A new formulation of the extended Jacobian method and its use in mapping algorithmic singularities for kinematically redundant manipulators

The extended Jacobian method resolves the redundancy of a kinematically redundant manipulator such that a secondary criterion is kept at an optimal value. This paper describes a new formulation of this algorithm that is well suited numerically for systems with multiple degrees of redundancy and for more general choices of the secondary criterion. This formulation is used here for tracing algorithmic singularities, which mark a boundary of operation for any algorithm using the same secondary criterion to resolve the redundancy. Examples of tracing algorithmic singularities are presented for both planar and spatial systems