The University of British Columbia

Good robot performance often relies upon the selection of design parameters that lead to a well conditioned Jacobian or impedance ldquo;design rdquo; matrix. In this paper a new design matrix normalization technique is presented to cope with the problem of nonhomogeneous physical units. The technique pre and post-multiplies a design matrix by diagonal scaling matrices corresponding to the range of joint and task space variables. In the case of the Jacobian, normalization leads to a practical interpretation of a robot's ldquo;characteristic length rdquo; as the desired ratio between maximum linear and angular force or velocity. The scale factors can also be used to set relative required strength or speed along any axes of end-point motion and/or can be treated as free design parameters to improve isotropy through asymmetric actuation. The effect of scaling on actual designs is illustrated by a number of design examples using a global search method previously developed by the authors