Spiral Motion of Nonholonomic Space Robots

Abstract

A free-flying space robot with a 6-DOF manipulator cannot follow an arbitrary trajectory in the 9D generalized coordinates (3 of the satellite attitude and 6 of the manipulator joints) with only manipulator joint control, though it was shown to be commonly controllable in the literature. In this paper, we propose a method to approximate an arbitrary 9D path by introducing a perturbation around the specified path. We call thus approximated trajectory a “spiral motion”. A computational scheme for the optimal spiral motion is presented, and is followed by computer simulation. Relationship of singular points and computational convergency is also discussed.