The Reduced Gradient Method for Solving Redundancy in Robot Arms

Abstract

An efficient compuUltional scheme for solving inverse kinematic problems in redundant robot anns is presented. lWJen following a given end-effector trajectory. successive intemal ann configurations are in general selected by local optimization of a given performance criterion. Typically, joint displacements are derived using the Projected Gradient method, involving pseudoinversion of the robot Jacobian and projection in its null-space. However, this technique is computationally intensive. In this paper, an altemative approach is proposed based on the Reduced Gradient method, which allows to deal explicitly only with the redundant degrees of freedom. The superiority of this technique for solving redundancy is i1Justrated analytically in a simple case, and numerically by simulation of a four-link planar ann. Optimization of various criteria like manipulabiIity, available joint range, and disUlnce from obsUlcles is considered, gi ving quite satisfactory results. Also, possible generalizations of the method are briefly discussed.