Exact nonlinear control of spacecraft slewing maneuvers with internal momentum transfer

The recent literature on spacecraft slewing maneuvers relies on two techniques for taking nonlinear effects into acount: suboptimal torque commands are either generated by continuation techniques from open-loop laws arising from Pontryagin's Maximum Principle, or obtained by polynomial truncation of analytic feedback laws arising from Bellman's Qptimality Principle. Correction for suboptimality and unmodeled disturbances must then be carried out on-line based on a time-varying approximation of the error dynamics along the nominal state trajectory* In this paper it is shown how exact command generation and tracking can be obtained by standard linear methods through the prior construction of nonlinear coordinate transformations together with nonlinear feedback. The nonlinear equations of motion of a spacecraft controlled by internal reaction wheels are thereby transformed into three decoupled double integrators, driven by acceleration commands in attitude parameter space. Maneuver specifications are then transformed into the equivalent linear representation thus obtained, and codified into linear optimal control or path-planning problems with exact solutions, which are then transformed back. Moreover, correction for disturbances can also be carried out in the transformed linear representation, making gain scheduling unnecessary. Hardware and software implementation of the linearizing transformations is discussed, and corroborating simulation results are presented.