Gauss-Legendre Accelerated Double Iteration Method for Asteroid Landing Trajectory Planning

Asteroid landing trajectory planning remains computationally challenging owing to the irregular gravitational field, the associated complex dynamical environment, and strict terminal accuracy requirements. Although indirect optimal control methods offer high-precision continuous-time solutions, their costate shooting processes typically suffer from high sensitivity, slow convergence, and numerical instability. To address these issues, this study proposes a Gauss-Legendre accelerated double iteration method that unifies a semi-analytical initial costate formulation, efficient multifold Gauss-Legendre integral evaluation, and a Jacobian guided homotopy continuation strategy within one indirect solution framework. The main contributions are threefold: (i) a semi analytical expression for the initial costate is derived, enabling effi cient iterative updates within the indirect framework; (ii) multifold Gauss-Legendre integration is incorporated into the initial costate update process to efficiently evaluate the high-order integral terms arising in each iteration step; and (iii) a Jacobian-based convergence criterion with adaptive homotopy step size adjustment is developed to ensure stable and theoretically predictable convergence. Simulation experiments on asteroid 433 Eros demonstrate that the proposed method reduces computation time by approximately 67.5% compared to traditional shooting methods while achieving robust trajectory re-planning capabilities under significant task mismatches. These features make the method potentially suitable for future onboard applications.