Trajectory Planning for Formation Reconfiguration near Sun-Earth L2 Libration Point Based on Convex Optimization Method

This paper proposes a trajectory planning method based on convex optimization for spacecraft formation reconfiguration near the Sun-Earth L2 libration points. Firstly, an optimal control problem is formulated with the objective of minimizing fuel consumption, which subjects to constraints including relative dynamics, thrust magnitude, initial and terminal states and collision avoidance. The nonlinear equations of motion are linearized around the periodic nominal orbit in the vicinity of the libration point to obtain a linearized relative dynamics model. Subsequently, the nonconvex terms of the dynamics related to mass are eliminated by initializing and iteratively refining the mass sequence of the spacecraft. As the collision avoidance constraints are nonconvex, the linearized formulation is derived via convexification based on the reference trajectory. Then, to improve convergence, a trust variable is introduced to bound the deviation between the actual and nominal trajectories. The successive convex optimization framework is employed to solve the problem, where the first iteration excludes collision avoidance constraints and its solution is used as the nominal trajectory for subsequent iterations. Finally, these results confirm that the proposed method can efficiently solve the formation reconfiguration problem near libration points, and the convexified optimal control problem is equivalent to the original nonconvex problem.