A mathematical optimization methodology for the optimal design of a planar robotic manipulator

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 revolute-joint planar manipulator. The end-effector carries out a prescribed vertical motion for which, respectively, the average torque requirement from electrical driving motors, and the electric input energy to the driving motors are 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 and the allowable joint angles between successive links 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 singularities (also known as 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 are feasible and practical with reductions in the objective functions in comparison to that of arbitrarily chosen infeasible initial designs. Copyright © 1999 John Wiley & Sons, Ltd.