On the Global Behavior of Kinematically Redundant Manipulators

Most methods for controlling redundant manipulators are based on local or instantaneous solutions of the kinematic velocity equation, for a given hand-space path or displacement. However, the global behavior needs to be determined a-priori to avoid unexpected problems like non-repeatability, instability and more. Global motion planning must pertain not only to the motion of the end-effector but to the whole arm. The mathematical model of redundancy control that we have developed, is based on analyzing certain structures or skeletons of surfaces in the joint space. The advantages of this approach are twofold. For one, it helps explain certain behavior patterns that are induced by given control strategies, while taking into account the geometry of the robot itself. But more important is the fact that it helps devise "better" strategies with which to control the robot and plan its motions.