admittance control law (i.e., a single nominal velocity in conjunction with a single mapping of forces to motions) can guarantee the proper assembly of a given pair of mating parts. As a testbed application of force-assembly, the insertion of a workpiece into a fixture consisting of multiple rigid fixture elements (fixels) is addressed. Previous work in this area has shown that, when workpiece/fixture contact is frictionless and positional error is infinitesimal, there always exists an admittance control law that will ensure the proper insertion of a workpiece into a deterministic fixture. When workpiece/fixture contact is frictionless, the workpiece/fixture contact force contains the relative positional information required to identify error-reducing motions. Friction between the workpiece and fixture, however, provides a disturbance to the geometrical information contained in the contact force. This paper addresses: 1) the identification of the conditions that must be satisfied for force-assembly with friction, and 2) the formulation and results of an optimization of the admittance control law to obtain the maximum value of friction that will satisfy the force-assembly conditions for a given workpiece/fixture combination. Results indicate that force-assembly fails when the contact forces are no longer characteristic. Forces are characteristic if the possible contact forces that may occur for one type of misalignment are unique to that type of misalignment