A closed-form solution for the control of manipulators with kinematic redundancy

A closed-form equation for inverse kinematics of manipulators with redundancy is derived, using the Lagrangian multiplier method. The proposed equation is proved to provide the exact equilibrium state for the resolved motion method, and is shown to be a general expression that yields the extended Jacobian method. The repeatability problem in the resolved motion method does not exist in the proposed equation. The equation is demonstrated to give more accurate trajectories than the resolved motion method.