Constrained station change in GEO using a Legendre pseudo-spectral method

The algorithm for numerical approximation of the optimal control is formulated using a Legendre pseudo-spectral method to solve the problem of constrained station change in GEO. A collision avoidance term, which is included in the objective function as an integral form, is considered during transfer by specifying a maximum or minimum radius depending on whether the transfer is in the east or west-direction. Several east-and-west-direction station change transfer maneuvers are simulated; the histories of the states and control behavior are obtained and all the variables are found to be within feasible ranges. Multiple revolutions and large longitude station change cases are also demonstrated using this method. The transfer time is found to be only weakly affected by the initial thrust acceleration for the multi-revolution change cases. This method would be possible to implement using very low-thrust engines, in particular, by employing attitude control thrusters.