Kinetic limitations on the use of redundancy in robotic manipulators

The kinematic specification of motion for redundant manipulators has relied primarily on a formulation that treats the redundant degrees of freedom as independent of those required to maintain a desired end effector trajectory. While such a formulation is conceptually appealing, it has been shown to be physically inaccurate when applied to the kinetic behavior of redundant manipulators. The kinetic effects of homogeneous solutions are analyzed with emphasis on placing realistic limitations on how redundancy can be utilized without adversely affecting the primary goal of a desired end effector trajectory. It is shown that it is possible to identify manipulator configurations that possess the desirable characteristic of being able either to remove or to impart a homogeneous velocity while simultaneously reducing the torque requirements on the manipulator. The conditions that govern these configurations are shown to be directly related to the conditions for guaranteeing global stability for the local torque minimization formulation