Reformulation of dynamic manipulability ellipsoid for robotic manipulators

A reformulation of the dynamic manipulability ellipsoid for robotic manipulators is established. This ellipsoid is a common tool in robotics for measuring the ability of a manipulator to produce arbitrary accelerations of the end effector for a given set of torques at the joints. As opposed to the original approach where gravitational forces were imputed to compress the volume of the ellipsoid, it is shown that the effect of gravity can be taken into account by translating the center of the ellipsoid without affecting its volume. The ellipsoid for redundant manipulators is characterized by investigating the properties of the manipulator Jacobian involved in the core of the ellipsoid. Numerical case studies are developed