Isotropic compliance in E(3): Feasibility and workspace mapping

A manipulator control system, for which isotropic compliance holds in the Euclidean space Eð3Þ, can be significantly simplified by means of diagonal decoupling. However, such simplification may introduce some limits to the region of the workspace where the sought property can be achieved. The present investigation reveals how to detect which peculiar subset, among four different classes, a given manipulator belongs to. The paper also introduces the concept of control gain ratio for each specific single-input/single-output joint control law in order to limit the maximum gain required to achieve the isotropic compliance condition.