Near-Optimal Guidance and Pulse-Modulated Reduced-Attitude Control for Orbit Injection

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Modeling and Optimization in Space Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 200))

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Abstract

In most mission scenarios, precise orbit injection represents a crucial requirement, and affects the subsequent phases of spaceflight. This research proposes a new guidance, control, and actuation architecture for upper stage orbit injection maneuvers. A novel, explicit near-optimal guidance algorithm is developed that is based on the local projection of the position and velocity variables, in conjunction with the real-time solution of the associated minimum-time problem. A new, nonlinear reduced-attitude control algorithm is introduced, which enjoys quasi-global stability properties, and is capable of driving the actual longitudinal axis toward the commanded thrust direction. Actuation is based on the joint use of modulated side jets – for the roll control action – and thrust vectoring. The overall dynamics of the upper stage, regarded as a system of two connected bodies, is modeled using Kane’s method. An upper stage with realistic propulsion parameters is selected for numerical testing. Monte Carlo simulations prove that the guidance, control, and actuation architecture at hand is effective for precise orbit injection.

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References

  1. 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 

  2. 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 

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

    Google Scholar 

  4. 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)

    Article  Google Scholar 

  5. 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 

  6. 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  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. Palaia, G., Pallone, M., Pontani, M., Teofilatto, P.: 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, 144, 343–371 (2019)

    Chapter  Google Scholar 

  9. 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 

  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. 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 

  12. 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 

  13. 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 

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

    Book  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. 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 

  17. 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 

  18. 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 

  19. 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 

  20. Geller, D.K.: Linear Covariance Techniques for Orbital Rendezvous Analysis and Autonomous Onboard Mission Planning. J. Guid. Control Dynam. 29(6), 1404–1414 (2006)

    Article  Google Scholar 

  21. Marcos, A., Peñín, L.F., Sommer, J., Bornschlegl, E.: Guidance and Control Design for the Ascent Phase of the Hopper RLV. AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu (2008)

    Google Scholar 

  22. Lam, Q.M., McFarland, M.B., Ruth, M., Drake, D., Ridgely, D.B., Oppenheimer, M.W.: Adaptive Guidance and Control for Space Access Vehicle Subject to Control Surface Failures. AIAA Guidance, Navigation and Control Conference and Exhibit, Honolulu (2008)

    Google Scholar 

  23. Tian, B., Fan, W., Zong, Q.: Integrated guidance and control for reusable launch vehicle in reentry phase. Nonlin. Dyn. 80(1–2), 397–412 (2015)

    Article  MATH  Google Scholar 

  24. Yeh, F.-K.: Sliding-mode-based contour-following controller for guidance and autopilot systems of launch vehicles. Proc. Instit. Mechan. Eng. Part G: J. Aerosp. Eng. 227(2), 285–302 (2015)

    Article  Google Scholar 

  25. Pontani, M., Celani, F.: Neighboring optimal guidance and constrained attitude control applied to three-dimensional lunar ascent and orbit injection. Acta Astronaut. 156, 78–91 (2019)

    Article  Google Scholar 

  26. Pontani, M., Celani, F.: Variable-time-domain neighboring optimal guidance and attitude control of low-thrust lunar orbit transfers. Acta Astronaut. 175, 616–626 (2020)

    Article  Google Scholar 

  27. Pontani, M., Celani, F.: Neighboring Optimal Guidance and Constrained Attitude Control for Accurate Orbit Injection. Aerotecn. Miss. & Spazio, online 12 May 2021

    Google Scholar 

  28. Hughes, P.C.: Spacecraft Attitude Dynamics. Dover Publications, Inc., Mineola, 55–61 (2004)

    Google Scholar 

  29. Perkins, F.M: Explicit Tangent-Steering guidance for Multi-Stage Boosters. Astronaut. Acta 12, 212–223 (1966)

    Google Scholar 

  30. Smith, I.E.: General Formulation of the Iterative Guidance Mode. NASA TM X-53414 (1966)

    Google Scholar 

  31. Brusch, R.G: Bilinear Tangent Yaw Guidance. Guidance and Control Conference, Boulder (1979)

    Google Scholar 

  32. Weiss, H.: Quaternion-based rate/attitude tracking system with application to gimbal attitude control. J. Guid. Control Dynam. 16(4), 609–616 (1993)

    Article  Google Scholar 

  33. Sastry, S.: Nonlinear Systems. Analysis, Stability, and Control. Springer, New York, 182–234 (1999)

    Google Scholar 

  34. Wertz, J.R.: Spacecraft Attitude Determination and Control. Springer, Dordrecht, 487–509; 206–209, 649–654 (1978)

    Book  Google Scholar 

  35. Knauber, R.N.: Roll Torques Produced by Fixed-Nozzle Solid Rocket Motors. J. Spacecr. Rock. 33(6), 789–485 (1996)

    Article  Google Scholar 

  36. Holmes, D.G., Lipo, T.A.: Pulse Width Modulation for Power Converters. Wiley-Interscience, 183–199 (2003)

    Book  Google Scholar 

  37. Tournes, C., Shtessel, Y.B., Wells, E.: Upper stage rocket guidance and control using discontinuous reaction control thrusters via sliding modes. American Control Conference, Albuqerque (1997)

    Google Scholar 

  38. Kienitz, K.H., J. Bals, J.: Pulse modulation for attitude control with thrusters subject to switching restrictions. Aerosol Sci. Technol. 9, 635–640 (2005)

    Article  MATH  Google Scholar 

  39. Anthony, T., Wei, B., Carroll, S.: Pulse Modulated Control Synthesis for a Spacecraft. J. Guid. Control Dynam. 13(6), 1014–1015 (1990)

    Article  Google Scholar 

  40. Navabi, M., Rangraz, H.: Comparing Optimum Operation of Pulse Width Pulse Frequency and Pseudo-Rate Modulators in Spacecraft Attitude Control Subsysteem Employing Thruster. Recent Advances in Space technologies (RAST), 625–630 (2013)

    Google Scholar 

  41. Chegeni, E., Hoseini, S.M., Madadpour Inallou, M.: Attitude Control of Satellite with PWPF Modulator Using Generalized Incremental Predictive Control. J. Knowl.-Based Eng. Innov. 1(2), 131–141 (2015)

    Google Scholar 

  42. Jalali-Naini, S.H., Darani, S.: Preliminary Design of Spacecraft Attitude Control with Pulse-Width Pulse-Frequency Modulator for Rest-to-Rest Maneuvers. J. Aerosol Sci. Technol. 11(1), 1–8 (2017)

    Google Scholar 

  43. Arantes, G. Jr., Martins-Filho, L.S., Santana, A.C.: Optimal On-Off Control for the Brazilian Multimission Platform. Mathem. Probl. Eng. (2009)

    Google Scholar 

  44. Kane, T.R., Levinson, D.A.: Dynamics, theory and applications. McGraw-Hill, New York (1985)

    Google Scholar 

  45. Roithmayr, C.M., Hodges, D.H.: Dynamics: Theory and Application of Kane’s Method. Cambridge University Press, 39–51, 100–117, 191–199 (2016)

    MATH  Google Scholar 

  46. Stoneking, E. T.: Implementation of Kane’s Method for a Spacecraft Composed of Multiple Rigid Bodies. AIAA Guidance, Navigation, and Control (GNC) Conference, Boston (2013)

    Google Scholar 

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Correspondence to Mauro Pontani .

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Pontani, M., Pianalto, A., Carletta, S., Teofilatto, P. (2023). Near-Optimal Guidance and Pulse-Modulated Reduced-Attitude Control for Orbit Injection. In: Fasano, G., Pintér, J.D. (eds) Modeling and Optimization in Space Engineering. Springer Optimization and Its Applications, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-031-24812-2_11

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