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

  • Ji-Yeon An
  • Chang-Hun Lee
  • Min-Jea Tahk
Original Paper


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.


Course-correction-projectile Collision geometry Guided projectile 


  1. 1.
    Morrison PH, Amberntson DS (1977) Guidance and control of a cannon-launched guided projectile. J Spacecr Rockets 14:328–334. CrossRefGoogle Scholar
  2. 2.
    Moorhead JS (ed) (2007) Precision guidance kits (PGKs): improving the accuracy of conventional cannon rounds. Field Artillery (magazine), January–February, pp 31–33.
  3. 3.
    Fresconi F, Plostins P (2010) Control mechanism strategies for spin-stabilized projectiles. Proc Inst Mech Eng G J Aerosp 224:979–991. CrossRefGoogle Scholar
  4. 4.
    Rogers J, Costello M (2010) Design of a roll-stabilized mortar projectile with reciprocating canards. J Guid Control Dyn 33:1026–1034. CrossRefGoogle Scholar
  5. 5.
    Gagnon E, Vachon A (2016) Efficiency analysis of canards-based course correction fuze for a 155-mm spin-stabilized projectile. J Aerosp Eng. CrossRefGoogle Scholar
  6. 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. CrossRefGoogle Scholar
  7. 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 2008Google Scholar
  8. 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 2014Google Scholar
  9. 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 2014Google Scholar
  10. 10.
    Burchett B, Costello M (2002) Model predictive lateral pulse jet control of an atmospheric rocket. J Guid Control Dyn 25:860–867. CrossRefGoogle Scholar
  11. 11.
    Ollerenshaw D, Costello M (2008) Model predictive control of a direct fire projectile equipped with canards. J Dyn Syst Meas Control. CrossRefGoogle Scholar
  12. 12.
    Jitpraphai T, Costello M (2001) Dispersion reduction of a direct fire rocket using lateral pulse jets. J Spacecr Rockets 38:929–936. CrossRefGoogle Scholar
  13. 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. CrossRefGoogle Scholar
  14. 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. CrossRefGoogle Scholar
  15. 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. CrossRefGoogle Scholar
  16. 16.
    Zarchan P (2007) Tactical and strategic missile guidance. AIAA, Washington, DCGoogle Scholar
  17. 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 5:1667–1676Google Scholar
  18. 18.
    Fresconi F (2011) Guidance and control of a projectile with reduced sensor and actuator requirements. J Guid Control Dyn 34:1757–1766. CrossRefGoogle Scholar
  19. 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. CrossRefGoogle Scholar
  20. 20.
    Costello M, Peterson A (2000) Linear theory of a dual-spin projectile in atmospheric flight. J Guid Control Dyn 23:789–797. CrossRefGoogle Scholar
  21. 21.
    Hainz LC III, Costello M (2005) Modified projectile linear theory for rapid trajectory prediction. J Guid Control Dyn 28:1006–1014. CrossRefGoogle Scholar
  22. 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 2006Google Scholar
  23. 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. CrossRefzbMATHGoogle Scholar
  24. 24.
    Parker GW (1977) Projectile motion with air resistance quadratic in the speed. Am J Phys 45:606–610. CrossRefGoogle Scholar
  25. 25.
    Hayen JC (2003) Projectile motion in a resistant medium part I: exact solution and properties. Int J Nonlinear Mech 38:357–369. MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Hayen JC (2003) Projectile motion in a resistant medium Part II: approximate solution and estimates. Int J Nonlinear Mech 38:371–380. MathSciNetCrossRefzbMATHGoogle Scholar
  27. 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. CrossRefGoogle Scholar
  28. 28.
    Harl H, Balakrishnan SN (2012) Impact time and angle guidance with sliding mode control. IEEE Trans Control Syst T 20:1436–1449. CrossRefGoogle Scholar
  29. 29.
    Reisner D, Shima T (2013) Optimal guidance-to-collision law for an accelerating exoatmospheric interceptor missile. J Guid Control Dyn 36:1695–1708. CrossRefGoogle Scholar
  30. 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 2016Google Scholar
  31. 31.
    He S, Lee C-H (2018) Gravity-turn-assisted optimal guidance law. J Guid Control Dyn 41:171–183. CrossRefGoogle Scholar
  32. 32.
    He S, Lee C-H (2018) Optimality of error dynamics in missile guidance problems. J Guid Control Dyn 41:1624–1633. CrossRefGoogle Scholar

Copyright information

© The Korean Society for Aeronautical & Space Sciences and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Korea Advanced Institute of Science and Technology (KAIST)DaejeonKorea

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