Terminal Multiple Surface Sliding Guidance for Planetary Landing: Development, Tuning and Optimization via Reinforcement Learning

Abstract

The problem of achieving pinpoint landing accuracy in future space missions to planetary bodies such as the Moon or Mars presents many challenges, including the requirements of higher accuracy and degree of flexibility. These new challenges may require the development of a new class of guidance algorithms. In this paper, a nonlinear guidance algorithm for planetary landing is proposed and analyzed. Based on Higher-Order Sliding Control (HOSC) theory, the Multiple Sliding Surface Guidance (MSSG) algorithm has been specifically designed to take advantage of the ability of the system to reach multiple sliding surfaces in a finite time. As a result, a guidance law that is both globally stable and robust against unknown, but bounded perturbations is devised. The proposed MSSG does not require any off-line trajectory generation, but the acceleration command is instead generated directly as function of the current and final (target) state. However, after initial analysis, it has been noted that the performance of MSSG critically depends on the choice in guidance gains. MSSG-guided trajectories have been compared to an open-loop fuel-efficient solution to investigate the relationship between the MSSG fuel performance and the selection of the guidance parameters. A full study has been executed to investigate and tune the parameters of MSSG utilizing reinforcement learning in order to truly optimize the performance of the MSSG algorithm in powered descent scenarios. Results show that the MSSG algorithm can indeed generate closed-loop trajectories that come very close to the optimal solution in terms of fuel usage. A full comparison of the trajectories is included, as well as a further Monte Carlo analysis examining the guidance errors of the MSSG algorithm under perturbed conditions using the optimized set of parameters.

This is a preview of subscription content, access via your institution.

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

References

  1. 1.

    Wolf, A.A., Tooley, J., Ploen, S., Ivanov, M., Acikmese, B., Gromov, K.: Performance Trades for Mars Pinpoint Landing, IEEE Aerospace Conference Proceedings, March 2006, IEEE-1661, March

  2. 2.

    Wolf, A., Sklyanskly, E., Tooley, J., Rush, B.: Mars Pinpoint Landing Systems Trades, AAS/AIAA Astrodynamics Specialist Conference Proceedings, AAS 07-310, August 19–23 (2007)

  3. 3.

    Phinney, W.C., Criswell, D., Drexler, E., Garmirian, J.: Lunar Resources and Their Utilization, Space-Based Manufacturing from Nonterrestial Materials, AIAA, p. 97–123 (1977)

  4. 4.

    Steltzner, A.D., Kipp, D.M., Chen, A., Burkhart, P.D., Guernsey, C.S., Mendeck, G.F., Mitcheltree, R.A., Powell, R.W., Rivellini, T.P., San Martin, A.M., Way, D.W.: Mars science laboratory entry, descent, and landing system, IEEE Aerospace Conference Paper No. 2006-1497, Big Sky, MT (2006)

  5. 5.

    Singh, G., SanMartin, A., Wong, E.: Guidance and control design for powered descent and landing on Mars. Aereospace Conference IEEE (2007)

  6. 6.

    Klumpp, A.R.: A manually retargeted automatic landing system for the lunar module (LM). J. Spacecr. Rocket. 5(2), 129–138 (1968)

    Article  Google Scholar 

  7. 7.

    Klumpp, A.R.: Apollo guidance, navigation, and control: Apollo lunar-descent guidance, massachusetts inst. of technology, charles stark draper Lab., TR R-695, Cambridge, MA (1971)

  8. 8.

    Klumpp, A.R.: Apollo Lunar Descent Guidance. Automatica 10(2), 133–146 (1974)

    Article  Google Scholar 

  9. 9.

    Topcu, U., Casoliva, J., Mease, K.: Fuel efficient powered descent guidance for mars landing, AIAA paper, 2005–6286 (2005)

  10. 10.

    Najson, F., Mease, K.: A computationally non-expensive guidance algorithm for fuel efficient soft landing, AIAA guidance, navigation, and Control Conference, San Francisco, AIAAPaper, 2005–6289 (2005)

  11. 11.

    Acikmese, B., Ploen, S.R.: Convex programming approach to powered descent guidance for mars landing. J. Guid. Control. Dyn. 30(5), 1353–1366 (2007)

    Article  Google Scholar 

  12. 12.

    D’Souza, C.: An optimal guidance law for planetary landing, AIAA guidance, navigation, and control conference, AIAA paper 1997–3709 (1997)

  13. 13.

    Benson, D.A., Huntington, G.T., Thorvaldsen, T.P., Rao, A.V.: Direct trajectory optimization and costate estimation via an orthogonal collocation method. J. Guid. Control. Dyn. 29(6), 1435–1440 (2006)

    Article  Google Scholar 

  14. 14.

    Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software 11(1), 625–653 (1999)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Acıkmese, B., Blackmore, L.: Lossless convexification of a class of optimal control problems with non-convex control constraints. Automatica 47(2) (2011)

  16. 16.

    Nesterov, Y., Nemirovsky, A.: Interior-point polynomial methods in convex programming, SIAM, Philadelphia, PA (1994)

  17. 17.

    Blackmore, L., Acıkmese, B., Scharf, D.P.: Minimum landing error powered descent guidance for Mars landing using convex optimization. AIAA J. Guid. Control. Dyn. 33(4), 1161–1171 (2010)

    Article  Google Scholar 

  18. 18.

    Levant, A.: Construction principles of 2-sliding mode design. Automatica 43 (4), 576–586 (2007)

    MATH  MathSciNet  Article  Google Scholar 

  19. 19.

    Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control. 58(6), 1247–1263 (1993)

    MATH  MathSciNet  Article  Google Scholar 

  20. 20.

    Levant, A.: Higher-order sliding modes, differentiation and output feedback control. Int. J. Control. 76(9/10), 924–941 (2003)

    MATH  MathSciNet  Article  Google Scholar 

  21. 21.

    Levant, A.: Homogeneity approach to high-order sliding mode design. Automatica 41(5), 823–830 (2005a)

    MATH  MathSciNet  Article  Google Scholar 

  22. 22.

    Levant, A.: Quasi-continuous high-order sliding-mode controllers. IEEE Trans. Autom. Control 50(11), 1812–1816 (2005b)

    MathSciNet  Article  Google Scholar 

  23. 23.

    Shtessel, Y.B., Shkolnikov, I.A.: Aeronautical and space vehicle control in dynamic sliding manifolds. Int. J. Control. 76(9/10), 1000–1017 (2003)

    MATH  MathSciNet  Article  Google Scholar 

  24. 24.

    Salamci, M.U., Ozgoren, M.K., Banks, S.P.: Sliding mode control with optimal sliding surfaces for missile autopilot design. J. Guid. Control. Dyn. 23, 4 (2000)

    Article  Google Scholar 

  25. 25.

    Shtessel, Y., Tournes, C.: Integrated higher-order sliding mode guidance and autopilot for dual-control missiles. J. Guid. Control. Dyn. 32, 1 (2009)

    Article  Google Scholar 

  26. 26.

    Tournes, C., Shtessel, Y., Shkolnikov, I.: Missile controlled by lift and divert thrusters using nonlinear dynamic sliding manifolds. J. Guid. Control. Dyn. 29, 3 (2006)

    Article  Google Scholar 

  27. 27.

    Koren, A., Idan, M., Golan, O.M.: Integrated mode guidance and control for a missile with on-off actuators. J. Guid. Control. Dyn. 31, 1 (2008)

    Article  Google Scholar 

  28. 28.

    Furfaro, R., Selnick, S., Cupples, M.L., Cribb, M.W.: Non-linear sliding guidance algorithms for precision lunar landing, in advances in the astronautical sciences, volume 140, Proceedings of the 21st AAS/AIAA space flight mechanics meeting held February 13-17, 2011, New Orleans, Louisiana

  29. 29.

    Furfaro, R., Cersosimo, D., Wibben, D.R.: Asteroid precision landing via multiple sliding surfaces guidance techniques. J. Guid. Control. Dyn. 36(4), 1075–1092 (2013)

    Article  Google Scholar 

  30. 30.

    Furfaro, R., Cersosimo, D.O., Bellerose, J.: Close proximity asteroid operations using sliding control modes, proceedings of the annual AAS/AIAA space flight mechanics conference, AAS 12-132, Jan 31-Feb 4, 2012, Charleston, Louisiana

  31. 31.

    Harl, N., Balakrishnan, S.N.: Reentry terminal guidance through sliding control mode, vol. 33 (2010)

  32. 32.

    Sutton, R., Barto, A.: Reinforcement Learning, pp 100–103 (1998)

  33. 33.

    Slotine, J., Li, W.: Applied nonlinear control, Prentice Hall (1991)

  34. 34.

    Vincent, T.L., Grantham, W.J.: Nonlinear and optimal control systems. Wiley, New York (1997)

  35. 35.

    Fridman, L.: An averaging approach to chattering. IEEE Trans. Autom. Control 46(8), 1260–1265 (2001)

    MATH  MathSciNet  Article  Google Scholar 

  36. 36.

    Rao, A.V., Benson, D.A., Darby, C., Patterson, M.A., Francolin, C., Sanders, I., et al.: Algorithm 902: GPOPS, a MATLAB software for solving multiple phase optimal control problems using the Gauss pseudospectral method. ACM Trans. Math. Softw. 37(2), 22:1-22:39 (2010)

    Article  Google Scholar 

  37. 37.

    Gill, P.E., Saunders, M.A., Murray, W.: SNOPT: An SQP algorithm for large scale constrained optimization. Technical Report NA 96-2, University of California, San Diego (1996)

  38. 38.

    Amato, M., Garvin, J.B., Burt, I.J., Gardner, T., Karpati, G.: Lower-cost, relocatable lunar polar lander and lunar surface sample return probes, Paper for the Iinternational Planetary Probe Workshop (2010)

  39. 39.

    Spall, J.: Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control. Wiley, Hoboken. Chapter 2 (2003)

  40. 40.

    Sutton, R.S., Barto, A.G.: Introduction to reinforcement learning. MIT Press (1998)

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Roberto Furfaro.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Furfaro, R., Wibben, D.R., Gaudet, B. et al. Terminal Multiple Surface Sliding Guidance for Planetary Landing: Development, Tuning and Optimization via Reinforcement Learning. J of Astronaut Sci 62, 73–99 (2015). https://doi.org/10.1007/s40295-015-0045-1

Download citation

Keywords

  • Planetary landing
  • Mars
  • Reinforcement learning
  • Sliding guidance