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Autonomous Optimal Trajectory Planning for Orbital Rendezvous, Satellite Inspection, and Final Approach Based on Convex Optimization

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Abstract

Convex optimization techniques have deterministic convergence properties, do not require an initial guess, and have been tested in real-time environments. These optimization techniques are applied to the trajectory planning problem for orbital rendezvous and proximity operations. Spacecraft rendezvous, inspection, and final approach trajectories are considered. Optional trajectory constraints are considered, including approach corridors, keep-out zones, and maximum thrust acceleration levels. Two linear dynamics models are investigated: Clohessy-Wiltshire dynamics to describe the relative motion in a local-horizontal local-vertical frame, and a new relative orbital motion dynamics model to describe the motion relative to a spinning or uncontrolled spacecraft. In both cases, an algorithm based on a second-order cone program is developed and used to generate optimal rendezvous and proximity operation trajectories. Results for several scenarios are presented and implemented in a nonlinear orbital simulation.

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References

  1. Zagaris, C., Baldwin, M., Jewison, C., Peterson, C.: Survey of spacecraft rendezvous and proximity guidance algorithms for On-Board implementation. Amer. Astronom. Soc. 15–334 (2015)

  2. Acikmese, B., Ploen, S.R.: Convex programming approach to powered descent guidance for mars landing. J. Guidance Control Dynam. 30(5), 1353–1366 (2007)

    Article  Google Scholar 

  3. Blackmore, L., Acikmese, B., Scharf, D.P.: Minimum-landing-error powered-descent guidance for Mars landing using convex optimization. J. Guidance Control Dynam. 33(4), 1161–1171 (2010)

    Article  Google Scholar 

  4. Richards, A., How, J.P.: Model predictive control of vehicle maneuvers with guaranteed completion time and robust feasibility. In: American Control Conference, 2003. Proceedings of the 2003, vol. 5, pp. 4034–4040. IEEE (2003)

  5. Richards, A., Schouwenaars, T., How, J.P., Feron, E.: Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming. J. Guidance Contro Dynam. 25(4), 755–764 (2002)

    Article  Google Scholar 

  6. Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of second-order cone programming. Linear Algebra Appl. 284(1), 193–228 (1998)

    Article  MathSciNet  Google Scholar 

  7. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  8. Liu, X., Lu, P.: Robust trajectory optimization for highly constrained rendezvous and proximity operations. In: AIAA Paper, vol. 4720 (2013)

  9. Liu, X., Lu, P.: Solving nonconvex optimal control problems by convex optimization. J. Guidance Control Dynam. 37(3), 750–765 (2014)

    Article  Google Scholar 

  10. Lu, P., Liu, X.: Autonomous trajectory planning for rendezvous and proximity operations by conic optimization. J. Guidance Control Dynam. 36(2), 375–389 (2013)

    Article  Google Scholar 

  11. Geller, D., Lovell, T.: Relative orbital motion and angles-only relative state observability in cylindrical coordinates. In: Proceedings of the AAS-AIAA Space Flight Mechanics Meeting, No. AAS-14-211, Santa Fe, New Mexico (2014)

  12. Wiltshire, R., Clohessy, W.: Terminal guidance for rendezvous in space. J. Aerospace Sci. 27(9), 653–658 (1960)

    Article  Google Scholar 

  13. Ortolano, N., Geller, D.K., Avery, A.: Relative orbital motion dynamics with respect to a rotating spacecraft-fixed frame. In: Proceedings of AAS GN&c Conference - Rocky Mountain Section (2017)

  14. Lu, P., Liu, X.: Autonomous trajectory planning for rendezvous and proximity operations by conic optimization. J. Guidance Control Dynam. 36(2), 375–389 (2013)

    Article  Google Scholar 

  15. CVX Research, I.: CVX: Matlab software for disciplined convex programming, version 2.0, http://cvxr.com/cvx (2012)

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Authors and Affiliations

  1. Mechanical and Aerospace Engineering Department, Utah State University, 4130 Old Main Hill, Logan, UT, 84322-4130, USA

    Nicholas Ortolano & David K. Geller

  2. Space Dynamics Laboratory, 1695 Research Pkwy, North Logan, UT, 84341, USA

    Aaron Avery

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  1. Nicholas Ortolano
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  2. David K. Geller
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  3. Aaron Avery
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Correspondence to Nicholas Ortolano.

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Ortolano, N., Geller, D.K. & Avery, A. Autonomous Optimal Trajectory Planning for Orbital Rendezvous, Satellite Inspection, and Final Approach Based on Convex Optimization. J Astronaut Sci 68, 444–479 (2021). https://doi.org/10.1007/s40295-021-00260-5

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  • DOI: https://doi.org/10.1007/s40295-021-00260-5

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