A general formulation of the redundancy resolution of robotic manipulators is developed and resolved as the Lagrange problem of optimal control. It is shown that, many well known methods for optimal redundant manipulation in the literature, including Extended Jacobian Technique, most of constraint function based methods, and most of the previously reported methods based on global optimization techniques, are all the special cases of the formulation provided here.

Furthermore, the necessary conditions of the global optimality for this general formulation are derived in explicit form. Based on these conditions, the source of “algorithmic singularity” is rigorously identified and resolved.

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