PASSIVITY ANALYSIS FOR FLEXIBLE MULTILINK SPACE MANIPULATORS

The important input-output property of passivity is explored for a general flexible space manipulator with chain topology. The manipulator is assumed to consist of rigid and/or flexible links interconnected via revolute joints, and a free rigid spacecraft and cantilevered payload are modeled at the base and tip, respectively. Actuation on the spacecraft and torques at the joints serve as control inputs and a suitably modified input variable is constructed. The notion of reflected tip position introduced by Wang and Vidyasagar for a single flexible link is extended to the multilink case and used to define a corresponding modified output variable. The dynamics governing the system are developed using a Lagrangian approach and both linearized and nonlinear forms of the mapping relating modified inputs to modified outputs are examined. Our major result shows that the transfer function in the linear case is positive real when the spacecraft and payload are much more massive than the manipulator links. The corresponding nonlinear analysis shows that the mapping is, in fact, passive and uncovers an approximate static relationship between the elastic coordinates and applied torques. A numerical example employing the Space Shuttle, remote manipulator system, and payload is used to demonstrate the validity of the theoretical results. Applications to control system design are indicated.