Nonlinear receding horizon guidance for spacecraft formation reconfiguration on libration point orbits using a symplectic numerical method.

This paper studies a nonlinear receding horizon control guidance strategy for spacecraft formation reconfiguration on libration orbits in the Sun-Earth system. For comparison, a linear quadratic soft terminal control strategy is also considered for the same reconfiguration missions. A novel symplectic iterative numerical algorithm is proposed to obtain the optimal solution for the nonlinear receding horizon control strategy at each update instant. With the aid of the quasilinearization method, a high-efficiency structure-preserving symplectic method is introduced in the iterations, and the optimal control problem is replaced successfully by a series of sparse symmetrical linear equations. Several typical spacecraft formation reconfiguration missions including resizing, rotating and slewing reconfigurations and their combinations are numerically simulated to show the effectiveness of the nonlinear receding horizon guidance strategy based on the proposed symplectic algorithm. Through these simulations, the nonlinear receding horizon control strategy is shown to have obvious advantages in convergence and parameter sensitivity compared with a linear quadratic soft terminal control strategy. Monte Carlo stochastic simulations are used to test the robustness of the nonlinear receding horizon control guidance in dealing with measurement and execution errors.