Emily Gerber, Ten One Aerospace; Michael Mercurio, Ten One Aerospace; Jason Crane, Ten One Aerospace; Christopher Roscoe, Ten One Aerospace; Jason Westphal, Ten One Aerospace
Keywords: RPO, Maneuver Detection, Deep Learning
Abstract:
When two or more satellites are operating in close proximity, it is imperative that the states are well known and any deviation from the predicted state, as the result of a maneuver, is quickly identified and quantified to evaluate any potential danger of collision or operational impediment. In the case where Clohessy-Wiltshire-Hill (CWH) assumptions hold and a simple along track delta-V is applied to the chaser spacecraft, the analytic relation between geometric parameters of the co-planar trajectory is well characterized in academic literature [1]–[6].
As the relative motion between satellites becomes more complex and complicating factors such as eccentricity and orbital perturbations are introduced, the need to characterize these classes of maneuvers becomes even more important. In this work, we reformulate the analytical approaches for the simplest CWH cases but from the perspective of relative pixel spatial-temporal geometry gathered by a ground-based optical sensor observing maneuvers for closely spaced objects (CSOs) in Geostationary orbit. We then introduce increased complexities into the problem such as adding inclination, eccentricity, orbital perturbations, and altering period (non-geosynchronous). We explore if this class of analytic solutions, from the perspective of a fixed ground sensor, can be obtained in various combinations of cases (ablation study). Inevitably, the analytic solutions will break down as more confounding factors are introduced, hence, we examine if simple first-order delta-V estimates can be obtained.
Once this class of analytic and first-order solutions from the pixel-spatial-temporal/ground-based-sensor framework are obtained, we compare them with an alternative data-centric machine learning-based approach to the problem. We apply deep learning techniques to train and validate regression and classification models to estimate maneuver characteristics, including delta-V, for increasingly complex orbits and RPO scenarios. The data used to train and validate models include variations of multiple RPO scenarios such as simple along track delta-V, V-bar hop, relative football orbit, and R-bar station keeping [1], [5] using our validated RPO simulation capability. The results of the simulations include sets of stacked images that characterize the maneuver. These data are used to train deep learning regression and classification models to estimate the delta-V and type of maneuver, respectively. Results from the deep learning models are validated against the simplified cases where analytic approaches hold, and regression accuracy of the model outside simplified cases are readily estimated since applied delta-V’s in each simulation case is known.
The goal of this work is to create a “secondary path” for ground-sensors to rapidly characterize a maneuver using a well-trained deep neural network model based solely on the raw observations of pixel data from their sensors, without the need for first going through post-processing and classical orbit determination techniques. The value of these results will be timely capture of maneuver events to support both safe space operations and rapid task prioritization to support custody maintenance.
[1] D. Woffinden, “Angles-Only Navigation for Autonomous Orbital Rendezvous,” Grad. Theses Diss., Dec. 2008, doi: https://doi.org/10.26076/15dc-267c.
[2] T. A. Lovell and M. V. Tollefson, “Calculation of impulsive hovering trajectories via relative orbit elements,” Adv. Astronaut. Sci., vol. 123, pp. 2533–2548, 2006.
[3] Y. Rao, J. Yin, and C. Han, “Hovering Formation Design and Control Based on Relative Orbit Elements,” J. Guid. Control Dyn., vol. 39, no. 2, pp. 360–371, Feb. 2016, doi: 10.2514/1.G001238.
[4] T. A. Lovell and D. L. Brown, “Impulsive-hover satellite trajectory design for rendezvous and proximity operation missions,” presented at the AAS Rocky Mountain Guidance, Navigation, and Control Conference, 2007.
[5] D. C. Woffinden, “On-orbit satellite inspection?: navigation and [Delta]v analysis,” Thesis, Massachusetts Institute of Technology, 2004. Accessed: Feb. 23, 2023. [Online]. Available: https://dspace.mit.edu/handle/1721.1/28862
[6] E. Prince and R. G. Cobb, “Optimal Guidance for Relative Teardrops with Lighting and Collision Constraints,” in 2018 AIAA Guidance, Navigation, and Control Conference, American Institute of Aeronautics and Astronautics. doi: 10.2514/6.2018-0867.
Date of Conference: September 19-22, 2023
Track: Conjunction/RPO