Lyapunov Controller for Cooperative Space Manipulators

Abstract

The cooperative control of multiplemanipulatorsattached to the samebase asthey reposition a common payload is discussed. The theory is easily appliedto inertially based problems, as well asspace-based free- oating platforms. 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 manipulatorsis reduced by altering the order of the reference trajectory polynomial and its coef cients. Results from a two-dimensional, dual-arm con guration are included. Compared to the Lyapunov point controller alone, the addition of a fth-order polynomial reference trajectory leads to superior performance in terms of actuator torque magnitudes,spacecraft centerbody attitude control, and payload repositioning accuracy and time. An eighth-order polynomial reference trajectory results in only small improvement over the fth-order case. The cooperative control of multiplemanipulatorsattached to the samebase asthey reposition a common payload is discussed. The theory is easily appliedto inertially based problems, as well asspace-based free- oating platforms. 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 manipulatorsis reduced by altering the order of the reference trajectory polynomial and its coef cients. Results from a two-dimensional, dual-arm con guration are included. Compared to the Lyapunov point controller alone, the addition of a fth-order polynomial reference trajectory leads to superior performance in terms of actuator torque magnitudes,spacecraft centerbody attitude control, and payload repositioning accuracy and time. An eighth-order polynomial reference trajectory results in only small improvement over the fth-order case. The cooperative control of multiplemanipulatorsattached to the samebase asthey reposition a common payload is discussed. The theory is easily appliedto inertially based problems, as well asspace-based free- oating platforms. 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 manipulatorsis reduced by altering the order of the reference trajectory polynomial and its coef cients. Results from a two-dimensional, dual-arm con guration are included. Compared to the Lyapunov point controller alone, the addition of a fth-order polynomial reference trajectory leads to superior performance in terms of actuator torque magnitudes,spacecraft centerbody attitude control, and payload repositioning accuracy and time. An eighth-order polynomial reference trajectory results in only small improvement over the fth-order case. The cooperative control of multiplemanipulatorsattached to the samebase asthey reposition a common payload is discussed. The theory is easily appliedto inertially based problems, as well asspace-based free- oating platforms. 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 manipulatorsis reduced by altering the order of the reference trajectory polynomial and its coef cients. Results from a two-dimensional, dual-arm con guration are included. Compared to the Lyapunov point controller alone, the addition of a fth-order polynomial reference trajectory leads to superior performance in terms of actuator torque magnitudes,spacecraft centerbody attitude control, and payload repositioning accuracy and time. An eighth-order polynomial reference trajectory results in only small improvement over the fth-order case.