Inverse kinematics for redundant manipulators using the fast similarity factorization

The singular value decomposition(SVD)[1] has been frequently used for solving the inverse kinematics of the serial links manipulator since it provides the singular values which are effectively utilized for evaluating the manipulator's posture. However SVD requests heavy computational load parallel to the third order of the degrees of freedom(DOF), so that the parallel professing is requested for the real time control or simulation[2]. This paper presents the alternative algorithm for solving the inverse kinematics for serial link manipulators especially with redundant DOF. The main idea is to introduce the fast similarity factorization(FSF) which the authors developed[3] in order to solve the generalized inverse of Jacobian. The FSF provides us the singular values as same as the SVD, but is faster than the SVD. This advantage is getting to be more prominent as the DOF is becoming large since the computational load of the proposed method is in parallel to the second order of the DOF. The simulation for the seven DOF redundant manipulator reveales the proposed method is several times faster than the SVD based method in some cases.