Compensability of End-Effector Position Errors for Flexible Robot Manipulators

This paper presents kinematic analysis of the end-effector position errors of flexible robot manipulators. The analysis gives kinematic fundamentals for their trajectory control. The end-effector position errors due to the link flexibility cannot be controlled directly but can be compensated only indirectly by the joint angles or displacements. The compensation, however, is sometimes impossible if the manipulator arm takes certain configurations. The analysis of this leads to a new concept of compensability that tells if the compensation is possible or not. A theorem and lemmas are derived to clarify the necessary and sufficient conditions of the compensability. A measure of the compensability is also presented to evaluate the easiness of the compensation. Moreover, noting the compensability, the manipulability of the flexible robot manipulator is discussed, and the relation between the compensability and the manipulability is clarified. It is shown that the manipulability of the flexible robot manipulator is worse than that of the rigid robot manipulator because of the link deflections.