Cooperative Control of Multiple Space Manipulators

Abstract

This paper concerns the cooperative control of multiple manipulators attached to the same base as they reposition a common payload. The theory is easily applied to inertially based problems as well as space based free-floating plate forms. The system equations of motion are developed as well as a Lyapunov based controller which 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 center-body by the motion of the manipulators is minimized by altering the order of the reference trajectory polynomial and its coefficients. Results from a two dimensional, dual arm configuration are included. Compared to the Lyapunov point controller alone, a fifth 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 minimal improvement over the fifth order case. A modified Lyapunov controller which approximates a PD controller produces results better than the Lyapunov point controller but not as good as either reference trajectory simulation. This paper concerns the cooperative control of multiple manipulators attached to the same base as they reposition a common payload. The theory is easily applied to inertially based problems as well as space based free-floating plate forms. The system equations of motion are developed as well as a Lyapunov based controller which 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 center-body by the motion of the manipulators is minimized by altering the order of the reference trajectory polynomial and its coefficients. Results from a two dimensional, dual arm configuration are included. Compared to the Lyapunov point controller alone, a fifth 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 minimal improvement over the fifth order case. A modified Lyapunov controller which approximates a PD controller produces results better than the Lyapunov point controller but not as good as either reference trajectory simulation. This paper concerns the cooperative control of multiple manipulators attached to the same base as they reposition a common payload. The theory is easily applied to inertially based problems as well as space based free-floating plate forms. The system equations of motion are developed as well as a Lyapunov based controller which 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 center-body by the motion of the manipulators is minimized by altering the order of the reference trajectory polynomial and its coefficients. Results from a two dimensional, dual arm configuration are included. Compared to the Lyapunov point controller alone, a fifth 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 minimal improvement over the fifth order case. A modified Lyapunov controller which approximates a PD controller produces results better than the Lyapunov point controller but not as good as either reference trajectory simulation. This paper concerns the cooperative control of multiple manipulators attached to the same base as they reposition a common payload. The theory is easily applied to inertially based problems as well as space based free-floating plate forms. The system equations of motion are developed as well as a Lyapunov based controller which 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 center-body by the motion of the manipulators is minimized by altering the order of the reference trajectory polynomial and its coefficients. Results from a two dimensional, dual arm configuration are included. Compared to the Lyapunov point controller alone, a fifth 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 minimal improvement over the fifth order case. A modified Lyapunov controller which approximates a PD controller produces results better than the Lyapunov point controller but not as good as either reference trajectory simulation. This paper concerns the cooperative control of multiple manipulators attached to the same base as they reposition a common payload. The theory is easily applied to inertially based problems as well as space based free-floating plate forms. The system equations of motion are developed as well as a Lyapunov based controller which 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 center-body by the motion of the manipulators is minimized by altering the order of the reference trajectory polynomial and its coefficients. Results from a two dimensional, dual arm configuration are included. Compared to the Lyapunov point controller alone, a fifth 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 minimal improvement over the fifth order case. A modified Lyapunov controller which approximates a PD controller produces results better than the Lyapunov point controller but not as good as either reference trajectory simulation. This paper concerns the cooperative control of multiple manipulators attached to the same base as they reposition a common payload. The theory is easily applied to inertially based problems as well as space based free-floating plate forms. The system equations of motion are developed as well as a Lyapunov based controller which 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 center-body by the motion of the manipulators is minimized by altering the order of the reference trajectory polynomial and its coefficients. Results from a two dimensional, dual arm configuration are included. Compared to the Lyapunov point controller alone, a fifth 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 minimal improvement over the fifth order case. A modified Lyapunov controller which approximates a PD controller produces results better than the Lyapunov point controller but not as good as either reference trajectory simulation.