Compensability of end-effector position errors for flexible robot manipulators

A kinematic analysis of the end-effector position errors of flexible robot manipulators is presented. 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 for only indirectly by the joint angles or displacements. The compensation, however, is very difficult if the manipulator arm takes on certain configurations. The analysis of these situations 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 presented to evaluate the ease of compensation. It is shown that the manipulability of a flexible robot manipulator is worse than that of a rigid manipulator because of link deflections.