Comments on "Global task space manipulability ellipsoids for multiple-arm systems" and further considerations" [with reply] P. Chiacchio, et al

The manipulability ellipsoids are used in robotics as a measure of manipulators´ performances achievable during task execution. The definition of these geometrical entities is based on the Jacobian of the manipulator, and the physical meaning given to the ellipsoids is related to the capability of the mechanism to apply forces with the end effector or to move the tool in some directions of the task-space. P. Chiacchio et al. (ibid., vol.7, p.678-685, 1991) have extended this concept to the case of cooperating manipulators. Nevertheless, some questions are still open, both with respect to the basic definition and use of manipulability ellipsoids. The commenter shows by simple examples that the use of manipulability ellipsoids for multiarm systems gives misleading results, and he disagrees with the above authors´ definition of ellipsoids. The authors defend their work.<>