Symbolic Singular Value Decomposition for Simple Redundant Manipulators and Its Application to Robot Control

Abstract

Solving the inverse kinematic problem in the vicinity of singu larities by the use of the damped least squares method is one of the most efficient means to overcome numeric problems in singularities. The high numeric complexity of numeric algo rithms for the singular value decomposition (SVD) has so far prevented a broader application of this method. The use of the symbolic SVD in robot control for nonredundant manipulators was proposed in Kirćanski and Borić (1993). In this article symbolic expressions for singular values and singular vectors for a 7-DOF redundant manipulator are derived, together with the damped least squares joint velocities. Numeric complexity is reduced by about seven times. Simulation results show that the position error is reduced to a minimum, while joint rates are limited. Symbolic expressions are used to describe robot dex terity and isotropic configurations. Application to other simple redundant robot geometries with special Jacobian structures is discussed.