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