3On the Inverse Kinematics of Redundant Manipulators

Many conventional nonredundant manipulators have singu-lar configurations, near which some small motions of the end-effector require excessive and physically unrealizable joint speeds. Consequently, the usable workspace of the ma-nipulator is effectively reduced. It has been proposed that high joint speeds could be avoided by introducing redundant joints and using an appropriate kinematic inversion algo-rithm. For a very general class of kinematic inversion algo-rithms, the theorems of this paper state some fundamental relations between the properties of the algorithm and its ability to resolve such problems. These results have practical implications in the design of controllers for redundant ma-nipulators, especially when real-time sensory input is used to modify the manipulator’s trajectory. 1