Neural-Network-Based Optimal Guidance for Lunar Vertical Landing

This paper addresses an optimal guidance problem concerning the vertical landing of a lunar lander with the objective of minimizing fuel consumption. The vertical landing imposes a final attitude constraint, which is treated as a final control constraint. To handle this constraint, we propose a nonnegative small regularization term to augment the original cost function. This ensures the satisfaction of the final control constraint in accordance with Pontryagin's Minimum Principle. By leveraging the necessary conditions for optimality, we establish a parameterized system that facilitates the generation of numerous optimal trajectories, which contain the nonlinear mapping from the flight state to the optimal guidance command. Subsequently, a neural network trained by the mapping is able to generate the optimal guidance command in milliseconds. Finally, numerical examples are presented to validate the proposed method, showing that the vertical landing can be achieved with the cost of negligible extra fuel consumption.