Force-assembly with friction

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.)