Seminar - On the Fusion of Invariant Manifolds, Orthogonal Approximation and Optimal Control: For Cis-Lunar Fun and Profit! - Oct. 21

John Junkins
Distinguished Professor of Aerospace Engineering, Texas A&M University
Friday, Oct. 21 | 10:40 A.M. | AERO 120

Abstract: 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 the quasi-stable periodic orbits near the libration points.  Each point on the surface 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” the 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 fact that the periodic orbits and their associated invariant manifolds of the CR3BP do not rigorously exist when we use a high fidelity dynamical model with solar perturbations and lunar gravity anomalies accounted for?
• How does all of the above relate to design of trajectories for actual missions envisioned over the coming decade?

This presentation will report significant progress toward answering the above questions.  

Bio: John 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 PhD graduates becoming professors and giving rise to a three generation family of about 160 PhD descendants.   He time shares various University leadership roles with research and graduate student mentorship.  His interests span astrodynamics, estimation, controls and space robotics.  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.