Optimal Coupled Spacecraft Rendezvous and Docking Using Gauss Pseudospectral Method and Step by Step Linearization

In this work the coupled nonlinear problem of optimal spacecraft rendezvous and docking (RVD) is addressed. In most of the previous studies on the subject of optimal RVD, decoupling is presumed to exist between the trajectory translational and the attitude motions and hence the optimal coupled analysis has not been yet addressed properly. However there are circumstances where these two motions are in fact coupled and interdependent and one such situation is investigated and analyzed in this article. By utilizing thrusters for the translational control and reaction wheels for the attitude control, one can uncouple the translational and rotational control to a high degree of approximation. However it can be shown that due to even very small thrust misalignments, the uncoupled problem changes to a highly coupled one. In this article, the nonlinear rendezvous and docking problem is assumed to be coupled and its optimal fuel-trajectory closed loop solution is obtained using two approaches of local linearization and Gauss Pseudospectral methods. Therefore the designed controllers are able to handle the highly nonlinear coupled rendezvous and docking optimally in the presence of system uncertainties as well as environmental disturbances. The results of the two solution approaches and their pertinent control strategies are compared and the merits and weaknesses of each are fully analyzed. Finally, a sensitivity analysis is also performed that shows the effects of thrust misalignments levels on the final state diversions.