Skip to main content
SpringerLink
Log in

An Iterative Convex Programming Method for Rocket Landing Trajectory Optimization

  • Original Article
  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

A rapid trajectory optimization method is proposed to solve the fuel-optimal Earth-landing problem of reusable rockets, in which the nonlinear aerodynamic drag force is non-negligible. To enable the online and autonomous operation ability, the method is designed based on convex optimization, which features rapid and deterministic convergence properties, and a homotopic-iterative strategy is proposed to convexify the nonlinear system dynamics of the rocket. In the proposed iterative algorithm, the problem is first solved based on the lossless convexification method while the drag force is considered to be zero. Then, during subsequent iterations, the drag profile is approximated by the last solution and homotopically added to the problem. Thus, the nonlinear drag is gradually included while the problem remains convex. Because the convexification of the nonlinear terms is not based on linearization, no reference trajectory or initial guess is needed, which greatly enhances the autonomy of the algorithm. Numerical experiments are provided to demonstrate the effectiveness, rapidness, and accuracy of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3.
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Data Availability

Not applicable.

References

  1. Açıkmeşe, B., Ploen, S.R.: Convex programming approach to powered descent guidance for Mars landing. J. Guid. Control. Dyn. 30, 1353–1366 (2007)

    Article  Google Scholar 

  2. Açıkmeşe, B., Carson, J., Blackmore, L.: Lossless Convexification of nonconvex control bound and pointing constraints of the soft landing optimal control problem. IEEE Trans. Control Syst. Technol. 21, 2104–2113 (2013)

    Article  Google Scholar 

  3. Andersen, E.D., Roos, C., Terlaky, T.: On implementing a primal-dual interior-point method for conic quadratic optimization. Math. Program. 95, 249–277 (2003)

    Article  MathSciNet  Google Scholar 

  4. Bai, X., Turner, D., Junkins, J.: Bang-bang Control Design by Combing Pseudospectral Method with a novel Homotopy Algorithm. AIAA Guidance, Navigation, and Control Conference, pp. 2009–5955. AIAA Paper, Chicago (2009)

    Google Scholar 

  5. Betts, J.T.: Survey of numerical methods for trajectory optimization. J. Guid. Control. Dyn. 21, 193–207 (1998)

    Article  Google Scholar 

  6. Blackmore, L., Açıkmeşe, B., Scharf, D.P.: Minimum-landing-error powered-descent guidance for Mars landing using convex optimization. J. Guid. Control. Dyn. 33, 1161–1171 (2010)

    Article  Google Scholar 

  7. Bollino, K.P.: High-Fidelity Real-Time Trajectory Optimization for Reusable Launch Vehicles. Monterey California USA, Naval Postgraduate School (2006)

    Google Scholar 

  8. Brendel, E., Hérissé, B., Bourgeois, E.: Optimal Guidance for Toss Back Concepts of Reusable Launch Vehicles. 8th European Conference for Aeronautics and Aerospace Science, Madrid (2019)

    Google Scholar 

  9. Cheng, X., Li, H., Zhang, R., Cheng, X., Li, H., Zhang, R.: Efficient Ascent Trajectory Optimization using Convex Models based on the Newton–Kantorovich/Pseudospectral Approach. Aerosp. Sci. Technol. 66, 140–151 (2017)

    Article  Google Scholar 

  10. Dueri, D., Açıkmeşe, B., Scharf, D.P., Harris, M.: Customized real time interior-point methods for onboard powered-descent guidance. J. Guid. Control. Dyn. 40, 197–212 (2017)

    Article  Google Scholar 

  11. Garg, D.: Advances in Global Pseudospectral Methods for Optimal Control. Univ. of Florida, Gainesville Florida (2011)

    Google Scholar 

  12. Gill, P., Murray, W., Saunders, M.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev. 47, 99–131 (2005)

    Article  MathSciNet  Google Scholar 

  13. Guo, T., Jiang, F., Li, J.: Homotopic approach and Pseudospectral method applied jointly to low thrust trajectory optimization. Acta Astronaut. 71, 38–50 (2012)

    Article  Google Scholar 

  14. Harris, M.W., Açıkmeşe, B.: Maximum divert for planetary landing using convex optimization. J. Optim. Theory Appl. 162, 975–995 (2013)

    Article  MathSciNet  Google Scholar 

  15. Huntington, G.T.: Advancement and Analysis of a Gauss Pseudospectral Transcription for Optimal Control. Cambridge Massachusetts USA. Massachusetts Inst. of Technology, USA (2007)

    Google Scholar 

  16. Liu, X., Shen, Z., Lu, P.: Entry trajectory optimization by second order cone programming. J. Guid. Control. Dyn. 39, 227–241 (2016)

    Article  Google Scholar 

  17. Liu, X., Lu, P., Pan, B.: Survey of convex optimization for aerospace applications. Astrodynamics. 1, 23–40 (2017)

    Article  Google Scholar 

  18. Liu, X.: Fuel-optimal rocket landing with aerodynamic controls. J. Guid. Control. Dyn. 42, 65–77 (2018)

    Article  Google Scholar 

  19. Lu, P., Sun, H., Tsai, B.: Closed-loop Endoatmospheric ascent guidance. J. Guid. Control. Dyn. 26, 283–294 (2003)

    Article  Google Scholar 

  20. Lu, P.: Entry guidance: a unified method. J. Guid. Control. Dyn. 37, 713–728 (2014)

    Article  Google Scholar 

  21. Lu, P.: Introducing computational guidance and control. J. Guid. Control. Dyn. 40, 193–193 (2017)

    Article  Google Scholar 

  22. Mao, Y., Szmuk, M., Açıkmeşe, B.: Successive Convexification of Non-Convex Optimal Control Problems and its Convergence Properties. IEEE 55th Conference on Decision and Control (CDC), pp. 3636–3641. IEEE Publ, Piscataway (2016)

    Google Scholar 

  23. Pan, B., Lu, P., Pan, X., Ma, Y.: Double-Homotopy method for solving optimal control problems. J. Guid. Control. Dyn. 39, 1706–1720 (2016)

    Article  Google Scholar 

  24. Patterson, M.A., Rao, A.V.: GPOPS-II: a Matlab software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming. ACM Trans. Math Software. 41, 1–37 (2014)

    Article  MathSciNet  Google Scholar 

  25. Ross, I.M., Sekhavat, P., Fleming, A., Gong, Q.: Optimal feedback control: foundations, examples, and experimental results for a new approach. J. Guid. Control. Dyn. 31, 307–321 (2008)

    Article  Google Scholar 

  26. Sagliano, M., Mooij, E., Theil, S.: Onboard trajectory generation for entry vehicles via adaptive multivariate Pseudospectral interpolation. J. Guid. Control. Dyn. 40, 466–476 (2017)

    Article  Google Scholar 

  27. Sagliano, M.: Pseudospectral convex optimization for powered descent and landing. J. Guid. Control. Dyn. 41, 320–334 (2018)

    Article  Google Scholar 

  28. Sagliano, M.: Generalized hp Pseudospectral-convex programming for powered descent and landing. J. Guid. Control. Dyn. 42, 1562–1570 (2019)

    Article  Google Scholar 

  29. Sagliano, M., Mooij, E.: Optimal Drag-Energy Entry Guidance via Pseudospectral Convex Optimization. AIAA Guidance, Navigation, and Control Conference, pp. 2018–1871. AIAA Paper, Kissimmee (2018)

    Google Scholar 

  30. Simplício, P., Andrés, M., Samir, B.: Guidance of reusable launchers: improving descent and landing performance. J. Guid. Control. Dyn. 42, 2206–2219 (2019)

    Article  Google Scholar 

  31. Simplício, P., Andrés, M.: Reusable launchers: development of a coupled flight mechanics, guidance, and control benchmark. J. Spacecraft. Rockets. 57, 74–89 (2020)

    Article  Google Scholar 

  32. Scharf, D.P., Açıkmeşe, B., Dueri, D., Benito, J., Casoliva, J.: Implementation and experimental demonstration of onboard powered descent guidance. J. Guid. Control. Dyn. 40, 213–229 (2017)

    Article  Google Scholar 

  33. Szmuk, M., Reynolds, T., Açıkmeşe, B.: Successive Convexification for real-time six-degree-of-freedom powered descent guidance with state-triggered constraints. J. Guid. Control. Dyn. 43, 1399–1413 (2020)

    Article  Google Scholar 

  34. Wang, J., Cui, N.: A Pseudospectral-Convex Optimization Algorithm for Rocket Landing Guidance. AIAA Guidance, Navigation, and Control Conference, pp. 2018–1871. AIAA Paper, Kissimmee (2018)

    Google Scholar 

  35. Wang, J., Cui, N., Wei, C.: Rapid trajectory optimization for hypersonic entry using convex optimization and Pseudospectral method. Aircr. Eng. Aerosp. Technol. 91, 669–679 (2019a)

    Article  Google Scholar 

  36. Wang, J., Cui, N., Wei, C.: Optimal rocket landing guidance using convex optimization and model predictive control. J. Guid. Control. Dyn. 42, 1078–1092 (2019b)

    Article  Google Scholar 

  37. Yang, H., Li, S., Bai, X.: Fast Homotopy method for asteroid landing trajectory optimization using approximate initial Costates. J. Guid. Control. Dyn. 42, 585–597 (2019)

    Article  Google Scholar 

  38. Zhou, D., Zhang, Y., Li, S.: Receding horizon guidance and control using sequential convex programming for spacecraft 6-DoF close proximity. Aerosp. Sci. Technol. 87, 459–477 (2019)

    Article  Google Scholar 

Download references

Funding

This research is supported by the Fundamental Research Funds for the Central Universities (191gpy288).

Author information

Authors and Affiliations

  1. School of Systems Science and Engineering, Sun Yat-Sen University, Guangzhou, 510275, People’s Republic of China

    Jinbo Wang, Huixu Li & Hongbo Chen

Authors
  1. Jinbo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huixu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongbo Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinbo Wang.

Ethics declarations

Conflicts of Interest/Competing Interests

No conflict of interest exits in this paper.

Code Availability

Not applicable.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, J., Li, H. & Chen, H. An Iterative Convex Programming Method for Rocket Landing Trajectory Optimization. J Astronaut Sci 67, 1553–1574 (2020). https://doi.org/10.1007/s40295-020-00235-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40295-020-00235-y

Keywords

Search

Navigation