Relation between global velocity and local torque optimization of redundant manipulators

Abstract

In this article, the relation between the global optimization of joint velocity and local optimization of joint torque is investigated. The local minimization of the weighted joint torques can be matched to the global optimization of the corresponding weighted joint velocities when the weighted matrices satisfy certain sufficient conditions. A straightforward matching is obtained using the local optimization of the inertia inverse weighted dynamic torque and the global minimization of the kinetic energy. Another easy solution can be found, as will be shown later, if the inertia matrix is a constant and gravity is neglected. Based on that, it can be seen why a Cartesian robot, which has a constant inertia matrix, is always stable.