Skip to main content
SpringerLink
Log in

A Novel Indirect Scheme for Optimal Lunar Soft Landing at a Target Site

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series C Aims and scope Submit manuscript

Abstract

The problem of precise and soft lunar landing in a pre-specified target location is solved using a numerical scheme based on indirect approach. In indirect approach, the problem is transformed into a two-point boundary value problem using Pontryagin’s principle and solved. The challenge in the indirect approach lies in finding suitable initial co-states with no prior knowledge available about them. In the proposed numerical scheme, the differential transformation (DT) technique is employed to determine the unknown initial co-states using the information on the target site and the flight time. The flight time, the only unknown, is handled by differential evolution, an optimization technique. The novel computational scheme combines differential transformation and differential evolution techniques and uses differential transformation in multi-steps, to ensure the precise landing at the target site. The guidelines that help fixing the bounds for the flight time are provided. The proposed scheme is uniformly valid for various performance measures such as minimum fuel, minimum control and minimum time. Also, it is capable of introducing coasting during descent while maximizing the landing mass.

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

Similar content being viewed by others

References

  1. F. V. Bennett, Apollo Lunar descent and ascent trajectories. NASA TM-X-58040, March (1970)

  2. A. W. Wilhite, J. Wagner. Lunar module descent mission design. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit. AIAA 2008–6939, August 18–21, (2008), Honolulu,Hawaii, USA

  3. H. Chu, L. Maa, K. Wang, Z. Shao, Z. Song, Trajectory optimization for lunar soft landing with complex constraints. Adv. Space Res. 60(2017), 2060–2076 (2017)

    Article  Google Scholar 

  4. H. Leeghim, D.-H. Cho, D. Kim, An optimal trajectory design for the lunar vertical landing. Proc IMechE Part G: Journal of Aerospace Engineering 230(11), 2077–2208 (2016)

    Google Scholar 

  5. S. Mathavaraj, R. Pandiyan, R. Padhi, Constrained optimal multi-phase lunar landing trajectory with minimum fuel consumption. Adv Space Res 60(2017), 2477–2490 (2017)

    Article  Google Scholar 

  6. B.G. Park, M.J. Tahk, Three dimensional trajectory optimization of soft lunar landings from the parking orbit with considerations of the landing site. Int J Cont Automat Syst 9(6), 1164–1172 (2011)

    Article  Google Scholar 

  7. R.V. Ramanan, Madanlal. , Analysis of optimal strategies for soft landing on the moon from lunar parking orbits. J Earth Syst Sci (2005). https://doi.org/10.1007/BF02715967

    Article  Google Scholar 

  8. N. Remesh, R.V. Ramanan, V.R. Lalithambika, Fuel optimum lunar soft landing trajectory design using different solution schemes. Int Rev Aerospace Eng (IREASE) (2016). https://doi.org/10.15866/irease.v9i5.10119

    Article  Google Scholar 

  9. F. Fahroo, I.M Ross, Costate estimation by Legdendre Pseudo spectral method. J Guid Control Dyn, 24, No.2 March-April (2001), pp.270-277

  10. D. A. Benson, G. T. Huntington, T. P. Thorvaldsen, A. V Rao, Direct trajectory optimization and co-state estimation via an orthogonal Collocation, Journal of Guidance, Control, and Dynamics, 29, No. 6, November–December (2006), pp.1435–1440.

  11. E. Taheri, N. I.Li, I. Kolmanovsky Co-states initialization of minimum-time low thrust trajectories using shape-based methods. In: 2016 American Control Conference, July 6-8, (2016), Boston, MA, USA

  12. G. E. Pukhov. G.E, Expansion formulas for differential transforms. Cybernetics and System analysis, (1981), 17, Issue 4, pp.460–464.

  13. I. Hwang, J. Li, D. Du (2008) A numerical algorithm for optimal control of a class of hybrid systems: differential transformation based approach. Int J Cont, Vol 81, No.2, (2008), pp. 277–293

  14. H. Rosemary, H. Inseok, C. Martin, A new nonlinear model predictive control algorithm using Differential Transformation with application to interplanetary low-thrust trajectory tracking. (2009) American Control Conference, June 10–12 2009.

  15. A.D. Olds, C. A. Kluever, M. Cupples, Interplanetary mission design using differential evolution. J Spacecraft Roc, Vol.44, No.5, (2007), pp.1060-1070

Download references

Author information

Authors and Affiliations

  1. Flight Mechanics Group, ISRO- Vikram Sarabhai Space Centre , Trivandrum, India

    N. Remesh

  2. Department of Aerospace Engineering, Indian Institute of Space Science and Technology , Trivandrum, India

    R. V. Ramanan

  3. Directorate of Human Space Flight Program, ISRO Head Quarters, Bangalore, India

    V. R. Lalithambika

Authors
  1. N. Remesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. V. Ramanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. R. Lalithambika
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Remesh.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

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

Remesh, N., Ramanan, R.V. & Lalithambika, V.R. A Novel Indirect Scheme for Optimal Lunar Soft Landing at a Target Site. J. Inst. Eng. India Ser. C 102, 1379–1393 (2021). https://doi.org/10.1007/s40032-021-00748-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40032-021-00748-x

Keywords

Search

Navigation