Constrained Station Relocation in Geostationary Equatorial Orbit Using a Legendre Pseudospectral Method

An algorithm for numerical approximation is formulated using a Legendre pseudospectral method to solve the problem of constrained station relocation, changing current position to another longitude, in geostationaryequatorial orbit. The problem was stated as a Bolza form in optimal control theory to calculate the control. A collision avoidance term, which is included in the objective function as an integral form and serves as a soft constraint, 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 relocation maneuvers are simulated; the states and control behavior are obtained and all the variables are found to be within feasible ranges. This method would be possible to implement using very-low-thrust engines, in particular, by employing attitude control thrusters.