A zonotope-based approach for manipulability study of redundant robot limbs

Kinematic efficiency of robot limbs can be analyzed by means of the manipulability concept defined by T. Yoshikawa. However when it is applied to redundant serial chains, that are the most common case in humanoid robotics, Yoshikawa´s manipulability measure is not able to take into account the joint velocity range of each robot joint. In order to overcome this difficulty we propose to substitute for the manipulability ellipsoid a manipulability zonotope resulting from the robot Jacobian transform of the joint velocities parallelotope. The proposed manipulability zonotope notion is similar to the well-known manipulability polytope notion but its associated volume measure can take beneficit of the so-called zonotope theory. By means of a famous and powerful theorem about the cubical dissection of any zonotope, an original formula of manipulability measure is proposed from which is also derived a mean manipulability estimate associated to a given joint space working. The proposed tools are applied to a kinematic analysis of a 4R-regional structure model of the upper limb.