Deep networks as approximators of optimal low-thrust and multi-impulse cost in multitarget missions

Abstract

In the design of multitarget interplanetary missions, there are always many options available, making it often impractical to optimize in detail each transfer trajectory in a preliminary search phase. Fast and accurate estimation methods for optimal transfers are thus of great value. In this paper, deep feed-forward neural networks are employed to estimate solutions to three types of optimization problems: the transfer time of time-optimal low-thrust transfers, fuel consumption of fuel-optimal low-thrust transfers, and the total ∆v of minimum-∆v J 2 -perturbed multi-impulse transfers. To generate the training data, low-thrust trajectories are optimized using the indirect method and J 2 -perturbed multi-impulse trajectories are optimized using J 2 homotopy and particle swarm optimization. The hyper-parameters of our deep networks are searched by grid search, random search, and the tree-structured Parzen estimators approach. Results show that deep networks are capable of estimating the final mass or time of optimal transfers with extremely high accuracy; resulting into a mean relative error of less than 0.5% for low-thrust transfers and less than 4% for multi-impulse transfers. Our results are also compared with other off-the-shelf machine-learning algorithms and investigated with respect to their capability of predicting cases well outside of the training data. Nomenclature a = semi-major axis e = eccentricity i = inclination Ω = right ascension of ascending node * PhD Candidate, School of Aerospace Engineering, lihy15@mails.tsinghua.edu.cn. † Graduate Student, School of Aerospace Engineering, chen-sy16@mails.tsinghua.edu.cn.

Neural Networks in Time-Optimal Low-Thrust Interplanetary Transfers

“…Random search [37] is applied in this paper to find hyperparameters [26]. The hyper-parameters that must be defined are: number of layers (n layer ), number of neurons at each hidden layer (n neuron ), activation function (f ), initial learning rate (η), optimizer (opt), batch size (B), weights initializer (ini), decay model (dm), decay step (ds), and decay rate (c).…”

“…In astrodynamics applications, NNs are trained mainly as predictors and optimal controllers. As predictors, NNs are trained to learn the optimal time and fuel of low-thrust transfers [26]- [28]. As controllers, NNs are trained to learn the optimal state-control pairs [29]- [32] or image-control relations [33].…”

PSO-Based Soft Lunar Landing with Hazard Avoidance: Analysis and Experimentation

“…In this case, deep neural networks have been employed to compute the solution. The same technique has been used to solve optimal low-thrust multi-target interplanetary missions [37]. Moreover, the combination of machine learning and metaheuristic algorithms is exploited in [38], where offline optimization is first carried out and then Evolutionary Genetic Algorithm and general regression neural networks, together with learning algorithms, are used for online execution to achieve real-time optimal missile guidance.…”

Fast Solver for J2-Perturbed Lambert Problem Using Deep Neural Network

“…Sánchez-Sánchez and Izzo [19] used DNNs to achieve online real-time optimal control for precise landing. Li et al [16] used DNN to estimate the parameters of low-thrust and multi-impulse trajectories in multi-target missions. Zhu and Luo [20] proposed a rapid assessment approach of low-thrust transfer trajectory using a classification multilayer perception and a regression multilayer perception.…”