Semi-analytic approximate time-optimal asteroid landing with dimensionality reduction shooting

Pinpoint landing on asteroid is very challenging due to the uncertainties of the gravitational field, which highlights the urgent need for autonomous landing algorithms under such uncertainties. Some well-known guidance algorithms, such as APDG and real-time convex programming, either ignore thrust boundary constraints or are severely time consuming. In addition, these algorithms have the same difficulty in analyzing landing errors due to model uncertainty propagation, making the reliability of the algorithms in actual landings questionable. To address these challenges, we propose a landing framework that combines model identification, trajectory analytical solution and closed-loop corrections to achieve near-optimal real-time landing control. Firstly, we simplified the landing scenario, focusing on reducing the dimension of shooting variables to enable rapid trajectory calculation. Secondly, we derived error propagation equations and established criteria for trajectory replanning based on landing error prediction. Finally, we validated our approach with practical examples of the Shoemaker probe landing on Eros 433. Through real-time landing error estimation, our proposed framework enables spacecraft to achieve near time-optimal land within a given error threshold.