Title
Impedance Restrictions on Independent Finger Grippers

Abstract
The impedance matrices of independent point fingers of a multifingered gripper map to the impedance matrix of a grasped workpart. We find that in a planar geometry, three fingers are enough to allow an unrestricted range of workpart impedances, if finger impedances are selectable. In a spatial geometry however, five fingers are necessary for the broadest range of workpart impedances, and even so there is one impedance matrix that a workpart cannot attain regardless of the number of fingers that grasp it. We find this 'unattainable' impedance matrix. We also characterize the impedance restrictions on workparts grasped with fewer than five spatial or three planar fingers.

Source: IEEE Transactions on Robotics and Automation, accepted April, 1996

Title
Force-Assembly with Friction

Abstract
If an admittance control law is properly designed, a workpiece can be guided into a fixture using only the contact forces for guidance (force-assembly). Previously, we have shown that: 1) a space of accommodation control laws that will ensure force-assembly without friction always exists, and 2) as friction is increased, a control law that allows force- assembly can be obtained as long as the forces associated with positional misalignment are characteristic. A single accommodation control law that allows force-assembly at the maximum value of friction can be obtained by an optimization procedure.

The single accommodation control law obtained by the optimization procedure, however, is not unique. There exists a space of accommodation control laws that will allow force-assembly at, or below, the value of friction that marginally violates the characteristic forces condition. Here, for the purpose of the accommodation control law design, a set of linear sufficient conditions is used to generate accommodation basis matrices. Any nonnegative linear combination of the accommodation basis matrices that, when combined, yields a positive definite accommodation matrix is guaranteed to provide force-assembly at or below a specified value of friction. (Basis matrices exist only if that specified value of friction is less than the value for which forces are still characteristic.)

Source: IEEE Transactions on Robotics and Automation 10(4), August 1994, 465-479

Title
Admittance Matrix Design for Force Guided Assmebly

Abstract
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]) 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, 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.

Source: IEEE Transactions on Robotics and Automation 8(2) April 1992, 213-227

Title
Programmed Compliance for Error-Corrective Assembly

Abstract
Suppose that before an assembly task commences we can specify at will the manipulator's response to assembly forces, by providing a single compliance (or damping) matrix to be used for the duration of the operation. Can we choose the matrix elements so that the force which characterizes every possible error condition maps into a motion which reduces it? If so we are assured that the operation will evolve toward decreased errors and eventual success. In this paper we describe a framework and a method of synthesis of an error-corrective matrix.

Source: IEEE Transactions on Robotics and Automation 6:4, August 1990