Leveraging Artificial Neural Networks to Systematically Explore Solar Gravity Driven Transfers in the Martian System

Current solar electric propulsion and launch vehicle technology allow sending multiple spacecraft to Mars simultaneously. For capture orbits with very high apoareion, the solar gravity perturbations deploy the spacecraft in vastly different areocentric orbits. This application requires knowledge of possible transfers and an efficient way to identify them; for example, a well-defined and easily accessed database of solutions. First, a method is developed to identify the required initial orbital elements and timing to target a final orbit, for a dynamical model ignoring the Martian eccentricity. This method can be applied to any planetary system with low heliocentric eccentricity. Second, the effect of Mars’ eccentricity and the corresponding time-dependence of solar distance are analyzed. This analysis requires a much larger number of numerical integrations. The research is therefore limited to placing bounds on the solution space. Third, this paper determines the way artificial neural networks can reduce the large number of required integrations by order(s) of magnitude while maintaining sufficient accuracy to enable preliminary transfer design. The neural networks enable the design of transfers between a low, near-polar orbit to Phobos and Deimos in an approximation of the eccentric model. These transfers are then validated in a higher fidelity ephemeris model.

[1]  D. Scheeres,et al.  New Class of Optimal Plane Change Maneuvers , 2003 .

[2]  B. Villac.  Dynamics in the Hill problem with applications to spacecraft maneuvers , 2003 .

[3]  Shane D. Ross,et al.  Low Energy Transfer to the Moon , 2001 .

[4]  Terrence L. Fine,et al.  Feedforward Neural Network Methodology , 1999, Information Science and Statistics.

[5]  Kenneth Levenberg.  A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[6]  Aggelos Chariatis.  Very Fast Online Learning of Highly Non Linear Problems , 2007, J. Mach. Learn. Res..

[7]  Ronald Davis,et al.  Neural networks and deep learning , 2017 .

[8]  Daniel J. Scheeres,et al.  Dynamics and Stability of Sun-Driven Transfers from Low Earth to Geosynchronous Orbit , 2018 .

[9]  Christopher T. Russell,et al.  The Dawn Mission to Vesta and Ceres , 2011 .

[10]  Amanpreet Singh,et al.  A review of supervised machine learning algorithms , 2016, 2016 3rd International Conference on Computing for Sustainable Global Development (INDIACom).

[11]  Rodney L. Anderson,et al.  Low-Energy Lunar Trajectory Design: Parker/Low-Energy , 2014 .

[12]  L. L. Rogers,et al.  Optimization of groundwater remediation using artificial neural networks with parallel solute transport modeling , 1994 .

[13]  Johannes Benkhoff,et al.  BepiColombo—Comprehensive exploration of Mercury: Mission overview and science goals , 2010 .

[14]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[15]  Third-Body-Driven vs. One-Impulse Plane Changes , 2009 .

[16]  Dario Izzo,et al.  Machine Learning of Optimal Low-Thrust Transfers Between Near-Earth Objects , 2017, HAIS.

[17]  Jules Simo,et al.  Neural-based trajectory shaping approach for terminal planetary pinpoint guidance , 2013 .

[18]  Hecht-Nielsen.  Theory of the backpropagation neural network , 1989 .

[19]  David Haussler,et al.  What Size Net Gives Valid Generalization? , 1989, Neural Computation.

[20]  Hiroki Matsuo,et al.  Japanese first double lunar swingby mission “Hiten” , 1991 .

[21]  M. J. Walker.  A set of modified equinoctial orbit elements , 1985 .

[22]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[23]  Klaus-Robert Müller,et al.  Efficient BackProp , 2012, Neural Networks: Tricks of the Trade.

[24]  山川 宏,et al.  On earth-moon transfer trajectory with gravitational capture , 1993 .

[25]  Shun-ichi Amari,et al.  Network information criterion-determining the number of hidden units for an artificial neural network model , 1994, IEEE Trans. Neural Networks.

[26]  Rich Caruana,et al.  Multitask Learning , 1997, Machine Learning.

[27]  Roberto Furfaro,et al.  Waypoint-Based generalized ZEM/ZEV feedback guidance for planetary landing via a reinforcement learning approach , 2017 .

[28]  J. Kawaguchi,et al.  The Rubble-Pile Asteroid Itokawa as Observed by Hayabusa , 2006, Science.

[29]  Kuldip K. Paliwal,et al.  Bidirectional recurrent neural networks , 1997, IEEE Trans. Signal Process..

[30]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[31]  Stacia M. Long,et al.  Trans-Lunar Cruise Trajectory Design of GRAIL (Gravity Recovery and Interior Laboratory) Mission , 2010 .

[32]  Holger R. Maier,et al.  The effect of internal parameters and geometry on the performance of back-propagation neural networks: an empirical study , 1998 .

[33]  Y. Tsuda,et al.  System design of the Hayabusa 2—Asteroid sample return mission to 1999 JU3 , 2013 .

[34]  Holger R. Maier,et al.  Neural networks for the prediction and forecasting of water resource variables: a review of modelling issues and applications , 2000, Environ. Model. Softw..

[35]  Daniel J. Scheeres,et al.  Spacecraft dynamics in the vicinity of a comet , 2008 .