Operator approach to recursive Jacobian inversion and pseudoinversion

Operator forms of the inverse and Moore-Penrose pseudoinverse of the Jacobian for a nonsingular n-link serial spatial manipulator are developed. It is shown that the Jacobian pseudoinverse operation that maps an end-effector velocity to a corresponding joint-space velocity can be performed using an O(n) recursive algorithm involving one 6×6 matrix inversion. It is also shown that an alternative recursive algorithm that produces a kinematic singularity measure as a byproduct can be used to perform the Jacobian inverse operation without the need for a matrix inversion