Some facts concerning the inverse kinematics of redundant manipulators

Many conventional nonredundant manipulators have singular configurations, near which some small motions of the end-effector require excessive and physically unrealizable joint speeds. Consequently, the usable workspace of the manipulator is effectively reduced. It has been proposed that high joint speeds could be avoided by introducing redundant joints and using an appropriate kinematic inversion algorithm. For a very general class of kinematic inversion algorithms, the theorems of this paper state some fundamental relations between the properties of the algorithm and its ability to resolve these problems. These results have practical implications in the design of controllers for redundant manipulators, especially when real-time sensory input is used to modify the manipulator's trajectory.