Advertisement

Lyapunov-Based Three-Dimensional Terminal Angle Constrained Guidance Laws

  • Mingu KimEmail author
  • Yongwoo Lee
  • Seokwon Lee
  • Youdan Kim

Abstract

Three-dimensional nonlinear guidance laws are proposed considering terminal angle constraints. Unlike conventional two-dimensional guidance laws, the three-dimensional geometry is considered without the assumption that the yaw channel and the pitch channel are decoupled. It is shown that the states converge to the desired values by using Lyapunov stability theory and LaSalle’s invariance theorem. Numerical simulation results are presented to demonstrate the performance of the proposed guidance laws.

Keywords

Unmanned Aerial Vehicle Angle Error Lyapunov Stability Theory Lyapunov Candidate Function Proportional Navigation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kim, M., Grider, K.V.: Terminal Guidance for Imapct Attitude Angle Constrained Flight Trajectories. IEEE Transactions on Aerospace Electron Systems 9(6), 852–859 (1973)CrossRefGoogle Scholar
  2. 2.
    Song, T., Shin, S., Cho, H.: Impact Angle Control for Planar Engegements. IEEE Transactions on Aerospace Electron Systems 35(4), 1439–1444 (1999)CrossRefGoogle Scholar
  3. 3.
    Ryoo, C., Cho, H., Tahk, M.: Optimal Guidance Law with Terminal Impact Angle Constraint. Journal of Guidance, Control, and Dynamics 28(4), 724–732 (2005)CrossRefGoogle Scholar
  4. 4.
    Lee, C., Tahk, M., Lee, J.: Generalized Formulation of Weighted Optimal Guidance Laws with Impact Angle Control. IEEE Transactions on Aerospace Electron Systems 49(2), 1317–1322 (2013)CrossRefGoogle Scholar
  5. 5.
    Cho, H., Ryoo, C., Tsourdos, A., White, B.: Optimal Impact Angle Control Guidance Law Based on Linearization About Collision Triangle. Journal of Guidance, Control, and Dynamics 37(3), 958–964 (2014)CrossRefGoogle Scholar
  6. 6.
    Ratnoo, A., Ghose, D.: Impact Angle Constrained Interception of Stationary Targets. Journal of Guidance, Control, and Dynamics 31(6), 1816–1821 (2008)CrossRefGoogle Scholar
  7. 7.
    Ratnoo, A., Ghose, D.: Impact Angle Constrained Guidance Against Nonstationary Nonmaneuvering Targets. Journal of Guidance, Control, and Dynamics 33(1), 269–275 (2010)CrossRefGoogle Scholar
  8. 8.
    Ratnoo, A., Ghose, D.: State-Dependent Riccati-Equation Based Guidance Law for Impact-Angle-Constrained Trajectories. Journal of Guidance, Control, and Dynamics 32(1), 320–325 (2009)CrossRefGoogle Scholar
  9. 9.
    Kim, K., Jung, B., Kim, Y.: Practical Guidance Law Controlling Impact Angle. Journal of Aerospace Engineering, Proceedings on the Institution of Mechanical Engineers Part G 221(1), 755–774 (2007)CrossRefGoogle Scholar
  10. 10.
    Kim, M., Kim, Y.: Lyapunov-Based Pursuit Guidance Law with Impact Angle Constraint. In: Proc. of the 19th IFAC World Congress, Cape Town, South Africa, pp. 2509–2514 (2014)Google Scholar
  11. 11.
    Song, S., Ha, I.: A Lyapunov-Like Approach to Performance Analysis of 3-Dimensional Pure PNG Laws. IEEE Transactions on Aerospace Electron Systems 30(1), 238–248 (1994)CrossRefGoogle Scholar
  12. 12.
    Oh, J., Ha, I.: Capturability of the 3-Dimensional Pure PNG Law. IEEE Transactions on Aerospace Electron Systems 35(2), 491–503 (1999)CrossRefGoogle Scholar
  13. 13.
    Ma, P., Zhang, Y., Ji, J., Zhang, X.: Three-Dimensional Guidance Law with Terminal Impact Angle Constraint. In: Proc. of the IEEE International Conference on Mechatronics and Automation, Changchun, China, pp. 4162–4166 (2009)Google Scholar
  14. 14.
    Yoon, M.: Relative Circular Navigation Guidance for Three-Dimensional Impact Angle Control Problem. Journal of Aerospace Engineering 23(4), 300–308 (2010)CrossRefGoogle Scholar
  15. 15.
    Oza, H., Padhi, R.: Impact-Angle-Constrained Suboptimal Model Predictive Static Programming Guidance of Air-to-Ground Missiles. Journal of Guidance, Control, and Dynamics 35(1), 153–164 (2012)CrossRefGoogle Scholar
  16. 16.
    Indig, N., Ben-Asher, J., Farber, N.: Near-Optimal Spatial Midcourse Guidance Law with an Angular Constraint. Journal of Guidance, Control, and Dynamics 37(1), 214–223 (2014)CrossRefGoogle Scholar
  17. 17.
    Wang, X., Wang, J.: Partial Integrated Guidance and Control for Missiles with Three-Dimensional Impact Angle Constraints. Journal of Guidance, Control, and Dynamics 37(2), 644–657 (2014)CrossRefGoogle Scholar
  18. 18.
    Lee, Y., Kim, Y.: Three-Dimensional Impact Angle Control Guidance Law for Missiles Using Dual Sliding Surfaces. In: Proc. of the 19th IFAC Symposium on Automatic Control in Aerospace, Wurzburg, Germany, pp. 137–142 (2013)Google Scholar
  19. 19.
    Kumar, S.R., Ghose, D.: Three-Dimensional Impact Angle Constrained Guidance Law using Sliding Mode Control. In: Proc. of the 2014 American Control Conference, Portland, OR, pp. 2474–2479 (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mingu Kim
    • 1
    Email author
  • Yongwoo Lee
    • 1
  • Seokwon Lee
    • 1
  • Youdan Kim
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringSeoul National UniversitySeoulKorea

Personalised recommendations