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A New, General Neighboring Optimal Guidance for Aerospace Vehicles

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Book cover Variational Analysis and Aerospace Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 116))

Abstract

This work describes and applies the recently introduced, general-purpose perturbative guidance termed variable-time-domain neighboring optimal guidance, which is capable of driving an aerospace vehicle along a specified nominal, optimal path. This goal is achieved by minimizing the second differential of the objective function (related to the flight time) along the perturbed trajectory. This minimization principle leads to deriving all the corrective maneuvers, in the context of an iterative closed-loop guidance scheme. Original analytical developments, based on optimal control theory and adoption of a variable time domain, constitute the theoretical foundation for several original features. The real-time feedback guidance at hand is exempt from the main disadvantages of similar algorithms proposed in the past, such as the occurrence of singularities for the gain matrices. The variable-time-domain neighboring optimal guidance algorithm is applied to two typical aerospace maneuvers: (1) minimum-time climbing path of a Boeing 727 aircraft and (2) interception of fixed and moving targets. Perturbations arising from nonnominal propulsive thrust or atmospheric density and from errors in the initial conditions are included in the dynamical simulations. Extensive Monte Carlo tests are performed, and unequivocally prove the effectiveness and accuracy of the variable-time-domain neighboring optimal guidance algorithm.

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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. Bryson, A.E.: Dynamic Optimization. Addison Wesley Longman, Boston (1999)

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Chuang, C.-H.: Theory and computation of optimal low- and medium-thrust orbit transfers. NASA-CR-202202, NASA Marshall Space Flight Center, Huntsville (1996)

    Google Scholar 

  6. Hull, D.G.: Robust neighboring optimal guidance for the advanced launch system. NASA-CR-192087, Austin (1993)

    Google Scholar 

  7. Hull, D.G.: Optimal Control Theory for Applications. Springer, New York (2003)

    Book  MATH  Google Scholar 

  8. Jo, J.-W., Prussing, J.E.: Procedure for applying second-order conditions in optimal control problems. J. Guid. Control. Dyn. 23 (2), 241–250 (2000)

    Article  Google Scholar 

  9. Kugelmann, B., Pesch, H.J.: New general guidance method in constrained optimal control, part 1: numerical method. J. Optim. Theory Appl. 67 (3), 421–435 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. 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 

  13. 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  MATH  Google Scholar 

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

    Article  Google Scholar 

  15. 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  MATH  Google Scholar 

  16. 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  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  19. 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 

  20. Vinh, N.X.: Optimal Trajectories in Atmospheric Flight. Elsevier, New York (1981)

    Google Scholar 

  21. Yan, H., Fahroo, F., Ross, I.: Real-time computation of neighboring optimal control laws. AIAA Guidance, Navigation and Control Conference, Monterey. AIAA Paper 2002–465 (2002)

    Google Scholar 

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Authors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Mauro Pontani

Authors
  1. Mauro Pontani
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Correspondence to Mauro Pontani .

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Editors and Affiliations

  1. Department of Civil and Industrial Engineering, University of Pisa, Pisa, Italy

    Aldo Frediani

  2. Montpellier Institute Alexander Grothen, University of Montpellier, Montpellier, France

    Bijan Mohammadi

  3. LJLL-UPMC Boite, Paris, France

    Olivier Pironneau

  4. Department of Industrial and Civil Engineering, University of Pisa Aerospace Section, Pisa, Italy

    Vittorio Cipolla

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Pontani, M. (2016). A New, General Neighboring Optimal Guidance for Aerospace Vehicles. In: Frediani, A., Mohammadi, B., Pironneau, O., Cipolla, V. (eds) Variational Analysis and Aerospace Engineering. Springer Optimization and Its Applications, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-45680-5_16

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