Global task space manipulability ellipsoids for multiple-arm systems

New definitions of force and velocity manipulability ellipsoids for multiple-arm systems are given. A suitable kinetostatic formulation for multiple cooperating arms is adopted that allows a global task space description of external and internal forces as well as absolute and relative velocities at the object level. The concept of a force manipulability ellipsoid for a single arm is formally extended to the multi-arm case by regarding the whole system as a mechanical transformer from the extended joint space to the global task space. Kinetostatic duality properties are then exploited to derive velocity manipulability ellipsoids for the multiple-arm system. The proposed method is compared with other approaches using numerical examples