Estimate of the two smallest singular values of the Jacobian Matrix: Application to damped least-squares inverse kinematics

The smallest singular value of the Jacobian matrix is known to be the sole reliable measure of closeness to singular configurations; its computation via a full singular value decomposition, however, is demanding in view of real-time applications. In this article, a standard singular value estimation procedure is extended to improve the handling of singular values crossing along a given trajectory. The proposed algorithm maintains the computational efficiency of the original technique and shows higher estimation accuracy with respect to the original procedure. Case studies are developed to verify the effectiveness of the estimation procedure applied to an industrial manipulator. © 1993 John Wiley & Sons, Inc.