Fuel Optimal Maneuver of Passive and Periodic Circular-Like Satellite Formation: Legendre Pseudospectral Approach

In this paper, an effective method was proposed to formulate and solve a fuel-optimal satellites maneuver control problem using a continuous low-thrust system. The design of the bounded desired final satellite formation is a passive and periodic circular-like formation at critical inclination underperturbation, which adjusts to long-term flying formation. The nonlinear optimal control problem is converted into a nonlinear programming problem by the application of the Legendre pseudospectral method. Due to the design includes the free final time and the precise final condition constraint, fuel-optimal maneuver is more reasonable, thereby it will achieve the minimum fuel consumption.