Admittance Matrix Design for Force-Guided Assembly

This paper addresses the design of manipulator admittance for reliable force-guided assembly. Our goal is to design the admittance of the manipulator so that, at all possible bounded part misalignments, the contact forces always lead to error-reducing motions. If this objective can be accomplished for a given pair of mating parts, we call the parts force-assemblable. As a testbed application of manipulator admittance design for force-guided assembly, we investigate the insertion of a workpiece into a fixture consisting of multiple rigid fixture elements (fixels). Here, we define a linearly force-assemblable fixture to be one for which there exists an admittance matrix that ensures the unique positioning of a workpiece despite initial positional error. We show that, in the absence of friction, all deterministic fixtures are linearly force-assemblable. We also show how to design an admittance matrix that guarantees that the workpiece will be guided into the deterministic fixture by the fixel contact forces alone.