Influence of gravity on the manipulability ellipsoid for robot arms

The dynamic manipulability ellipsoid is a common tool in robotics to measure the ability of a manipulator to produce arbitrary accelerations of the end-effector for a given set of torques at the joints. This article is intended to demonstrate that for a robot arm, when gravitational forces (due to arm and payload) are properly embedded into the derivation of the ellipsoid, these do not cause a compression in the volume of the ellipsoid, as stated in the original approach, but they just produce a translation of the ellipsoid which in general occurs along all task space directions. Further, we characterize the ellipsoid for redundant manipulators by investigating the properties of the manipulator Jacobian involved in the core of the ellipsoid. Numerical case studies are developed.