Redundancy resolution for robot manipulators-comparison of computational efficiency between the SVDs, the fast similarity factorization and recursive formulation

This paper discusses the computational efficiency of some procedures for solving the inverse kinematics problem of serial-link manipulators with redundant DOF. Two procedures that the author has newly developed, are compared to the most widely used SVD methods. One is called the fast similarity factorization (FSF) method, in which the symmetric matrix JJ^T J is the Jacobian of the manipulator) is factorized to GDG^T (G is the orthogonal matrix and D is the diagonal matrix). Another procedure, that the author also developed, is a recursive formulation, in which the joint-variable variations are obtained n (the number of DOF of the manipulator) times recursive calculations. Both methods are fast and robust. The computer simulation for a seven DOF anthropomorphic type manipulator reveals the proposed methods are several times faster than the conventional algorithms based on the SVD.