Globally stable feedback laws for near-minimum-fuel and near-minimum-time pointing maneuvers for a landmark-tracking spacecraft

摘要

Utilizing unique properties of a recently developed set of attitude parameters, the modified Rodrigues parameters, we develop feedforward/feedback type control laws that globally control a spacecraft undergoing large nonlinear motions, using three or more reaction wheels. The method is suitable for tracking given smooth reference trajectories that spline smoothly into a target slate or pure spin motion; these reference trajectories may be exact or approximate solutions of the system equations of motion. In particular, we illustrate the ideas using both near-minimum-time and near-minimum fuel rotations about Euler's principal rotation axis, with parameterization of the sharpness of the control switching for each class of reference maneuvers. Lyapunov stability theory is used to prove rigorous stability of closed loop motion in the end game, and qualified Lyapunov stability during the large nonlinear path tracking portion of the closed loop tracking error dynamics. The methodology is illustrated by designing example control laws for a prototype landmark tracking spacecraft; simulations are reported that show this approach to be attractive for practical applications. The inputs to the reference trajectory are designed with user-controlled sharpness of all control switches, to enhance the trackability of the reference maneuvers in the presence of structural flexibility.