Fast solution continuation of time-optimal asteroid landing trajectories using deep neural networks

To improve the autonomy and reliability of asteroid landing control, a fast solution continuation approach for time-optimal asteroid landing trajectories is presented in this study. The contributions of this study are threefold. First, a deep neural network (DNN) is developed to approximate the gravitational field of asteroids, and the corresponding time consumption of gravity calculation in trajectory propagation is significantly reduced. Second, the original 3-dimensional (3D) landing control problem is connected to a simplified 2D one according to the continuation relationship between these model dynamics. Third, the 2D control problem is further transformed into a multi-variable root-finding problem with analytical shooting equations with the help of a Gauss-Legendre integral method and could be quickly solved by shooting methods. Taking the solution of this root-finding problem as an initial guess, the accurate solution of the original time-optimal landing problem can be quickly obtained through a backward solution continuation process. Finally, numerical simulations of landings on 443 Eros are given to verify the effectiveness of the proposed techniques and thus to illustrate the excellent performance on rapidity, convergence and solution accuracy of the developed algorithm for the generation of time-optimal landing trajectories.