Real-time SVD for the control of redundant robotic manipulators

The process of reducing the computational expense of determining the singular value decomposition (SVD) of the Jacobian matrix to such an extent that online calculation becomes feasible is presented. It is shown that the incremental manner in which the Jacobian changes, along with the perturbation bounds on singular values and vectors, allows the reduction of the computational expense of calculating the SVD in three ways. First, the singular vectors from the previous calculation can be used to preorthogonalize the current Jacobian. Second, by virtue of nearly orthogonal columns, the iterative nature of the calculations can be prevented, thus avoiding convergence tests. Finally, since the few rotations required for orthogonalization are small in magnitude, approximations can be used.>