Abstract: To solve the problem of vertical return landing of reusable rocket, an adaptive fuel optimal powered descent initiation(PDI) approach is proposed. Firstly, two analytical forms are used to describe the profiles of the thrust and the angle of attack for the fuel optimal powered descent trajectory of the fuel optimal PDI state. In these forms, the angle of attack profile is determined by the current state, the thrust profile only depends on one unknown variable. Secondly, the PDI state is determined by predicting the powered descent trajectory with the above analytical profiles. The terminal position constraint is relaxed to solve the unknown variable of the thrust profile. The predicted trajectory meets the terminal position constraint means that the current state is close to the fuel optimal PDI state. The above strategy simplifies the problem of determining the fuel optimal PDI state into the problem of solving the single unknown variable, so as to solve the problem quickly. Finally, numerical simulations demonstrate the proposed approach is numerically stable and efficient, and achieves comparable fuel efficiency with numerical optimization approaches.

Key words: Reusable rocket, Return guidance, Fuel optimal, Adaptive powered descent initiation