For a kinematically redundant manipulator, some performance indices can be optimized while carrying out a given task. So far, the redundancy resolution has been solved at the joint angle level, the joint velocity level, or joint acceleration level depending on the performance indices. According to the resolution level, the solution is represented by high-order differential equations or superfluous number of equations. We propose a unified approach to the inverse kinematic solution which optimizes it at the joint velocity level regardless of the types of the performance indices. A unified approach to obtain an optimal joint velocity is derived by using the necessary condition for optimality so that the proposed method provides an optimal solution for any performance indices and tasks. The optimal solution becomes a set of the minimum number of first-order differential equations which requires a minimum search dimension.To show the validity of the approach, it is applied to a three-link planar manipulator for various types of performance indices.
