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

• Published in: Acta astronautica Vol. 166; pp. 469 - 481
• Main Authors: Li, Haiyang, Chen, Shiyu, Izzo, Dario, Baoyin, Hexi
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.01.2020; Elsevier BV
• Subjects: Algorithms; Low thrust optimization; Machine learning; Mission planning; Multi impulse optimization; Multitarget mission design; Neural network approximators; Neural networks; Particle swarm optimization; Searching; Space missions; Thrust; Training; Trajectory optimization; Low thrust optimization; Multitarget mission design; Multi impulse optimization; Neural network approximators
• ISSN: 0094-5765; 1879-2030
• DOI: 10.1016/j.actaastro.2019.09.023

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 optimal transfer costs to three types of optimization problems: the transfer time of time-optimal low-thrust transfers, the fuel consumption of fuel-optimal low-thrust transfers, and the total Δv of minimum-Δv J2-perturbed multi-impulse transfers. To generate the training data, both considered categories of low-thrust trajectories are optimized using the indirect method, and the J2-perturbed multi-impulse trajectories are optimized using J2 homotopy and particle swarm optimization. The hyper-parameters of deep networks are determined 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 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 the generalization capabilities of the developed deep networks for predicting cases well outside the training data are investigated. Applications in multitarget mission design are also investigated. •The mean relative error for low-thrust transfers is less than 0.5%.•The mean relative error for J2-perturbed multi-impulse transfers is less than 4%.•Deep networks are superior to other algorithms.•Deep networks show an excellent extrapolation capability.•Applications in multitarget mission design are investigated.