## 1 Introduction
converted the guidance problem of the re-entry glide vehicle to the energy domain, reduced the non-convexity of the equation, and solved it with the pseudo-spectral method. [PERSON] [14] et al. realized the conversion of the guidance problem of the vehicle to the altitude domain and also realized the practical re-entry guidance. From the above methods, it can be seen that changing the described domain of dynamic equations may realize effective convexity and convergence. At the same time, the operation of the variable trust region is also worded to increase the convergence accuracy of the generated trajectory. For the grid point adjustment method of re-entry trajectory generation, the Gaussian and Radau pseudo-spectral method are proven to be effective [23]. The hp pseudo-spectral method is used to select the root of the orthogonal polynomial as the grid points [24], which can be dynamically adjusted with iteration. [PERSON] [25] et al. proposed a multi-segment grid point modified Radau pseudo-spectral method to realize the generation and fast convergence of convex optimized trajectory. However, the pseudo-spectral method is better for linear problems and convex constraints and is not fully applicable to sequential planning problems. In addition to the pseudo-spectral method, some adaptive grid points adjustment methods are also proposed. [PERSON] [26] et al. proposed an adaptive grid point adjustment method, which solved the problem of Mars re-entry trajectory optimization by analyzing iteration errors to realize insertion and deletion points. [PERSON] [27] put forward the concept of nonlinear illegal degree and used the error threshold to be the insertion and deletion rules of grid points, thus realizing the dynamic adjustment of grid points. The concept of nonlinear illegal degree proposed by the above methods has an excellent guidingsignificance for grid point adjustment, but the grid point adjustment method is fixed, and the increase or decrease may be significantly affected by the convergence process. To solve the problem that the description of re-entry trajectory generation in the time domain is not direct enough, the initial trajectory of iteration affects the convergence speed, and the grid point adjustment mode is fixed, a new convex optimized trajectory generation with the flight range domain and distributed grid points adjustment are proposed in this paper. Firstly, based on the definition of range-to-go, the concept of projected range-to-go is proposed, by which the dynamic model of the vehicle is transformed to the flight range domain for representation. At the same time, the states of the vehicle are expanded, and the dynamic model and constraints of the glider are convex and discrete. Then, the re-entry trajectory generation problem is transformed into a sequential programming problem. In order to improve the solving speed, the initial trajectory that basically meets the guidance requirements is obtained through transformation and interpolation according to the landing points of the vehicle under different constant control laws. In order to further improve the trajectory generation accuracy and speed up the trajectory convergence, a grid points probability density function is proposed according to the nonlinear illegal degree of the iterative trajectory, which is used to change the rules of generating new grid points and adjust the location of grid points. Through ablation experiments, the effectiveness of the improved part is proved. Additionally, by changing the initial and terminal positions and conducting Monte Carlo experiments, the robustness of our method is verified. The generation errors of our method are less than 1 km. Finally, through comparison with other mainstream methods, we prove the superiority of our method in search speed and accuracy. The innovation of this paper mainly includes the following three parts:  
1. According to the concept of range-to-go in the guidance of re-entry glide vehicles, the projected range-to-go is proposed.