Embry-Riddle Professor Earns Prestigious NSF Grant to Study Chaotic Motion in Space

Research that could greatly improve space mission design efficiency and trajectory planning just got a boost from the National Science Foundation — in the form of a $200,000 Engineering Research Initiative (ERI) grant to Dr. David Canales of Embry-Riddle Aeronautical University.

Canales, assistant professor in the Department of Aerospace Engineering, is focusing on how to efficiently enhance engineering design of chaotic systems, in particular the motion of spacecraft in the cislunar region, where gravitational forces from both the Earth and Moon influence the spacecraft.

“Just as understanding ocean currents improves navigation, deciphering space’s energy landscape could significantly enhance fuel efficiency and trajectory predictions,” Canales said.

Seur Gi Jo, a Ph.D. student in Canales’ Space Trajectories and Applications Research (STAR) lab, said, “Trajectories in the cislunar region exhibit chaotic behavior because both Earth’s and the moon’s gravities act together, meaning that even small errors or perturbations in position or velocity can lead to completely different trajectories.”

Current trajectory analysis and design methods typically rely on two-dimensional mapping to represent spacecraft motion. In reality, however, the problem is inherently six-dimensional; three dimensions describing position and three dimensions describing velocity. Developing methods that can account for multiple dimensions simultaneously, rather than comparing across separate two-dimensional maps, would enable a far more efficient and integrated approach to trajectory design.

“Imagine trying to describe where a car is when it’s moving. You need both its location and its speed and direction,” Canales said. To analyze a spacecraft’s trajectory, “we need to consider all six dimensions together, not just a simplified 2D picture.”

The research requires extensive computational power and highly sophisticated visual tools.

Canales’ research will use augmented reality “to let engineers step inside” higher-dimensional maps of possible spacecraft motion, so “instead of flipping through many 2D plots, you could see 3D bubbles, or tubes, of possible spacecraft motion and even interact with them in real time,” he said.

Jo said the researchers are exploring augmented reality “to make these visualizations more intuitive.”

The research also calls on a type of AI known as reinforcement learning, in which the AI attempts different solutions and is given feedback on them. “It’s like training a dog with rewards,” Canales said. To speed the the reinforcement learning, it will transform lessons from one problem to another, accept guidance from the researchers during the learning process and draw on a branch of mathematics called “knot theory,” which studies patterns in how loops can be twisted and linked.

Chaotic motion in space can “look like tangled loops,” Canales said, and classifying chaotic paths as different kinds of loops provides a structural map for the AI to follow, rather than guessing randomly.

“The hypothesis for this research is that synthesizing higher-dimensional data, visualization with knot theory-informed learning will greatly improve our ability to analyze, predict and design within chaotic regimes,” Canales said.