Programming a damping matrix for error-corrective assembly

The author considers the situation in which the response of a manipulator to forces imposed on it is given by a user-selectable damping matrix (a six-by-six matrix which maps forces and torques into translational and rotational velocities). He then seeks to determine whether it is possible to choose the 36 matrix elements so that the forces which characterize every error condition map into the motions that correct it. He proposes three desired properties of the damping matrix: the bounded-forces, error-reduction, and nonorthogonal-motion properties. It is shown how the damping matrix most closely attaining these properties under all contact configurations can be constructed. For some tasks a `perfect´ damping matrix possessing all three properties exists, and under its direction assembly must necessarily proceed to completion. For some tasks a perfect damping matrix does not exist, and it is conjectured that the three properties may still be useful as heuristics; the damping matrix most closely attaining them will likely be appropriate to the task. To test this conjecture, the author considers the canonical peg-into-chamfered-hole task and finds that no ´perfect´ damping matrix is possible