In this paper, a closed-form formulation for inverse kinematics for redundant manipulators with inequality constraints has been proposed. This formulation has been derived by using the Kuhn-Tucker condition, the Lagrange multiplier method, and the active/working set method, so that its solution may satisfy the necessary and sufficient condition for optimization subject to equality and inequality constraints. From the formulation, computationally efficient kinematic control methods have been derived using differential kinematics and gradient projection method. The effectiveness of the proposed methods has been demonstrated with a 4-DOF planar manipulator, and then a 7-DOF spatial manipulator as a practical application to a nozzle dam task of a nuclear power plant.
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