Skip to main content
SpringerLink
Log in

Terrain Avoidance Nonlinear Model Predictive Control for Autonomous Rotorcraft

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

This paper describes a terrain avoidance control methodology for autonomous rotorcraft applied to low altitude flight. A simple nonlinear model predictive control (NMPC) formulation is used to adequately address the terrain avoidance problem, which involves stabilizing a nonlinear and highly coupled dynamic model of a helicopter, while avoiding collisions with the terrain as well as preventing input and state saturations. The physical input saturations are made intrinsic to the model, such that the control is always admissible and the MPC design is simplified. A comparison of several optimization approaches is provided, where the performance of the traditional gradient method with fixed step is compared with the quasi-Newton method and a line search algorithm. The simulation results show that the adopted strategy achieves good performance even when the desired path is on collision course with the terrain.

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

Similar content being viewed by others

References

  1. Alamir, M., Bornard, G.: Stability of a truncated infinite constrained receding horizon scheme: the general discrete nonlinear case. Automatica 31(9), 1353–1356 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bemporad, A., Morari, M., Pistikopoulos, E.N., Dua, V.: The explicit linear quadratic regulator for constrained systems. Automatica 38(1), 3–20 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, C.C., Shaw, L.: On receding horizon feedback control. Automatica 18(3), 349–352 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, H., Allgöwer, F.: A quasi-infinite horizon nonlinear model predictive control with guaranteed stability. Automatica 34(10), 1205–1217 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cunha, R.: Modeling and Control of an Autonomous Robotic Helicopter. Master’s thesis, Department of Electrical and Computer Engineering, Instituto Superior Técnico, Lisbon, Portugal (2002)

  6. Cunha, R., Guerreiro, B., Silvestre, C.: Vario-xtreme Helicopter Nonlinear Model: Complete and Simplified Expressions. Technical report, Instituto Superior Técnico, Institute for Systems and Robotics (2005)

  7. Cutler, C.R., Ramaker, B.L.: Dynamic matrix control: a computer control algorithm. In: Proceedings of the Joint Automatic Control Conference. San Francisco, CA (1980)

  8. de Nicolao, G., Magnani, L., Magni, L., Scattolini, R.: A stabilizing receding horizon controller for nonlinear discrete time systems. In: American Control Conference. Chicago, Illinois (2000)

  9. Findeisen, R., Imsland, L., Allgöwer, F., Foss, B.A.: State and output feedback nonlinear model predictive control: an overview. Europ. J. Contr. 9, 179–195 (2003)

    Google Scholar 

  10. Garcia, C.E., Prett, D.M., Morari, M.: Model predictive control: theory and practice—a survey. Automatica 25(3), 335–348 (1989)

    Article  MATH  Google Scholar 

  11. Garcia, C.E., Morari, M.: Internal model control. A unifying review and some new results. Ind. Eng. Chem. Process Des. Dev. 21(2), 308–323 (1982)

    Article  Google Scholar 

  12. Goerzen, C., Kong, Z., Mettler, B.: A survey of motion planning algorithms from the perspective of autonomous uav guidance. J. Intell. Robot. Syst. 57, 65–100 (2010)

    Article  MATH  Google Scholar 

  13. Grancharova, A., Kocijan, J., Johansen, T.A.: Explicit stochastic predictive control of combustion plants based on gaussian process models. Automatica 44, 1621–1631 (2008)

    Article  MathSciNet  Google Scholar 

  14. Guerreiro, B., Silvestre, C., Cunha, R.: Terrain avoidance model predictive control for autonomous rotorcraft. In: Proceedings of the 17th IFAC World Congress (IFAC’08), pp. 1076–1081. Seoul, Korea (2008)

  15. Jadbabaie, A., Yu, J., Hauser, J.: Unconstrained receding-horizon control of nonlinear systems. IEEE Trans. Automat. Contr. 46(5), 776–783 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Keerthi, S.S., Gilbert, E.G.: Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations. J. Optim. Theory Appl. 57(2), 265–293 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. Keviczky, T., Balas, G.J.: Receding horizon control of an f-16 aircraft: a comparative study. Control Eng. Pract. 14(9), 1023–1033 (2006)

    Article  Google Scholar 

  18. Kim, H., Shim, D., Sastry, S.: Nonlinear model predictive tracking control for rotorcraft-based unmanned aerial vehicles. In: American Control Conference, vol. 5, pp. 3576–3581. Anchorage, AK (2002)

  19. Lapp, T., Singh, L.: Model predictive control based trajectory optimization for nap-of-earth flight including obstacle avoidance. In: American Control Conference, pp. 891–892. Boston, MA (2004)

  20. Magni, L.: On robust tracking with non-linear model predictive control. Int. J. Control 75(6), 399–407 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  21. Magni, L., Raimondo, D.M., Allgöwer, F. (eds.): Nonlinear Model Predictive Control: Towards New Challenging Applications. Lecture Notes in Control and Information Sciences, vol. 384. Springer, New York (2009)

    MATH  Google Scholar 

  22. Mayne, D., Rawlings, J., Rao, C., Scokaert, P.: Constrained model predictive control: stability and optimality. Automatica 36, 790–814 (2000). Survey Paper

    Article  MathSciNet  Google Scholar 

  23. Mehra, M., Rouhani, R., Eterno, J., Richalet, J., Rault, A.: Model algorithmic control: review and recent development. In: Proceedings of the Eng. Foundation Conf. on Chemical Process Control II, pp. 287–310. Sea Island, Georgia (1982)

  24. Mettler, B., Goerzen, C., Kong, Z., Whalley, M.: Benchmarking of obstacle field navigation algorithms for autonomous helicopters. In: Proceedings of the American Helicopter Society 66th Annual Forum. Phoenix, AZ (2010)

  25. Michalska, H., Mayne, D.Q.: Robust receding horizon control of constrained nonlinear systems. IEEE Trans. Automat. Contr. 38(11), 1623–1633 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  26. Nocedal, J., Wright, S.: Numerical Optimization. Springer Series in Operation Reasearch. Springer, New York (1999)

    Google Scholar 

  27. Gareth, D., Padfield.: Helicopter Flight Dynamics: The Theory and Application of Flying Qualities and Simulation Modeling. AIAA Education Series. AIAA, Washington DC (1996)

    Google Scholar 

  28. Paulino, N., Silvestre, C., Cunha, R.: Affine parameter-dependent preview control for rotorcraft terrain following. AIAA J. Guid. Contr. Dynam. 29(6), 1350–1359 (2006)

    Article  Google Scholar 

  29. Propoi, A.I.: Use of linear programming methods for synthesizing sample-data automatic systems. Autom. Remote Control 24, 837 (1963)

    MathSciNet  Google Scholar 

  30. Qin, S.J., Badgwell, T.A.: A survey of industrial model predictive control technology. Control Eng. Int. 11, 733–764 (2003)

    Google Scholar 

  31. Rawlings, J.B., Muske, K.R.: The stability of constrained receding horizon control. IEEE Trans. Automat. Contr. 38(10), 1512–1516 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  32. Richalet, J., Rault, A., Testud, J.L., Papon, J.: Model predictive heuristic control: applications to industrial processes. Automatica 14, 413–428 (1978)

    Article  Google Scholar 

  33. Shim, D., Kim, H., Sastry, S.: Decentralized reflective model predictive control of multiple flying robots in dynamic environment. In: Conference on Decision and Control, USA (2003)

  34. Sutton, G., Bitmead, R.: Computational implementation of nonlinear model predictive control to nonlinear submarine. In: Allgöwer, F., Zheng, A. (eds.) Nonlinear Model Predictive Control, Progress in Systems and Control Theory, pp. 461–471. Birkhäuser, Basel-Boston-Berlin (2000)

    Chapter  Google Scholar 

  35. Yoon, Y., Shin, J., Kim, H., Park, Y., Sastry, S.: Model-predictive active steering and obstacle avoidance for autonomous ground vehicles. Control Eng. Pract. 17, 741–750 (2009)

    Article  Google Scholar 

  36. Zadeh, L.A., Whalen, B.H.: On optimal control and linear programming. IRE Trans. Automat. Contr. 7(4), 45–46 (1962)

    Article  Google Scholar 

  37. Zavala, V.M., Biegler, L.T.: The advanced-step nmpc controller: optimality, stability, and robustness. Automatica 45(1), 83–93 (2009)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Systems and Robotics (ISR), Instituto Superior Técnico (IST), Torre Norte Piso 8, Av. Rovisco Pais 1, 1049-001, Lisbon, Portugal

    Bruno J. N. Guerreiro, Carlos Silvestre & Rita Cunha

  2. Faculty of Science and Technology, University of Macau, Taipa, Macau

    Carlos Silvestre

Authors
  1. Bruno J. N. Guerreiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlos Silvestre
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rita Cunha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bruno J. N. Guerreiro.

Additional information

This work was partially supported by project FCT [PEst-OE/EEI/LA0009/2011], by project FCT AMMAIA (PTDC/HIS-ARQ/103227/2008), and by project AIRTICI from AdI through the POS Conhecimento Program that includes FEDER funds. The work of Bruno Guerreiro was supported by the PhD Student Grant SFRH/BD/21781/2005 from the Portuguese FCT POCTI program.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guerreiro, B.J.N., Silvestre, C. & Cunha, R. Terrain Avoidance Nonlinear Model Predictive Control for Autonomous Rotorcraft. J Intell Robot Syst 68, 69–85 (2012). https://doi.org/10.1007/s10846-012-9669-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-012-9669-6

Keywords

Mathematics Subject Classification (2010)

Search

Navigation