Novel dual quaternion based model and control for gravity recovery missions

I am conducting novel research on the use of dual quaternions for the modeling and control of spacecraft used for gravity recovery missions such as the GRACE and GRACE-FO NASA missions. Measuring Earth's temporal and spatially varying gravity field is of significant interest to many fields of study, including ocean dynamics, sea-level rise, post-glacial rebound, etc. The novelty of this research is that although the dual quaternion modeling approach has shown significant promise in past research for efficiently and accurately modeling the coupled relative dynamics of spacecraft, this approach has never been employed for gravity recovery missions. Gravity recovery missions make ideal candidates for proving the merit of dual quaternions because very precise measurements must be taken between formation flying spacecraft and taken between the spacecraft and their test masses. The assumptions needed to implement traditional modeling and control methods on gravity recovery missions increase error in these measurements. Therefore, it is expected that this work will be transformational for gravity recovery missions since dual quaternions are not limited by the assumptions of traditional methods, which gives dual quaternions the potential to improve calculations used to map Earth’s gravitational field. For this research, a dual quaternion modeling approach is compared to traditional modeling methods for modeling the 12 degree-of-freedom coupled relative dynamics of a spacecraft and its test mass. The two modeling approaches will be compared to existing GRACE-FO data products to compare the accuracy and utility of both methods. Controllers designed from the dual quaternion approach will also be explored and compared against the typical control approaches currently utilized on gravity recovery missions. I expect that the dual quaternion control and modeling approach will show an increase in performance and/or accuracy over traditional methods, and therefore prove the dual quaternion’s transformational potential for gravity recovery missions.

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