On the Fusion of Invariant Manifolds, Orthogonal Approximation and Optimal Control: For Cis-Lunar Fun and Profit!
Dec. 1, 2022
4:00 PM
Mulva Auditorium, EER 0.904

Reception to follow.

This is a hybrid event. Attend in person on the UT Austin campus or virtually via Zoom: https://utexas.zoom.us/j/91012361073
F  E  A  T  U  R  I  N  G
photo of John L. Junkins
John L. Junkins
Distinguished Professor of Aerospace Engineering
and Founding Director, Hagler Institute for Advanced Study
Texas A&M University


Motivated by a renewed interest in cis-lunar space vehicle operations and other Lunar missions, we consider how to make judicious use of the invariant manifolds associated with the periodic orbits near the five libration points of the classical circular restricted three body problem (CR3BP). The invariant manifolds are 6D surfaces of states (r, v) that are sliding surfaces of trajectories that coast into a boundary layer region near any of quasi-stable periodic orbits in the vicinity of the libration points. Each point on the invariant manifold has an associated time-to-go or arc length of a particular fiber on the surface that passes through the particular state (r, v). There are several practical questions that arise when we seek to utilize these manifolds for “ballistic capture” coast trajectories for actual mission design, viz:

  • How do we optimally “transfer onto” an invariant manifold from some arbitrary initial state in cis-lunar space, using for example, a low-thrust propulsion system?
  • How do we mathematically represent invariant manifolds for efficient trajectory optimization computational purposes?
  • As a practical matter, how do we account for the truth that the periodic orbits and their associated invariant manifolds of the CR3BP do not rigorously exist when we use a high fidelity dynamical model, including solar perturbations and lunar gravity anomalies?
  • How does all of the above relate to design of trajectories for actual missions?
This presentation will report significant progress toward answering the above questions. 

This presentation is a progress report on work being done in collaboration with my truly excellent Ph.D. students Patrick Kelly and Sandeep Singh. Sandeep is just beginning his appointment this fall as Assistant Professor at Rensselaer Polytechnic Institute, Patrick is expected to become my 60th Ph.D. graduate during 2023.

About Professor Junkins

Junkins’ half century+ of academic appointments have been at the University of Virginia, Virginia Tech and Texas A&M. He collaborates frequently with governmental and industrial partners. He is a prolific mentor with half of his 58 Ph.D. graduates becoming professors and giving rise to a three generation family of about 160 Ph.D. descendants. He time shares various university leadership roles with research and graduate student mentorship. His interests span astrodynamics, estimation, controls, space robotics and optical sensing technologies. He does analysis, computation, design, inventions and experiments. He has published seven books, seven patents and 350 archival papers. His results have been realized successfully in several space missions.

Questions? Contact Kristi Young.