# Robust Near-Optimal Aerocapture Guidance Method Based on Saturation Function
## 1 Introduction  
Aerocapture maneuvers make full use of the target planet's atmospheric resources (mainly atmospheric drag) to reduce the spacecraft's speed, and achieve the transfer from a hyperbolic orbit to an elliptical orbit through a single atmospheric crossing. Compared to orbit maneuvers that use only thrusters, aerocapture can save a lot of fuel, in return the spacecraft can carry more payloads to complete more scientific exploration missions. Since the concept of aerodynamic was invented, much research [1; 2; 3; 4; 5; 6; 7] has been done to analyze and prove its feasibility and advantages in interplanetary flight and deep space exploration. Unlike aerobraking, which needs to pass through the atmosphere many times, aerocapture can greatly shorten the orbital transfer time, on the other hand the spacecraft needs to bear higher peak heat flow and the process is more dangerous. In addition, there're significant uncertainties and disturbances involved in aerocapture maneuvers (i.e., variations in the atmospheric environment, aerodynamic coefficients, etc. ), so a robust, reliable, and accurate guidance scheme is very necessary. At present, mainly two kinds of technologies have been developed in aerocapture guidance: trajectory tracking guidance and predictor-corrector guidance. The trajectory tracking guidance, also named implicit guidance, attempts to track the preset reference trajectory [8]. [PERSON] [9] proposed an early Mars aerocapture tracking guidance method in 1993, which tracks the energy of the reference trajectory by adjusting the spacecraft's pitch attitude. For the Mars 2001 mission, [PERSON] et al. [10] developed a guidance algorithm based on the terminal-point controller (TPC). During aerocapture, the cosine of the bank angle is selected as the control variable to ensure that the spacecraft can fly near the predetermined optimal trajectory; finally, a suboptimal trajectory can be obtained. [PERSON] and [PERSON] [11] changed the independent variable from time to specific mechanical energy, and tracked reference trajectory's state space with variable structure control. This method does not need density estimation and can enhance thestability of guidance for specific tasks, but it has a great dependence on the nominal trajectory. If the actual environment changes greatly, the trajectory cannot be properly corrected and adjusted using this method, which will produce great errors. To enhance the robustness of the guidance, [PERSON] [12] proposed a time-varying control method based on TPC, which controls the angle of attack and bank angle at the same time. The optimality obtained by the two-parameter time-varying control is found to be the same as that of the single-variable optimal control. The disadvantage is that the dynamic model used in [12] does not consider gravitational perturbation and the rotation of the atmosphere, so the guidance accuracy cannot be guaranteed. [PERSON] [13] and [PERSON] [14] applied the convex programming method to optimize the Mars aerocapture guidance. This method has the potential for real-time execution, but its effectiveness needs to be further verified. [PERSON] et al. [15] implemented a novel integral sliding surface to avoid singularity, and the neural network is adopted to compensate for the lumped uncertain term, so the proposed tracking guidance law is robust against uncertainties. The predictor-corrector guidance, also known as explicit guidance, repeatedly searches for the optimal or near-optimal path from the current state to the target state [8]. According to different ways of predicting terminal states, it can be divided into analytical predictor-corrector (APC) guidance and numerical predictor-corrector (NPC) guidance. [PERSON] et al. [16] discussed and tested two APC guidance methods, also known as the hybrid predictor-corrector aerocapture scheme (HYPAS), for aerocapture in Mars sampling return mission. Both algorithms are derived from the algorithm in the aerocapture flight test (AFE) [17]. Based on HYPAS, [PERSON] et al.