Abstract: The hopping detection is a novel form of extraterrestrial body exploration mission, which is a combination of ascent missions and landing missions. The study of control methods that combine the entire process of hopping trajectory optimization and real-time performance is of great significance. In terms of nominal trajectory optimization, unlike traditional segmented optimization methods, a trajectory design method that combines analytical and partial differential approaches is proposed from the perspective of optimizing the entire hopping process. In terms of real-time trajectory control, based on the prediction-correction method, the Jacobian matrix is applied to ensure the achievement of terminal conditions by comprehensively correcting trajectory parameters and thrust directions. The calculation formulas for the Jacobian matrix used in real-time trajectory control are all explicit and analytical, and simulations show that only two iterations are enough to meet control requirements, proving that the algorithm proposed has high real-time performance. With the same simulation conditions, compared with the offline whole-process convex optimization results, the consumed fuel difference between the two methods is only 20g, indicating that its fuel optimization performance is relatively similar to the convex optimization one. This method can be applied to the whole-process thrust hopping trajectory optimization with constant thrust and real-time trajectory control, ensuring the whole-process optimality and real-time control performance.

Key words: hopping detection;trajectory design, analytical control, deep space probe