On the use of scaling matrices for task-specific robot design

Good robot performance often relies upon the selection of design parameters that lead to a well conditioned Jacobian or impedance “design” matrix. In this paper, a new design matrix normalization technique is presented to handle the problem of nonhomogeneous physical units and to provide a means of specifying a performance based design goal. The technique pre- and post-multiplies a design matrix by scaling matrices corresponding to a range of joint and task space variables. The task-space scale factors are used to set the relative required strength or speed along any axes of end point motion while the joint-space scale factors are treated as free design parameters to improve isotropy through nonhomogeneous 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