Toward a tensor formulation of some pseudoinverse redundant kinematics properties

Abstract

Using tensor notation in joint space, the geometric characteristics of pseudoinverse drift are studied. This analysis helps describe the joint-space drift in terms of the torsion of two space curves. It is discovered that the joint trajectory resulting from Moore-Penrose pseudoinverse control goes to zero if the drift undergoes asymptotic decay. Furthermore, the torsion of the self-motion curves also has zero crossings, but only at their intersection with closed, drift-free joint trajectories. This allows one to predict drift-free initial configurations for 3R manipulators with a single degree of redundancy. The tensor notation provides a framework for future analysis with higher dimensional systems and systems and additional degrees of redundancy, which cannot be described with familiar properties of space-curves such as torsion.<>