An order (N) recursive inversion of the Jacobian for an N-link serial manipulator

The Jacobian matrix, J, relates joint velocity to Cartesian velocity for an N-link serial manipulator. An operator factorization and inversion of ^J* ^J is shown to result in an order (N) spatially recursive filtering and smoothing algorithm that solves the inverse Jacobian problems of finding the joint angle velocities given the end-effector velocity or finding the joint angle accelerations given the end-effector acceleration. It is shown that, with a proper model, these inverse Jacobian problems are equivalent to solving the forward dynamics problem for the same model. The recursive algorithm developed by G. Rodriguez (1987) to solve the forward dynamics problem is applied directly to solve these inverse Jacobian problems