Skip to main content
SpringerLink
Log in

A Collision Geometry-Based Guidance Law for Course-Correction-Projectile

  • Original Paper
  • Published:
International Journal of Aeronautical and Space Sciences Aims and scope Submit manuscript

Abstract

This paper proposes a new guidance law for a course-correction-projectile (CCP) with very limited maneuverability. Compared to existing approaches, the proposed guidance law is derived directly from collision geometry, which is the fundamental concept of guidance process, so that it allows collisions with minimal guidance command and zero final guidance command. In the proposed method, the collision geometry considering the motions of CCP, called collision-ballistic-trajectory, and the corresponding heading error are first determined using the ballistic trajectory prediction technique, which is based on the partial closed-form solutions of the ballistic trajectory equations in conjunction with the sensitivity technique. The proposed guidance law that nullifies this heading error over a finite time is then derived using a specific form of error dynamic equation. In this paper, the characteristics of the proposed guidance law are also investigated. Finally, numerical simulations demonstrate the characteristics and effectiveness of the proposed guidance law compared to the existing methods.

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

Similar content being viewed by others

References

  1. Morrison PH, Amberntson DS (1977) Guidance and control of a cannon-launched guided projectile. J Spacecr Rockets 14:328–334. https://doi.org/10.2514/3.57205

    Article  Google Scholar 

  2. Moorhead JS (ed) (2007) Precision guidance kits (PGKs): improving the accuracy of conventional cannon rounds. Field Artillery (magazine), January–February, pp 31–33. http://sill-www.army.mil/firesbulletin/archives/2007/JAN_FEB_2007/JAN_FEB_2007_FULL_EDITION.pdf

  3. Fresconi F, Plostins P (2010) Control mechanism strategies for spin-stabilized projectiles. Proc Inst Mech Eng G J Aerosp 224:979–991. https://doi.org/10.1243/09544100JAERO705

    Article  Google Scholar 

  4. Rogers J, Costello M (2010) Design of a roll-stabilized mortar projectile with reciprocating canards. J Guid Control Dyn 33:1026–1034. https://doi.org/10.2514/1.47820

    Article  Google Scholar 

  5. Gagnon E, Vachon A (2016) Efficiency analysis of canards-based course correction fuze for a 155-mm spin-stabilized projectile. J Aerosp Eng. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000634

    Google Scholar 

  6. Theodoulis S, Gassmann V, Wernert P, Dritsas L, Kitsios I, Tzes A (2013) Guidance and control design for a class of spin-stabilized fin-controlled projectiles. J Guid Control Dyn 36:517–531. https://doi.org/10.2514/1.56520

    Article  Google Scholar 

  7. Wernert P, Leopold F, Bidino D, Juncker J, Lehmann L, Bar K, Reindler A (2008) Wind tunnel tests and open-loop trajectory simulations for a 155 mm canards guided spin stabilized projectile. In: Abstracts of the proceedings of AIAA atmospheric flight mechanics conference, Honolulu, Hawaii, 18–21 August 2008

  8. Jun BE, Lee CH (2014) Integrated pitch/yaw acceleration controller for projectile with rotating canards using linear quadratic control methodology. In: Paper presented at the 2014 IEEE conference on control applications (CCA), Antibes Congress Center, Juan Les Pins, 8–14 October 2014

  9. Lee CH, Jun BE (2014) Guidance algorithm for projectile with rotating canards via predictor-corrector approach. In: Paper presented at the 2014 IEEE conference on control applications (CCA), Antibes Congress Center, Juan Les Pins, 8–14 October 2014

  10. Burchett B, Costello M (2002) Model predictive lateral pulse jet control of an atmospheric rocket. J Guid Control Dyn 25:860–867. https://doi.org/10.2514/2.4979

    Article  Google Scholar 

  11. Ollerenshaw D, Costello M (2008) Model predictive control of a direct fire projectile equipped with canards. J Dyn Syst Meas Control. https://doi.org/10.1115/1.2957624

    Google Scholar 

  12. Jitpraphai T, Costello M (2001) Dispersion reduction of a direct fire rocket using lateral pulse jets. J Spacecr Rockets 38:929–936. https://doi.org/10.2514/2.3765

    Article  Google Scholar 

  13. Rogers J, Costello M (2008) Control authority of a projectile equipped with a controllable inertial translating mass. J Guid Control Dyn 31:1323–1333. https://doi.org/10.2514/1.33961

    Article  Google Scholar 

  14. Rogers J, Costello M (2009) A variable stability projectile using an internal moving mass. Proc Inst Mech Eng G J Aerosp 223:927–938. https://doi.org/10.1243/09544100JAERO509

    Article  Google Scholar 

  15. Frost G, Costello M (2006) Control authority of a projectile equipped with an internal unbalanced part. J Dyn Syst Meas Control 128:1005–1012. https://doi.org/10.1115/1.2363205

    Article  Google Scholar 

  16. Zarchan P (2007) Tactical and strategic missile guidance. AIAA, Washington, DC

    Google Scholar 

  17. Gkritzapis DN, Margaris DP, Panagiotopoulos EE, Kaimakamis G, Siassiakos K (2008) Prediction of the impact point for spin and fin stabilized projectiles. WSEAS Trans Inf Sci Appl 5:1667–1676

    Google Scholar 

  18. Fresconi F (2011) Guidance and control of a projectile with reduced sensor and actuator requirements. J Guid Control Dyn 34:1757–1766. https://doi.org/10.2514/1.53584

    Article  Google Scholar 

  19. Hahn P, Frederick R, Slegers N (2009) Predictive guidance of a projectile for hit-to-kill interception. IEEE Trans Control Syst T 17:745–755. https://doi.org/10.1109/TCST.2008.2004440

    Article  Google Scholar 

  20. Costello M, Peterson A (2000) Linear theory of a dual-spin projectile in atmospheric flight. J Guid Control Dyn 23:789–797. https://doi.org/10.2514/2.4639

    Article  Google Scholar 

  21. Hainz LC III, Costello M (2005) Modified projectile linear theory for rapid trajectory prediction. J Guid Control Dyn 28:1006–1014. https://doi.org/10.2514/1.8027

    Article  Google Scholar 

  22. Pamadi KB, Ohlmeyer EJ (2006) Evaluation of two guidance laws for controlling the impact flight path angle of a naval gun launched spinning projectile. In: Paper presented at the American institute of aeronautics and astronautics (AIAA) guidance, navigation, and control conference and exhibit, Keystone, Colorado, 21–24 August 2006

  23. Yabushita K, Yamashita M, Tusboi K (2007) An analytical solution of projectile motion with the quadratic resistance law using the homotopy analysis method. J Phys A Math Theor 40:8403–8416. https://doi.org/10.1088/1751-8113/40/29/015

    Article  MATH  Google Scholar 

  24. Parker GW (1977) Projectile motion with air resistance quadratic in the speed. Am J Phys 45:606–610. https://doi.org/10.1119/1.10812

    Article  Google Scholar 

  25. Hayen JC (2003) Projectile motion in a resistant medium part I: exact solution and properties. Int J Nonlinear Mech 38:357–369. https://doi.org/10.1016/S0020-7462(01)00067-1

    Article  MathSciNet  MATH  Google Scholar 

  26. Hayen JC (2003) Projectile motion in a resistant medium Part II: approximate solution and estimates. Int J Nonlinear Mech 38:371–380. https://doi.org/10.1016/S0020-7462(01)00068-3

    Article  MathSciNet  MATH  Google Scholar 

  27. Park WS, Ryoo CK, Kim YH, Kim JJ (2011) A guidance law to maintain ballistic trajectory for smart munitions. J Korean Soc Aeronaut Space Sci 39:839–847. https://doi.org/10.5139/JKSAS.2011.39.9.839

    Google Scholar 

  28. Harl H, Balakrishnan SN (2012) Impact time and angle guidance with sliding mode control. IEEE Trans Control Syst T 20:1436–1449. https://doi.org/10.1109/TCST.2011.2169795

    Article  Google Scholar 

  29. Reisner D, Shima T (2013) Optimal guidance-to-collision law for an accelerating exoatmospheric interceptor missile. J Guid Control Dyn 36:1695–1708. https://doi.org/10.2514/1.61258

    Article  Google Scholar 

  30. Han SY, Hwang MC, Lee BY, Ahn JM, Tahk MJ (2016) Analytic solution of projectile motion with quadratic drag and unity thrust. In: Paper presented at the 20th international federation of automatic control symposium on automatic control in aerospace, Sherbrooke, Quebec, 21–25 August 2016

  31. He S, Lee C-H (2018) Gravity-turn-assisted optimal guidance law. J Guid Control Dyn 41:171–183. https://doi.org/10.2514/1.G002949

    Article  Google Scholar 

  32. He S, Lee C-H (2018) Optimality of error dynamics in missile guidance problems. J Guid Control Dyn 41:1624–1633. https://doi.org/10.2514/1.G003343

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Korea

    Ji-Yeon An, Chang-Hun Lee & Min-Jea Tahk

Authors
  1. Ji-Yeon An
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chang-Hun Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Min-Jea Tahk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Min-Jea Tahk.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

An, JY., Lee, CH. & Tahk, MJ. A Collision Geometry-Based Guidance Law for Course-Correction-Projectile. Int. J. Aeronaut. Space Sci. 20, 442–458 (2019). https://doi.org/10.1007/s42405-018-0114-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42405-018-0114-3

Keywords

Search

Navigation