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Ascent Trajectory Optimization and Neighboring Optimal Guidance of Multistage Launch Vehicles

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Modeling and Optimization in Space Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 144))

Abstract

Multistage launch vehicles are employed to place spacecraft and satellites in their operational orbits. If the rocket aerodynamics and propulsion are modeled appropriately, optimization of their ascent trajectory consists in determining the coast duration and the thrust time history that maximize the final mass at injection. This research derives all the necessary conditions for ascent path optimization of a multistage launch vehicle. With reference to an existing rocket, the indirect heuristic method is then applied, for the numerical determination of the overall ascent trajectory. An effective approach is used with the intent of satisfying the path constraint related to the maximum dynamical pressure in the atmospheric phase. Then, the recently introduced, implicit-type variable-time-domain neighboring optimal guidance is applied to the upper stage powered arc, for the purpose of obtaining the corrective control actions in the presence of nonnominal flight conditions. The guidance approach at hand, based on the second-order analytical conditions for optimality, proves to be rather effective (in terms of propellant budget), and guarantees very accurate orbit injection in spite of perturbations.

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References

  1. Afshari, H.H., Novinzadeh, A.B., Roshanian, J.: Determination of nonlinear optimal feedback law for satellite injection problem using neighboring optimal control. Am. J. Appl. Sci. 6(3), 430–438 (2009)

    Article  Google Scholar 

  2. Bayley, D.J., Hartfield, Jr R.J., Burkhalter, J.E., Jenkins, R.M.: Design optimization of a space launch vehicle using a genetic algorithm. J. Spacecr. Rocket. 45(4), 733–740 (2008)

    Article  Google Scholar 

  3. Calise, A.J., Melamed, N., Lee, S.: Design and evaluation of a three-dimensional optimal ascent guidance algorithm. J. Guid. Control Dynam. 21(6), 867–875 (1998)

    Article  Google Scholar 

  4. Calise, A.J., Tandon, S., Young, D.H., Kim, S.: Further Improvements to a Hybrid Method for launch Vehicle Ascent Trajectory Optimization. AIAA Guidance, Navigation and Control Conference and Exhibit, Denver (2000)

    Google Scholar 

  5. Charalambous, C.B., Naidu, S.N., Hibey, J.L.: Neighboring optimal trajectories for aeroassisted orbital transfer under uncertainties. J. Guid. Control Dynam. 18(3), 478–485 (1995)

    Article  Google Scholar 

  6. Di Sotto, E., Teofilatto, P.: Semi-analytical formulas for launcher performance evaluation. J. Guid. Control Dynam. 25(3), 538–545 (2002)

    Article  Google Scholar 

  7. Gath, P.F., Calise, A.J.: Optimization of launch vehicle ascent trajectories with path constraints and coast arcs. J. Guid. Control Dynam. 24(2), 296–304 (2001)

    Article  Google Scholar 

  8. Hull, D.G.: Robust Neighboring Optimal Guidance for the Advanced Launch System. NASA-CR-192087, Austin (1993)

    Google Scholar 

  9. Hull, D.G.: Optimal Control Theory for Applications. Springer, New York, pp. 199–254 (2003)

    Google Scholar 

  10. Jamilnia, R., Naghash, A.: Simultaneous optimization of staging and trajectory of launch vehicles using two different approaches. Aerosol Sci. Technol. 23, 65–92 (2012)

    Google Scholar 

  11. Lu, P.: Optimal feedback control laws using nonlinear programming. J. Optim. Theory Appl. 71(3), 599–611 (1991)

    Article  MathSciNet  Google Scholar 

  12. Lu, P., Griffin, B.J., Dukeman. G.A., Chavez, F.R.: Rapid optimal multiburn ascent planning and guidance. J. Guid. Control Dynam. 31(6), 45–52 (2008)

    Google Scholar 

  13. Lu, P., Pan, B.: Trajectory optimization and guidance for an advanced launch system. 30th Aerospace Sciences Meeting and Exhibit, Reno (1992)

    Google Scholar 

  14. Mangiacasale, L.: Meccanica del volo atmosferico. Terne di riferimento, equazioni di moto, linearizzazione, stabilità. Ingegneria 2000, Rome (2008)

    Google Scholar 

  15. Martinon, P., Bonnans, F., Laurent-Varin, J., Trélat, E.: Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher. J. Guid. Control Dynam. 32(1), 51–55 (2009)

    Article  Google Scholar 

  16. Miele, A.: Multiple-subarc gradient-restoration algorithm, part 1: algorithm structure. J. Optim. Theory Appl. 116(1), 1–17 (2003)

    Article  MathSciNet  Google Scholar 

  17. Miele, A., Multiple-subarc gradient-restoration algorithm, part 2: application to a multistage launch vehicle design. J. Optim. Theory Appl. 116(1), 19–19 (2003)

    Article  MathSciNet  Google Scholar 

  18. Pontani, M.: Particle swarm optimization of ascent trajectories of multistage launch vehicles. Acta Astronaut. 94(2), 852–864 (2014)

    Article  Google Scholar 

  19. Pontani, M., Conway, B.A.: Particle swarm optimization applied to space trajectories. J. Guid. Control Dynam. 33(5), 1429–1441 (2010)

    Article  Google Scholar 

  20. Pontani, M., Conway, B.A.: Particle swarm optimization applied to impulsive orbital transfers. Acta Astronaut. 74, 141–155 (2012)

    Article  Google Scholar 

  21. Pontani, M., Conway, B.A.: Optimal finite-thrust rendezvous trajectories found via particle swarm algorithm. J. Spacecr. Rocket. 50(6), 1222–1234 (2013)

    Article  Google Scholar 

  22. Pontani, M., Cecchetti, G., Teofilatto, P.: Variable-time-domain neighboring optimal guidance, part 1: algorithm structure. J. Optim. Theory Appl. 166(1), 76–92 (2015)

    Article  MathSciNet  Google Scholar 

  23. Pontani, M., Cecchetti, G., Teofilatto, P.: Variable-time-domain neighboring optimal guidance, part 2 application to lunar descent and soft landing. J. Optim. Theory Appl. 166(1), 93–114 (2015)

    Article  MathSciNet  Google Scholar 

  24. Pontani, M., Cecchetti, G., Teofilatto, P.: Variable-time-domain neighboring optimal guidance applied to space trajectories. Acta Astronaut. 115, 102–120 (2015)

    Article  Google Scholar 

  25. Pontani, M., Conway, B.A.: Optimal low-thrust orbital maneuvers via indirect swarming method. J. Optim. Theory Appl. 162(1), 272–292 (2014)

    Article  MathSciNet  Google Scholar 

  26. Pontani, M., Ghosh, P., Conway, B.A.: Particle swarm optimization of multiple-burn rendezvous trajectories. J. Guid. Control Dynam. 35(4), 1192–1207 (2012)

    Article  Google Scholar 

  27. Pontani, M., Teofilatto, P.: Simple method for performance evaluation of multistage rockets. Acta Astronaut. 94(1), 434–445 (2014)

    Article  Google Scholar 

  28. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: The Mathematical Theory of Optimal Processes. Princeton University Press, Princeton (1962)

    MATH  Google Scholar 

  29. Qazi, M.D., Linshu, H., Elhabian, T.: Rapid Trajectory Optimization Using Computational Intelligence for Guidance and Conceptual Design of Multistage Launch Vehicles. AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco (2005)

    Google Scholar 

  30. Roh, W., Kim, Y.: Trajectory optimization for a multi-stage launch vehicle using time finite element and direct collocation methods. Eng. Optim. 34(1), 15–32 (2002)

    Article  Google Scholar 

  31. Seywald, H., Cliff, E.M.: Neighboring optimal control based feedback law for the advanced launch system. J. Guid. Control Dynam. 17(3), 1154–1162 (1994)

    Article  Google Scholar 

  32. Teofilatto, P., De Pasquale, E.: A non-linear adaptive guidance algorithm for last-stage launcher control. J. Aerosp. Eng. 213, 45–55 (1999)

    Google Scholar 

  33. Townsend, G.E., Abbott, A.S., Palmer, R.R.: Guidance, Flight Mechanics and Trajectory Optimization, Volume VIII, Boost Guidance Equations. NASA Contractor Report, Washington (1968)

    Google Scholar 

  34. Vought Corporation: Scout User’s Manual. National Technical Information Service, Springfield (1980)

    Google Scholar 

  35. Weigel, N., Well, K.H.: Dual payload ascent trajectory optimization with a splash-down constraint. J. Guid. Control Dynam. 23(1), 45–52 (2000)

    Article  Google Scholar 

  36. Yan, H., Fahroo, F., Ross, I.: Real-Time Computation of Neighboring Optimal Control Laws. AIAA Guidance, Navigation and Control Conference, Monterey (2002)

    Google Scholar 

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Authors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Guido Palaia, Marco Pallone, Mauro Pontani & Paolo Teofilatto

Authors
  1. Guido Palaia
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  2. Marco Pallone
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  3. Mauro Pontani
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  4. Paolo Teofilatto
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Corresponding author

Correspondence to Mauro Pontani .

Editor information

Editors and Affiliations

  1. Thales Alenia Space, Turin, Italy

    Giorgio Fasano

  2. Department of Industrial and Systems Engineering, Lehigh University , Bethlehem, PA, USA

    János D. Pintér

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Palaia, G., Pallone, M., Pontani, M., Teofilatto, P. (2019). Ascent Trajectory Optimization and Neighboring Optimal Guidance of Multistage Launch Vehicles. In: Fasano, G., Pintér, J. (eds) Modeling and Optimization in Space Engineering . Springer Optimization and Its Applications, vol 144. Springer, Cham. https://doi.org/10.1007/978-3-030-10501-3_13

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