Lyapunov Controller for Cooperative Space Manipulators

The cooperativecontrol ofmultiplemanipulatorsattached to the samebase as they reposition a commonpayload is discussed. The theory is easily applied to inertiallybased problems, as well as space-based free- oatingplatforms. The system equations of motion are developed, as well as a Lyapunov-based controller that ensures stability. The closed chain aspect of the problem reduces the system’s degrees of freedom resulting in more actuators than degrees of freedom. This actuator redundancy is used to minimize a weighted norm of the actuator torques. A polynomial reference trajectory describes the path the payload will follow. The disturbance torque transmitted to the spacecraft centerbody by the motion of the manipulators is reduced by altering the order of the reference trajectory polynomial and its coefŽ cients. Results from a two-dimensional, dual-arm conŽ guration are included. Compared to the Lyapunov point controller alone, the addition of a Ž fth-order polynomial reference trajectory leads to superior performance in terms of actuator torquemagnitudes, spacecraft centerbody attitude control, and payload repositioning accuracy and time. An eighth-order polynomial reference trajectory results in only small improvement over the Ž fth-order case.