Symbolic Singular Value Decomposition for a PUMA Robot and Its Application to a Robot Operation Near Singularities

Abstract

Singular value decomposition has received considerable atten tion in robot control during the past several years because of the fact that it may be used in solving the problem of robot operation in singular configurations. However, its main draw back is its high computational complexity when compared with that of the Gaussian elimination or analytical inverse kinematic solution. In this article we have derived symbolic expressions for matrices of the decomposition for both a 2-DOF planar manipulator and a 6-DOF PUMA robot. This reduces the com putational burden by an order of magnitude and gives us more insight into the nature of the singularities. The symbolic ex pressions have been applied to obtain the damped least-squares solution for joint velocities. Some modifications of the damped least-squares solution are proposed, and the simulation results are included. The method can be applied to other robots when position and orientation problems can be separated.