HIGHER-ORDER METHODS AND APPLICATIONS IN ASTRODYNAMICS

Join the event online at the following link: https://politecnicomilano.webex.com/meet/camilla.colombo

Higher-order methods are very promising for astrodynamics applications, and have the potential to become more useful as future missions are planning to fly more complex and nonlinear trajectories.

Several implementations of higher-order methods have been extensively used in astrodynamics: in this seminar, two of these methods will be presented, namely differential algebra and state transition tensors.

Their mathematical equivalence and implementation differences will be discussed, and several examples of how these methods are currently being used for trajectory optimization and navigation within the SaCLaB research group at ISAE-SUPAERO will be presented.

Two applications will be discussed: stochastic trajectory optimization and navigation.

The first relies on a modular structure involving uncertainty propagation, stochastic-to-deterministic constraint transcription, and robust deterministic solvers.
It will be shown how the differential algebra framework helps transcribe these complex constraints and efficiently computing gradient and hessian information. The algorithm is applied to several complex examples in a variety of dynamic systems including cislunar space.

The second application will be focused on reducing the computation requirements for using higher-order methods.
The directional second-order extended Kalman filter will be introduced, which efficiently approximates second-order terms in nonlinear systems with a dominant direction of nonlinearity.

This method could be used to incorporate nonlinear effects into existing extended Kalman filter-based flight systems without incurring a significant additional computational burden.

Speakers:

Spencer Boone is a postdoctoral researcher in the SaCLaB research group. A graduate of the University of Colorado Boulder (MSc in 2016, PhD in 2022), he is currently conducting research on stochastic maneuver design around small bodies and cataloging and characterizing scientific orbits around Enceladus. During his doctoral studies supervised by Prof. Jay MCMAHON, Spencer developed expertise in nonlinear methods for guidance and trajectory optimization.

Stéphanie Lizy-Destrez is a full professor in Space Systems Design at ISAE-SUPAERO and leads the SaCLaB research group. With over 29 years of experience in space agencies, industry, and academia, she conducts research and teaches in the field of astrodynamics. Her specific interests include transfer trajectories, rendezvous, and end-of-service maneuvers for interplanetary missions. Stéphanie is also an Associate Editor of the Journal of Spacecraft and Rockets, a member of the IAF Astrodynamics Committee, and a correspondent of the Air and Space Academy. She has authored or co-authored over 140 journal and international conference articles.

9.5.2025