In this paper a new concept, named the Extended Operational Space Formulation, has been proposed for the effective analysis and real-time control of the robot manipulators with kinematic redundancy. The extended operational space consists of operational space and optimal null space. The operational space is used to describe robot end-effector motion; whereas the optimal null space, defined as the target space of the self motion manifold, is used to express the self motion for the secondary tasks. Based upon the proposed formulation, the kinematics, statics, and dynamics of redundant robots have been analyzed, and an efficient control algorithm has been proposed. Using this algorithm, one can optimize a performance measure while tracking a desired end-effector trajectory with a better computational efficiency than the conventional methods. The effective ness of the proposed method has been demonstrated with simulations.