In this paper, a closed-from formulation for inverse kinematics of robot manipulators with kinematic redundancy under the contrained environment has been derived using the KuhnTucker condition, the extended Lagrange multiplier method and the working set method. The proposed algorithm satisfies
the necessary and sufficient conditions for optimization subject to equality and inequality constraints. In addition, computationally efficient kinematic control methods have been proposed using differential
kinematics and gradient projection method. The effectiveness of the proposed methods has been demonstrated with a 4-dof planar robot, and then a 7-dof spatial robot as practical application to the nozzle dam task in the Nuclear Power Plant.