Trajectory Optimization Method for Spacecraft Close-range Approach with Low Thrust

In recent years，the rapid increase in the number of on-orbit satellites has made close-proximity operations for on-orbit servicing of space targets a critical phase in spacecraft maneuvering missions. Concurrently，with the swift development of electric propulsion technology，efficient low-thrust maneuvers have gradually become the primary form of current orbital maneuvers. A rapid optimization method for low-thrust approach trajectories based on convex optimization is proposed to address the requirements of close-proximity rendezvous / flyby missions targeting space targets. First，the nonlinear dynamics involved in the close-proximity low-thrust approach process are linearized through model assumptions and parameter approximations. Next，for the second-order equality constraints introduced by thrust vectors，a parameter regularization strategy is implemented to activate constraint boundaries，thereby achieving lossless convexification. Subsequently，to enhance the convergence of the low-thrust trajectory optimization problem，a penalty function term based on terminal constraint relaxation is constructed，improving the robustness of the trajectory optimization algorithm. Finally，numerical simulation results for close-proximity trajectories targeting rendezvous and flyby missions are presented， validating the effectiveness of the proposed method. This approach enables rapid generation of optimal low-thrust approach trajectories and can be applied to online decision-making and open-loop guidance design for future on-orbit servicing of space targets.