On the existence and the manipulability recovery rate of self-motion at manipulator singularities

This article investigates the escapability of redundant manipulators at a singularity. Escapability means that the manipulator can reconfigure itself from a singular posture to a nonsingular posture via self-motion. Criteria for the classifications of escapable and inescapable singularities are established based on multivariable calculus theorems. For the general case, we give necessary conditions for the escapability of singular configurations. For singular configurations with only one lost degree of freedom in the workspace, sufficient conditions for the escapability are provided. We then show how the arm can escape the singularity at the maximum rate if these sufficient conditions are satisfied Our method gives the best self-motion among the set of all feasible self-motions, in the sense that the manipulability measure of the arm increases most rapidly for the chosen self-motion. It is also shown that at a singular configuration with more than one lost degree of freedom in the workspace, the initial rate of recovery of manipulability is very slow, regardless of the possibility of self-motion. Examples are given to demonstrate the use of these criteria.