Matrix normalization for optimal robot design

TitleMatrix normalization for optimal robot design
Publication TypeConference Paper
Year of Publication1998
AuthorsStocco, L., S. E. Salcudean, and F. Sassani
Conference NameRobotics and Automation, 1998. Proceedings. 1998 IEEE International Conference on
Pagination1346 -1351 vol.2
Date Publishedmay.
Keywordsasymmetric actuation, diagonal scaling matrices, impedance design matrix, isotropy, joint space variables, matrix algebra, matrix normalization, maximum angular force, maximum angular velocity, maximum linear force, maximum linear velocity, nonhomogeneous physical units, optimal control, optimal robot design, robots, scale factors, task space variables, well-conditioned Jacobian matrix

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


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