Optimum Design of a Planar Robotic Manipulator

Abstract

Abstract A general optimization methodology for the optimal design of robotic manipulators is presented and illustrated by its application to a realistic and practical three link re volute-joint planar manipulator. The end-effector carries out a prescribed vertical motion for which the weighted average torque requirement from electrical driving motors is minimized with respect to positional and dimensional design variables. In addition to simple physical bounds placed on the variables the maximum deliverable torques of the driving motors represent further constraints on the system. The optimization is carried out via a penalty function formulation of the constrained problem to which a proven robust unconstrained optimization method is applied. The problem of degeneracy or lock-up, which may occur for certain choices of design variables, is successfully dealt with by means of a specially proposed procedure in which a high artificial objective function value is computed for such “lock-up trajectories”. Designs are obtained that represent substantial reduction in torque requirement in comparison to that of arbitrarily chosen practical designs.