The Singular Value Decomposition: Computation and Applications to Robotics

Abstract

The singular value decomposition has been extensively used for the analysis of the kinematic and dynamic characteristics of robotic manipulators. Due to a reputation for being nu merically expensive to compute, however, it has not been used for real-time applications. This work illustrates a for mulation for the singular value decomposition that takes advantage of the nature of robotics matrix calculations to ob tain a computationally feasible algorithm. Several applica tions, including the control of redundant manipulators and the optimization of dexterity, are discussed. A detailed illus tration of the use of the singular value decomposition to deal with the general problem of singularities is also presented.