A manipulator workspace generation algorithm using a singular value decomposition

This paper presents a manipulator workspace boundary generation algorithm that can be easily implemented as a computer algorithm. The algorithm searches the workspace boundary on the basis of slice curves which are defined as the cross-section of the workspace boundary with planes parallel to XY , YZ, or XZ plane. The collection of these slice curves represents a tomographic view of the workspace boundary. The proposed workspace boundary searching algorithm is composed of two stages. First stage is for estimating the boundary by using a linearization model of the forward kinematic equation, which searches the feasible direction vector at a current point while considering both the kinematic condition and the joint limits. The other is for correcting the estimated boundary point to an exact boundary point by solving an optimization problem that maximizes a fuzzy set like cost function.