Application of Global Optimization to Transfer Orbits for Fractionated Spacecraft

The global optimization can be applied to many fields,one of which is orbital dynamics.The optimal transfer orbits of fractionated spacecraft is focused on and proposed a scenario that all the modules transfer from the parking orbit successively,and arrived at the corresponding positions on the object orbit simultaneously.The optimal control problem is established.Performance index is selected to minimize the total orbital transfer time with limited fuel,which is defined as the sum of all the long-distance orbital transfer time of the modules and phase errors eliminating time of the spacecraft on the parking orbit.The optimization problem here is a very complicated dynamic optimal control problem if position and velocity are choosed as the states.However,it is transformed into static parameter optimization problem via the correct steady state parameters.In the end,the parameter optimization problem is solved by optimization algorithm based on Quasi-Newton Method in virtue of Matlab optimization tools.The optimization algorithm can converge promptly with high precision on condition of a favorable initial estimate.On the other hand,the initial guess value can be obtained according to the orbital dynamics with impulse assumption.The simulation demonstrates the availability of the fractionated spacecraft's orbit design strategy and the effectiveness of the algorithm.