An unconstrained optimization approach to the resolution of the inverse kinematic problem of redundant and nonredundant robot manipulators

Abstract

This paper presents a comparative study of some unconstrained optimization techniques applied to robotic kinematic control. We are concerned not only with the final location of the end-effector but also with the velocity at which the end-effector moves. The position and velocity kinematic problems are related since the Jacobian matrix depends on the values of the joint variables. In order to move the end-effector in a specified direction at a specified speed, it is necessary to solve, at the same time, a set of nonlinear and a set of linear equations. Some well-known optimization techniques (valid for both nonredundant and redundant robots): steepest descent, conjugate gradient and quasi-Newton methods, are applied to solve this inverse kinematic problem. All these techniques are tested on two manipulators (a nonredundant and a redundant one) and compared by means of simulation.