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 formin 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 transferby specifyingamaximumorminimum radius, depending onwhether the transferisinthe eastor 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.