Manipulability and singularity analysis of multiple robot systems: a geometric approach

We present a differential geometric analysis of manipulability for holonomic multiple robot systems containing active and passive joints. Our analysis treats both redundant and nonredundant systems, including the case of redundant actuation, in a uniform manner. Dynamic characteristics of the robot system and manipulated object can also be naturally included by an appropriate choice of Riemannian metric. Our geometric framework also suggests a classification of kinematic singularities into three basic types: (i) those corresponding to singular points of the joint configuration space (configuration space singularities), (ii) those induced by the choice of actuated joints (actuator singularities), and (iii) those configurations in which the end-effector loses one or more degrees of freedom of available motion (end-effector singularities). The proposed geometric classification provides a high-level taxonomy for kinematic singularities that is independent of the choice of local coordinates used to describe the robot kinematics.