Abstract
Space Domain Awareness (SDA) architectures must adapt to overcome the challenges present in cislunar space. Dynamical systems theory provides tools which may be leveraged to address some of the many challenges associated with cislunar space. The PSS is an analysis tool used to reduce dimensionality and help study the properties of the system flow. Invariant manifolds have been combined with the PSS to prescribe trajectories through various cislunar regimes by other researchers. In this work, the PSS and the invariant manifolds are used to pose a set of boundary value problems which define the \(\Delta \textbf{v}\) from a nominal \(L_2\) Lyapunov orbit through the PSS. By approximating the solutions through the PSS, the admissible controls onto these highways are approximated. One viable use for this formulation of a reduced reachable set will allow an SDA operator to intelligently task sensors to regain custody of a maneuver spacecraft. This paper examine uses concepts of a admissible region to intelligently reduce the reachability set for maneuver spacecraft and studies the efficacy for multiple maneuver windows and the affects of various user set parameters.
This material is based upon work supported jointly by the AFOSR grant FA9550-20-1-0176, FA9550-22-1-0092, as well as the DoD SMART Scholarship Program.
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References
The future of space 2060 & implications for U.S. strategy: report on the space futures workshop, Tech. rep., Air Force Space Command (2019)
Holzinger, M.J., Chow, C.C., Garretson, P.: A Primer on Cislunar Space. White Paper 2021–1271. AFRL (2021)
Perkins, J.: AFRL’s Cislunar Highway Patrol System Seeks Industry Collaboration (2022)
Hall, Z., Singla, P., Johnson, K.: A particle filtering approach to space-based maneuvering satellite location and estimation. In: AAS Astrodynamics Specialist Conference (2020)
Hall, Z., et al.: Reachability-based approach for search and detection of maneuvering cislunar objects. In: AIAA SCITECH 2022 Forum. AIAA SciTech Forum. San Diego, CA & Virtual: American Institute of Aeronautics and Astronautics (2022). https://doi.org/10.2514/6.2022-0853
Tommei, G., Milani, A., Rossi, A.: Orbit determination of space debris: admissible regions. Celest. Mech. Dyn. Astron. 97(4), 289–304 (2007). https://doi.org/10.1007/s10569-007-9065-x
Fujimoto, K., Scheeres, D.J.: Applications of the admissible region to space-based observations. Adv. Space Res. 52(4), 696–704 (2013). https://doi.org/10.1016/j.asr.2013.04.020
Schwab, D., Eapen, R., Singla, P.: Approximating admissible control onto the cislunar highways for detection and tracking of spacecraft. In: 2022 AAS/AIAA Astrodynamics Specialist Conference. Charlotte, North Carolina (2022)
Villac, B.F., Scheeres, D.J.: Escaping trajectories in the hill three-body problem and applications. J. Guidance Control Dyn. 26(2), 224–232 (2003). https://doi.org/10.2514/2.5062
Wang S.K., et al.: Dynamical Systems, the Three-Body Problem and Space Mission Design. Chapter 7: Invariant manifolds and end to end transfer. Useful information for trajectory planning. Marsden Books (2011). ISBN: 978-0-615-24095-4
Ohtsuka, T., Fujii, H.: Stabilized continuation method for solving optimal control problems. J. Guidance Control Dyn. 17(5), 950–957 (1994). https://doi.org/10.2514/3.21295
Vedantam, M., Akella, M.R., Grant, M.J.: Multi-stage stabilized continuation for indirect optimal control of hypersonic trajectories. In: AIAA Scitech 2020 Forum. Orlando, FL: American Institute of Aeronautics and Astronautics (2020). ISBN: 978-1-62410-595-1. https://doi.org/10.2514/6.2020-0472
Bolden, M., Craychee, T., Griggs, E.: An evaluation of observing constellation orbit stability, low signal-to-noise, and the too-short-arc challenges in the cislunar domain. In: Advanced Maui Optical and Space Surveillance Technologies Conference (AMOS). Maui, HI (2020)
Hall, Z., Singla, P.: Reachability analysis based tracking: applications to non-cooperative space object tracking. In: Darema, F., Blasch, E., Ravela, S., Aved, A. (eds.) DDDAS 2020. LNCS, vol. 12312, pp. 200–207. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-61725-7_24
Hall, Z.: A probabilistic framework to locate and track maneuvering satellites, Ph. D. thesis, University Park, PA: The Pennsylvania State University (2021)
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Schwab, D., Eapen, R., Singla, P. (2024). Reachability Analysis to Track Non-cooperative Satellite in Cislunar Regime. In: Blasch, E., Darema, F., Aved, A. (eds) Dynamic Data Driven Applications Systems. DDDAS 2022. Lecture Notes in Computer Science, vol 13984. Springer, Cham. https://doi.org/10.1007/978-3-031-52670-1_10
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