Admittance Matrix Design for Force Guided Assembly

This paper addresses manipulator admittance design with regard to reliable force guided assembly. Our goal is to design the admittance of the manipulator so that, at all possible part misalignments, the contact forces always lead to error-reducing motions. If this objective can be accomplished for a given set of 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). For reliable insertion, the fixture should have the property that contact with all fixels ensures a unique workpiece position (i.e., the fixture should be deterministic [Asada, 1985 #105]) and the property that contact with all fixels is ensured after the insertion motion terminates. Here, we define a linearly force-assemblable fixture to be one for which there exists an admittance matrix which necessarily results in workpiece contact with all fixels despite initial positional error. We show that, in the absence of friction, al l 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