Adaptive control of flexible manipulators carrying large uncertain payloads

An adaptive controller is presented for a manipulator with revolute joints and structurally flexible links which carries a rigid payload with unknown mass properties. Under the assumption that the payload mass is much greater than that of the manipulator, globally stable tracking of the Cartesian end-effector coordinates is established. Key ideas underlying the controller development are the passivity of a mapping involving the end-effector rates as part of the output and a fixed parameter feedforward which preserves this property. The concept of filtered error is borrowed from previous work on rigid arms and suitably modified in developing the adaptive law. Although measurements of the tip positions and rates are needed, there is no requirement for sensing of the elastic coordinates. A numerical example involving a six DOF manipulator with flexible links demonstrates excellent tracking with respect to a simulation based on the exact motion equations.