Kinematic redundancy and the control of robots with flexible components

The author studies robot manipulators which simultaneously exhibit features of joint elasticity and kinematic redundancy. More specifically, he discusses manipulators in which there are more controlled (joint space) degrees of freedom than task space degrees of freedom and in which at least one of these controlled joints is connected to an adjacent link through an elastic coupling. It is shown that there is a wide class of examples for which it is impossible to find joint space motions which track a given end effector trajectory and do not at the same time excite elastic dynamics. For this class of geometries, the most that can in general be achieved is motion without storage of elastic energy in the joints. For certain congenial manipulator geometries, it is shown that under certain assumptions it is possible to plan such motions. It is shown how trajectories interpolating prescribed endpoints in the work space may be planned using fifth-order splines. The problem of exactly tracking end effector trajectories with minimum average elastic energy storage is discussed