Rapid longitudinal trajectory planning for RLVs in the terminal area

A rapid longitudinal trajectory planning method has been developed for Reusable Launch Vehicles in the terminal area. It is based on existing research, which utilizes two continuous and smooth quadric curves to describe the reference altitude profile with respect to the ground range. In this study, the range-to-go at joint of these two quadric curves is free to be adjusted. Thus, there's one freedom of design variable for longitudinal trajectory design. A monotonic relation of the reference altitude and the design variable is found and proved theoretically. Consequently, the monotonic relation between the terminal velocity and the design variable is derived. The longitudinal trajectory planning is translated to a one-parameter searching problem, which can be solved easily with a simple Newton iteration scheme. A feasible reference trajectory can be determined in few iteration steps with a proper initial value interpolated from a one dimensional interpolation table, which is pre-established with different values of terminal velocity corresponding to changed design variable. Numerical simulations of tasks with different terminal flight-path angle and velocity constraints are conducted. The results show that reference trajectories, which are planned rapidly, can be tracked with small terminal errors under initial dispersions. It is indicated that the proposed trajectory planning method is feasible and potential for on-line application.