Design and optimal control of on-orbit servicing trajectory for target vehicle in non-coplanar elliptical orbit

Autonomous on-orbit servicing provides flexibility to space systems and has great value both in civil and in military. When a satellite performs on-orbit servicing tasks, flying around is the basic type of motion. This paper is concerned with the design and control problems of a chaser satellite flying around a target spacecraft in non-coplanar elliptical orbit for a long time. At first, a mathematical model used to design a long-term flying around trajectory is presented, which is applicable to the situation that the target spacecraft flies in an elliptical orbit. The conditions of the target at the centre of the flying around path are deduced. Considering the safety and task requirements, a long-term flying around trajectory is designed. Taking into account perturbations and navigation errors which can cause the trajectory unstable and mission impossible, a two-impulse control method is put forward. Genetic algorithm is used to minimize the cost function which considers fuel consumption and bias simultaneously. Some simulation works are carried out and the results indicate the flying around mathematical model and the trajectory control method can be used in the design and control of a long-term flying around trajectory.