The gravity assist (GA) plays an important role in space missions since itwas first applied by the Luna 3 vehicle in 1959. For preliminary trajectory design, the so-called patchedconics model provides a simple model for a gravity assist. This approach, based on twobody formulations, splits amulti-body probleminto a succession of two-body problems. This model has a fundamental assumption: the trajectory of the spacecraft is driven by one celestial body only. A boundary for switching the driving bodies is defined by the Sphere of Influence (SoI) of the GA body. The patched conics model cannot be used to study low-energy trajectories. Moreover, it fails to describe special dynamics existing in the multi-body regime, such as the invariant manifolds. The three-body formulation is a logical choice to study the dynamics in the multi-body problem. In order to reduce its inherent difficulty, the circular restricted three-body problem (CR3BP) formulation is developed to study the behavior of the motion of a particle influenced by two massive bodies simultaneously. Flybys in the CR3BP have been studied by many researchers, using a numerical or semi-analytical approach, e.g. the Flyby map (FM) and Keplerianmap (KM), respectively. Inspired by these approaches and the idea of artificial intelligence, this thesis focuses on the investigation of flybys froma machine-learning perspective. @en

In this work, we propose a new method to approximate the cost function of Low-Thrust, Multiple-Gravity-Assist interplanetary trajectories using a Machine Learning surrogate. We identified the computation time required to obtain training data as the main limitation when using Machine Learning methods for this purpose so we present a strategy to build the surrogate with limited training data. We built an Online-Sequential Extreme Learning Machine Multi-Agent System (OS-ELM-MAS) surrogate due to its theoretical good performance when the training data is limited. In addition, we define a method to include the surrogate during the optimization process that can be used with any gradient-free algorithm, and study the effect of several surrogate parameters on the optimization results. Finally, several interplanetary trajectories are optimized with and without the surrogate. Employing the surrogate results in up to 12% lower fuel cost values after a fixed optimization time. The parameters that control the interaction have to be carefully selected to achieve this improvement, and we show that the optimal value of these parameters can be narrowed down based on the characteristics of the transfers. @en

Inspired by the Keplerian Map and the Flyby Map, a Gravity Assist Mapping using Gaussian Process Regression for the fully spatial Circular Restricted Three-Body Problem is developed. A mapping function for quantifying the flyby effects over one orbital period is defined. The Gaussian Process Regression model is established by proper mean and covariance functions. The model learns the dynamics of flyby's from training samples, which are generated by numerical propagation. To improve the efficiency of this method, a new criterion is proposed to determine the optimal size of the training dataset. We discuss its robustness to show the quality of practical usage. The influence of different input elements on the flyby effects is studied. The accuracy and efficiency of the proposed model have been investigated for different energy levels, ranging from representative high- to low-energy cases. It shows improvements over the Kick Map, an independent semi-analytical method available in literature. The accuracy and efficiency of predicting the variation of the semi-major axis are improved by factors of 3.3, and 1.27×10⁴, respectively.

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We develop a Gravity Assist Mapping to quantify the effects of a flyby in a two-dimensional circular restricted three-body situation based on Gaussian Process Regression (GPR). This work is inspired by the Keplerian Map and Flyby Map. The flyby is allowed to occur anywhere above 300 km altitude at the Earth in the system of Sun-(Earth+Moon)-spacecraft, whereas the Keplerian map is typically restricted to the cases outside the Hill sphere only. The performance of the GPR model and the influence of training samples (number and distribution) on the quality of the prediction of post-flyby orbital states are investigated. The information provided by this training set is used to optimize the hyper-parameters in the GPR model. The trained model can make predictions of the post-flyby state of an object with an arbitrary initial condition and is demonstrated to be efficient and accurate when evaluated against the results of numerical integration. The method can be attractive for space mission design.

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Low-thrust trajectories can benefit the search for propellant-optimal trajectories, but increases in modeling complexity and computational load remain a challenge for efficient mission design and optimization. In this paper, an approach for developing models utilizing Gaussian Process (GP) regression and classification is proposed to perform computationally efficient optimization while obtaining acceptable accuracies for trajectories based on exponential sinusoid shaping. The goal of this work is to predict a combination of values of input variables which corresponds to a shape-based trajectory with the smallest total velocity increment (ΔV) or propellant mass fraction (J _m). A GP classification model is constructed to assess whether a given combination of values of input variables corresponds to a feasible trajectory. GP regression models are developed to predict the total ΔV and J _m corresponding to a combination of shape parameters, which can replace the required integration along the shape. In addition, advanced regression models are developed to predict the target values while requiring only three input parameters, thereby replacing the entire shape computation. In order to develop a GP model that fits the problem at hand, the underlying functions and parameters should be selected rationally. In this work, a novel model development approach is proposed to ensure that the mean function, covariance function, likelihood function, inference method, and hyperparameters, which dominate the performance of the models, are chosen rationally in terms of mean absolute percentage error (MAPE) and prediction time. Using this approach, GP models are developed and tested on transfer trajectories from Earth to Mars and Ceres, and from Mars to Earth, and their performance, in terms of MAPE and prediction time, is compared to that of more common optimization techniques in combination with the exponential sinusoid and other shape-based methods. The results demonstrate that the computation time can significantly be reduced while achieving promising MAPE’s, especially when the goal is to locate regions of feasible or near-optimal trajectories. The proposed model development procedure is tested for robustness, which provides confidence in the proposed approach. Furthermore, it is found that the models which map three input variables directly to a ΔV or J _m value perform better than the ones trained with shape information, which demonstrates the strength of GP models as applied to low-thrust trajectory optimization.

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