A methodology for sequential low thrust trajectory optimization using prediction models derived from machine learning techniques

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Casey, John Alexander
Mavris, Dimitri N.
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Spacecraft trajectory sequence optimization has been a well-known problem for many years. Difficulty in finding adequate solutions arises from the combinatorial explosion of possible sequences to evaluate, as well as complexity of the underlying physics. Since there typically exists only minuscule amounts of acceptable solutions to the problem, a large search of the solution space must be conducted to find good sequences. Low thrust trajectories are of particular interest in this field due to the significant increase in efficiency that low thrust propulsion methods offer. Unfortunately, in the case of low thrust trajectory problems, calculations of the cost of these trajectories is computationally expensive, so estimates are used to restrict the search space before fully solving the trajectory during the mission planning process. However, these estimates, such as Lambert solvers, have been shown to be poor estimators of low thrust trajectories. Recent work has shown that machine learning regression techniques can be trained to accurately predict fuel consumption for low thrust trajectories between orbits. These prediction models provide an order of magnitude increase in accuracy over Lambert solvers while retaining a fast computational speed. In this work, a methodology is developed for integration of these machine learning techniques into a trajectory sequence optimization technique. First a set of training data composed of low thrust trajectories is produced using a Sims-Flanagan solver. Next, this data is used to train regression and classification models that respectively predict the final mass of a spacecraft after a low thrust transfer and predict the feasibility of a transfer. Two machine learning techniques were used: Gradient boosting and artificial neural networks. These predictors are then integrated into a sequence evaluation evaluation scheme that scores a sequence of targets to visit according to the prediction models. This serves as the objective function of the global optimizer. Finally, this objective function is integrated into a Genetic Algorithm that optimizes sequences of targets to visit. Since the objective function of this algorithm uses predictions to score sequences, the final sequence is evaluated by a Sims-Flanagan low thrust trajectory solver to evaluate the efficacy of the method. Additionally, a comparison is made between the global optimization results with two different objective functions: One based that score sequences using the machine learning predictors, and one that uses Lambert solvers to score sequences. This allows for a measurement of the this method's improvement in the global optimization results. Results of this work demonstrate that the developed methodology provides a significant improvement in the quality of sequences produced by the Genetic Algorithm when paired with the machine learning predictor based objective function. Both gradient boosting and artificial neural networks are shown to be accurate predictors of both the fuel usage and feasibility of low thrust trajectories between orbits. However, gradient boosting is found to offer improved results when evaluating sequences of targets to visit. When paired with the Genetic Algorithm global optimizer, both the gradient boosting prediction model and the artificial neural network model produce similar results. Both are shown to offer a significant improvement over the Lambert solver based objective function while maintaining similar speeds. The positive results this methodology yields lends support to the notion that the use of machine learning techniques has the potential to improve the optimization of sequences of low thrust trajectories. This work lays down a framework that can be applied to preliminary mission planning for space missions outfitted with low thrust propulsion methods. Such missions include, but are not limited to, multiple main-belt asteroid rendezvous, debris removal from Earth orbit, or an interplanetary tour of the solar system.
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