Approximate inverse dynamics and passive feedback for flexible manipulators with large payloads

A derivation is presented of an approximate form of the dynamics governing a structurally flexible manipulator carrying a massive payload at its end-effector. An output called the mu-tip rate which incorporates end-effector and elastic motions is introduced. The input-output mapping relating a transformed version of the joint torques to the mu-tip rates is shown to be passive for large payloads. A feedforward torque strategy is developed which preserves the passivity property in the error dynamics and a suitable Lyapunov function is used to demonstrate global asymptotic stability of the tracking provided by a PD law. Implementation of the controllers without measurements of the elastic coordinates and rates is shown to be possible. Simulation studies of a six DOF manipulator with flexible links, modeled after the Shuttle Remote Manipulator System, demonstrate excellent tracking in all six Cartesian end-effector coordinates, even for payloads with modest mass properties. A major conclusion is that some of the problems normally associated with lack of collocation in flexible manipulators can be surmounted when large (massive) payloads are involved.