Skip to main content
SpringerLink
Log in

Pursuit-Evasion Games of High Speed Evader

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

Abstract

In this paper, we address pursuit-evasion games of high speed evader involving multiple pursuers and a single evader with holonomic constraints in an open domain. The existing work on this problem discussed the required formation and capture strategy for a group of pursuers. However, the formulation has mathematical errors and has raised concerns over the validity of the developed capture strategy. This paper uses the idea of Apollonius circle to develop an escape strategy for the high speed evader, resolving the shortfalls in the existing work. The strategy is built on a concept of perfectly encircled formation and the conditions required to construct the same are presented. The escape strategy contains two steps. Firstly, the evader employs a strategy that forces a gap in the formation against all the admissible strategies of a group of pursuers. In the second step, it uses this gap to escape. The strategy considers both direct and indirect gaps in the formations. The indirect gap is encountered when a group of three or four pursuers is employed to capture. The efficacy of the escape strategy is established using simulation results.

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. Balakrishnan, S.N., Tsourdos, A., White, B.A.: Advances in Missile Guidance, Control, and Estimation. Automation and Control Engineering. CRC Press, 2012. Chapter 9, doi:10.1201/b12503-10

  2. Bao-Fu, F., Qi-Shu, P., Bing-Rong, H., Lei, D., Qiu-Bo, Z., Zhaosheng, Z.: Research on high speed evader vs. multi lower speed pursuers in multi pursuit-evasion games. Inf. Technol. J. 11(8), 989–997 (2012). doi:10.3923/itj.2012.989.997

    Article  Google Scholar 

  3. Bopardikar, S.D., Bullo, F., Hespanha, J.P.: On discrete-time pursuit-evasion games with sensing limitations. IEEE Trans. Robot. 24(6), 1429–1439 (2008). doi:10.1109/TRO.2008.2006721

    Article  Google Scholar 

  4. Conway, B.A., Pontani, M.: Numerical solution of the three-dimensional orbital pursuit-evasion game. J. Guid. Control Dyn. 32(2), 474–487 (2009). doi:10.2514/1.37962

    Article  Google Scholar 

  5. Evans, L., Souganidis, P.: Differential games and representation formulas for solutions of hamilton-jacobi-isaacs equations. Indiana Univ. Math. J. 33(5), 773–797 (1984). doi:10.1512/iumj.1984.33.33040

    Article  MathSciNet  MATH  Google Scholar 

  6. Ho, Y., Bryson, A., Baron, S.: Differential games and optimal pursuit-evasion strategies. IEEE Trans. Autom. Control 10(4), 385–389 (1965). doi:10.1109/TAC.1965.1098197

    Article  MathSciNet  Google Scholar 

  7. Huang, H., Zhang, W., Ding, J., Stipanovic, D.M., Tomlin, C.J.: Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers. In: Proceedings of the Fifieth IEEE Conference on Decision and Control and European Control Conference, pp 4835–4840. IEEE, Orlando, FL (2011), doi:10.1109/CDC.2011.6161237

  8. Isaacs, R.: Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. Wiley, New York (1965). chapter 6

    MATH  Google Scholar 

  9. Isler, V., Kannan, S., Khanna, S.: Randomized pursuit-evasion in a polygonal environment. IEEE Trans. Robot. 21(5), 875–884 (2005). doi:10.1109/TRO.2005.851373

    Article  MATH  Google Scholar 

  10. Jarmark, B., Hillberg, C.: Pursuit-evasion between two realistic aircraft. J. Guid. Control Dyn. 7(6), 690–694 (1984). doi:10.2514/3.19914

    Article  MATH  Google Scholar 

  11. Jin, S., Qu, Z.: Pursuit-evasion games with multi-pursuer vs. one fast evader. In: Proceedings of the Eighth World Congress on Intelligent Control and Automation (WCICA), pp 3184–3189. IEEE, Jinan, China (2010), doi:10.1109/WCICA.2010.5553770

  12. Kothari, M., Manathara, J.G., Postlethwaite, I.: A cooperative pursuit-evasion game for nonholonomic systems. In: Proceedings of the Ninteenth IFAC World Congress, vol. 19, pp 1977–1984, Cape Town, South Africa (2014), doi:10.3182/20140824-6-ZA-1003.01992

  13. Makkapati, V.R.: Simulation: Evasion from a PEF of 4 pursuers

  14. Makkapati, V.R.: Simulation: Evasion from a PEF of 5 pursuers

  15. Makkapati, V.R.: Simulation: Evasion from a PEF of 6 pursuers

  16. Mitchell, I.M., Bayen, R.M., Tomlin, C.J.: Bayen a time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans. Autom. Control 50(7), 947–957 (2005). doi:doi:10.1109/TAC.2005.851439 doi:10.1109/TAC.2005.851439

    Article  Google Scholar 

  17. Pachter, M., games, Y.Y.: Simple-motion pursuit-evasion differential part 1: Stroboscopic strategies in collision-course guidance and proportional navigation. J. Optim. Theory Appl. 51(1), 95–127 (1986). doi:10.1007/BF00938604

    Article  MATH  Google Scholar 

  18. Rajan, N., Prasad, U.R., Rao, N.J.: Pursuit-evasion of two aircraft in a horizontal plane. J. Guid. Control Dyn. 3(3), 261–267 (1980). doi:10.2514/3.55982

    Article  MATH  Google Scholar 

  19. Ramana, M.V., Kothari, M.: A cooperative pursuit-evasion game of a high speed evader. In: Proceedings of the IEEE Fifty-Fourth Annual Conference on Decision and Control (CDC), pp 2969–2974. IEEE, Osaka, Japan (2015), doi:10.1109/CDC.2015.7402668

  20. Shinar, J., Gutman, S.: Three-dimensional optimal pursuit and evasion with bounded controls. IEEE Trans. Autom. Control 25(3), 492–496 (1980). doi:10.1109/TAC.1980.1102372

    Article  MathSciNet  MATH  Google Scholar 

  21. Shneydor, N.A.: Missile Guidance and Pursuit: Kinematics, Dynamics and Control. Horwood Series in Engineering Science. Horwood Publishing Limited, Chichester, England (1998). Chapter 4

    Book  Google Scholar 

  22. Takei, R., Huang, H., Ding, J., Tomlin, C.J.: Time-optimal multi-stage motion planning with guaranteed collision avoidance via an open-loop game formulation. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), pp 323–329. IEEE, Saint Paul, MN (2012), doi:10.1109/ICRA.2012.6225074

  23. Vidal, R., Shakernia, O., Jin Kim, H., Shim, D.H., Sastry, S.: Probabilistic pursuit-evasion games: Theory, implementation, and experimental evaluation. IEEE Trans. Robot. Autom. 18(5), 662–669 (2002). doi:10.1109/TRA.2002.804040

    Article  Google Scholar 

  24. Wang, X., Cruz Jr, J.B., Chen, G., Pham, K., Blasch, E.: Formation control in multi-player pursuit evasion game with superior evaders. In: Proceedings of the Defense Transformation and Net-Centric Systems, volume 6578. International Society for Optics and Photonics (2007), doi:10.1117/12.723300

  25. Mo, W., Chen, G., Cruz, J.B, Haynes, L., Pham, K., Blasch, E.: Multi-pursuer multievader pursuit-evasion games with jamming confrontation. J. Aerosp. Comput. Inform. Commun. 4(3), 693–706 (2007). doi:10.2514/1.25329

    Article  Google Scholar 

  26. Wei, M., Chen, G., Cruz, J.B., Haynes, L.S., Chang, M.-H., Blasch, E.: A decentralized approach to pursuer-evader games with multiple superior evaders in noisy environments. In: Proccedings of the IEEE Aerospace Conference, pp 1–10. IEEE, Big Sky, MT (2007), doi:10.1109/AERO.2007.353051

  27. Wei, M., Chen, G., Cruz Jr, J.B., Hayes, L., Chang, M.-H.: A decentralized approach to pursuer-evader games with multiple superior evaders. In: IEEE Intelligent Transportation Systems Conference, pp 1586–1591. IEEE (2006), doi:10.1109/ITSC.2006.1707450

  28. Zarchan, P.: Tactical and Strategic Missile Guidance, volume 239 of Progress in Astronautics and Aeronautics, 6th edn. American Institute of Aernautics and Astronautics, Inc., Reston, VA (2012). Chapters 2, 8

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    M. V. Ramana & Mangal Kothari

Authors
  1. M. V. Ramana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mangal Kothari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mangal Kothari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramana, M.V., Kothari, M. Pursuit-Evasion Games of High Speed Evader. J Intell Robot Syst 85, 293–306 (2017). https://doi.org/10.1007/s10846-016-0379-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-016-0379-3

Keywords

Search

Navigation