Use of an extended Jacobian method to map algorithmic singularities

The extended Jacobian method has been devised to operate a kinematically redundant manipulator such that a secondary criterion is kept at an optimal value. A formulation of this algorithm that is better suited numerically for systems with multiple degrees of redundancy and for more general choices of the secondary criterion is described. This formulation is particularly useful for tracing algorithmic singularities, which mark the bounds of operation for any algorithm using the same secondary criterion to resolve the redundancy. Examples of end effector positioning and tracing algorithmic singularities are presented for both planar and spatial systems