The Zero Initial Guess Algorithm for Low-Thrust Trajectory Optimization with Its Application in Cislunar Space

In this paper, a trajectory optimization method without an initial value guess is proposed. The method employs the Lagrange multipliers from the nonlinear programming process to estimate the costate of the optimal control problem. It utilizes a homotopic process to address the minimum-fuel problem. The estimated costate serves as a useful initial guess for the indirect shooting method, mitigating the initial value sensitivity. The sequential quadratic programming process used in the shooting process avoids the non-optimal results of the direct method. The minimum-time and minimum-fuel low-thrust rendezvous problems on cislunar L1-vicinity, L2-vicinity, and L2-south near rectilinear halo orbits are solved in this paper. The numerical results demonstrate that using low-thrust propulsion can reduce fuel consumption by 42.36% to 84.62% compared with traditional two-impulse maneuvers in the circular restricted three-body rendezvous problem.