A study on the manipulability measures for robot manipulators

Regarding the dexterousness measure of robot manipulators, two geometric tools, manipulability ellipsoids and manipulability polytopes, are examined and compared with each other. Even though the manipulability ellipsoid approach is the most widely used techniques, it is shown that the manipulability ellipsoid does not transform the exact joint velocity constraints into task space and so may fail to give exact dexterousness measure and optimal direction of motion in task space. After showing that the polytope approach can handle such problems, we propose a practical polytope method which can be applied to general 6-dimensional task space. The relation between manipulability ellipsoids and manipulability polytopes are also explored for a redundant case as well as nonredundant case.