Optimization method for high-precision multi-satellite rendezvous using multi-round iterative correction

With the rapid advancement of the space technology, the number of on-orbit satellites continuously grows, accompanied by the increase in both the scale and complexity of space missions. On-orbit servicing for multiple space targets has attracted much attention. An optimal rendezvous maneuver plan can minimize the fuel consumption while maximizing the number of target satellites being successfully serviced. For designing the optimal rendezvous trajectory of a single chase satellite serving multiple target satellites, it is essential to achieve the high rendezvous accuracy in engineering. However, the calculation of high-precision orbital propagation often leads to the increased computational burden and reduced efficiency. This paper aims to propose a multi-satellite rendezvous trajectory optimization method that yields maneuver impulse parameters with relative low computation cost while satisfying the high precision requirement.

A three-step serial optimization method based on the multi-round iterative correction is proposed. The rendezvous sequence and approximate impulse solutions based on the analytical J₂ perturbation model are obtained by using the differential evolution algorithm, the purpose of which is to minimize the velocity increment. The high-precision solution of the first rendezvous maneuver impulses is obtained by using the SQP (sequential quadratic programming) algorithm, which aims to reduce the rendezvous terminal deviations. Moreover, the propagation error between different models diffuses with the mission time, which causes the difficulty of convergence of the SQP in multi-satellite rendezvous trajectory planning. A multi-round iterative correction model is constructed to update the subsequent target satellites’ states and maneuver impulses to eliminate the influence of the error diffusion.

Firstly, a simulation example with 5 target satellites is given, the iterative processes of a single rendezvous arc are provided, and each step of the optimization converges within 300 iterations. Meanwhile, the trajectory of this single rendezvous is shown. At the rendezvous time, the orbital parameters of the chase satellite and the target satellite match well, and the relative error is less than 1×10^-6. The convergence and accuracy of the proposed method are demonstrated by the examples with the variations in orbital parameters during the entire mission process. Compared with the J₂ perturbation optimal solution, the approximate optimality of the high precision solution in the velocity increment is demonstrated, and the error between them is only 4.21%. Secondly, an example of 7 target satellites with larger orbital parameter deviations is calculated and analyzed. The results show that although the required velocity increment is increased, the rendezvous accuracy is still high. Finally, some comparisons are made to highlight the advantages of the three-step serial optimization method based on the multi-round iterative correction. Compared with the mixed integer optimization method, the proposed method can get similar optimization results, but has the advantage in the computing efficiency. The computing time of the proposed method is merely 16.92% of that of the mixed integer optimization. For the last step correction, the error diffusion of different dynamic models is analyzed, and the advantage of the multi-round iterative correction on the convergence ability is revealed by comparing it with the direct correction method. The relative distance errors at the rendezvous time are less than 1×10^-6 km.

High-precision multi-satellite rendezvous is one of the developing technologies of space missions, but the trajectory design of which has the difficulties in computation burden and convergence. A three-step optimization method with the multi-round iterative correction is proposed. Firstly, the three-step serial optimization method is used to solve the single high-precision rendezvous problem. Secondly, a multi-round iterative model is constructed to update the states of the subsequent target satellites and replan the approximate optimal solution, aiming to eliminate the error diffusion between different dynamic models. Simulation results show that the proposed method can stably obtain the high-precision maneuvering parameters with approximate minimum cost in a few iterations.