Globally stable feedback laws for near-minimum-fuel and near-minimum-time pointing maneuvers for a landmark-tracking spacecraft
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Utilizing unique properties of a recently developed set of attitude parameters the modified Rodrigues parameters, feedforward/feedback type control laws are developed for a spacecraft undergoing large nonlinear motions using three reaction wheels. The method is suitable for tracking given reference trajectories that spline smoothly into a target state; these reference trajectories may be exact or approximate solutions of the system equations of motion. An associated asymptotically stable nonlinear observer is formulated for state estimation. 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 global asymptotic stability of the closed-loop tracking error dynamics in the absence of external torques. If external torques are present, then the system is Lagrange stable. 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.