This paper demonstrates how artificial neural networks can be used to alleviate common problems encountered when creating a large database of Poincaré map responses. A general architecture is developed using a combination of regression and classification feedforward neural networks. This allows one to predict the response of the Poincaré map, as well as to identify anomalies, such as impact or escape. Furthermore, this paper demonstrates how an artificial neural network can be used to predict the error between a more complex and a simpler dynamical system. As an example application, the developed architecture is implemented on the Sun-Mars eccentric Hill system. Error statistics of the entire architecture are computed for both one Poincaré map and for iterated maps. The neural networks are then applied to study the long-term impact and escape stability of trajectories in this system.
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This research has been performed through funding provided by Advanced Space. This work utilized the RMACC Summit supercomputer, which is supported by the National Science Foundation (awards ACI-1532235 and ACI-1532236), the University of Colorado Boulder, and Colorado State University. The Summit supercomputer is a joint effort of the University of Colorado Boulder and Colorado State University.
Stijn De Smet is a researcher in astrodynamics. Dr. De Smet began his professional career at Delft University of Technology where he studied from 2009 to 2014, graduating with B.S. and M.S. degrees in aerospace engineering. In 2015, he started the doctoral program in aerospace engineering at the University of Colorado at Boulder, under Jeffrey S. Parker. In 2016, he joined the Celestial and Spaceflight Mechanics Laboratory, led by Daniel J. Scheeres, from which he graduated with a Ph.D. degree in 2018. His research focuses on low thrust trajectory design and on astrodynamics in challenging dynamical environments using machine learning techniques.
Daniel J. Scheeres is a University of Colorado Distinguished Professor and is the A. Richard Seebass Endowed Chair Professor in the Ann and H.J. Smead Department of Aerospace Engineering Sciences at the University of Colorado Boulder. Prior to this he held faculty positions in aerospace engineering at the University of Michigan and Iowa State University, and was a senior member of the Technical Staff in the Navigation Systems Section at the California Institute of Technologys Jet Propulsion Laboratory. He was awarded Ph.D. (1992), M.S. (1988) and B.S. (1987) degrees in aerospace engineering from the University of Michigan, and holds a B.S. in Letters and Engineering from Calvin College (1985). Scheeres is a member of the National Academy of Engineering, and a Fellow of both the American Institute of Aeronautics and Astronautics and the American Astronautical Society. He was awarded the Dirk Brouwer Award from the American Astronautical Society in 2013 and gave the John Breakwell Lecture at the 2011 International Astronautical Congress. Asteroid 8887 is named Scheeres in recognition of his contributions to the scientific understanding of the dynamical environment about asteroids.
Jefrey S. Parker is the chief technology officer at Advanced Space, a GNC service-providing company in Boulder, Colorado. He is the lead mission designer on a Mars mission and the PI on several GNC-related SBIR programs. Previously, from 2012 to 2016, he was an assistant professor of astrodynamics at the University of Colorado at Boulder, where he studied advanced concepts in mission design and navigation. From 2008 to 2012, Dr. Parker spent five years at the Jet Propulsion Laboratory, where he helped to navigate missions such as GRAIL and Chandrayaan to the Moon.
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De Smet, S., Scheeres, D.J. & Parker, J.S. Representing dynamics in the eccentric Hill system using a neural network architecture. Astrodyn 3, 301–324 (2019). https://doi.org/10.1007/s42064-019-0050-4
- Poincaré map
- artificial neural networks
- eccentric Hill system