Impulsive maneuver optimization for small body landing using irregular gravitational field model homotopy

The weak and irregular gravitational fields of small bodies complicate the impulsive maneuver optimization during probe landing, where velocity optimization at the deorbit point is crucial. The analytical gravitational field model offers low computational cost but limited accuracy, causing significant landing errors. In contrast, the high-precision polyhedral model is computationally intensive and highly nonlinear, slowing convergence in traditional impulsive maneuver optimization methods. This paper proposes an impulsive maneuver optimization method using irregular gravitational field model homotopy, enhancing computational efficiency while ensuring solution accuracy. By introducing a homotopic parameter, a smooth transition path is constructed from the deorbit velocity optimization problem under the analytical model to that under the polyhedral model, avoiding the direct solution of highly nonlinear problems. The Newton shooting method is employed to solve suboptimization problems across different homotopic parameters, enabling a dynamic transition of optimization results from the analytical to the polyhedral model. Under ideal conditions, the probe achieves the dual-impulse maneuver to reach the target landing point. For missions with uncertainties and disturbances, a multi-impulse LQR maneuver method is introduced to enable rapid trajectory corrections with low fuel consumption and strong robustness. Finally, numerical simulations on 433 Eros validate the effectiveness of the proposed algorithm.