# Robust Near-Optimal Aerocapture Guidance Method Based on Saturation Function
## 1 Introduction
[18] proposed an improved bank angle control law for the exit phase in Mars and Titan aerocapture. Through feedback linearization, the gain that is difficult to solve analytically and needs to change with mission parameters is eliminated. The improved guidance algorithm performs well in the limited test of the Mars mission. However, for Titan's aerocapture mission, which lacks a more accurate atmospheric model, severe atmospheric changes still bring problems to the algorithm. [PERSON] et al. [19] adopted two measures to improve the APC algorithm's robustness. The first is to add an energy controller in the capture and exit phases so that the switch between phases has a certain adaptability. Second, collect atmospheric density data in the capture phase to redefine the density scale height, and apply it to the exit phase. The improved algorithm can increase the width of the corridor and improve adaptability. However, when spacecraft need to fly a wide range, there may be a large deviation of atmosphere between the capture phase and the exit phase. Based on the segmented variable ballistic coefficient, [PERSON] et al. [20] proposed an analytical predictive guidance algorithm for single ballistic coefficient switching. The terminal velocity after ballistic coefficient switching can be obtained in real time through analytical calculation, and the adaptive control of the ballistic coefficient switching time is realized at the same time. [PERSON] [21] improved the [PERSON] numerical predictor-corrector guidance method (PredGuid) [22] by adding an energy controller in the gliding phase so that the algorithm can adapt to high-energy trajectory. [PERSON] et al. [23] varied the ballistic coefficient by changing the spacecraft reference area to modulate the trajectory using the NPC guidance method. [PERSON] et al. [24; 25; 26] proposed an NPC guidance algorithm FNPAG (full numerical predictor-corrector aerocapture guidance) based on the research of aerocapture optimal control theory (the bank angle control profile required to minimize the velocity increment of orbit correction has a bang-bang structure) [27; 28; 29]. The whole process consists of two phases. In phase 1, the control profile is stepped, that is, the spacecraft is assumed to first fly at the specified minimum bank angle, then switch to the relatively large bank angle. Once the current time reaches the switching time, start phase 2, in which the bank angle is set to a constant value. [PERSON] [30; 31] applied FNPAG to three different spacecrafts and obtained good results. Based on [PERSON]'s research, [PERSON] et al. [8] proposed a new APC guidance method. In the descending phase, guidance is open-loop, simultaneously, atmospheric parameters are measured and fitted by a third-order Fourier series so that the comprehensive effects of atmospheric density, aerodynamic coefficients, and spacecraft mass can be parameterized. Then in the ascending phase, closed-loop guidance is started. The analytical functions of atmospheric density and flight path angle are used to predict the velocity at atmospheric exit, so the target apogee altitude can be tracked. In the Earth aerocapture scenario, this APC guidance method's performance is very similar to the FNPAG algorithm. However, the advanced guidance methods mentioned above have the same shortcoming. That is, their performances are greatly affected by the selection of switching time from open-loop to closed-loop guidance, which degrades the methods' robustness, especially under significant uncertainties and disturbances. Moreover, the guidance process in literature [8] requires a lot of prior information, resulting in weak adaptability of the algorithm.